- All
- Chemistry
- JC Chemistry
- JC General Paper
- JC Mathematics
- JC Physics
- Mathematics
- Secondary Chemistry
- Secondary Math
- Studying Tips
- University Mathematics

#### 2021 A-level H1 Mathematics (8865) Paper 1 Suggested Solutions

All solutions here are suggested. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. I will not be doing much formatting in this post. Q1 [Maximum marks: 4] Discriminant Q2 [Maximum marks: 5] (a) (b) Q3 Q4 Q5 Q6 [Maximum marks: 4]Let be the height of a sunflower plant, in […]

#### Vectors: Reflection of a line in a line

I was talking with a student today about the reflection of a line in a line, where both lines are in the same plane (naturally). And I thought of sharing it. One reason why I decided to discuss this in class was also because A’levels has been moving towards questions that want students to engineer […]

#### 2021 A-level H2 Mathematics (9758) Suggested Solutions

The following are the links to the 2021 A-level H2 Mathematics (9758) suggested solutions by Mr. Teng. All solutions here are suggested. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. 2021 A-level H2 Mathematics (9758) Paper 1 2021 A-level H2 Mathematics (9758) Paper 2 Relevant materials MF26

#### 2021 A-level H2 Mathematics (9758) Paper 2 Suggested Solutions

All solutions here are suggested. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. Numerical Answers (workings/explanations are after the numerical answers.) Question 1: Question 2: Question 3: Question 4: ; away from the starting pointQuestion 5: Question 6: Question 7: Question 8: Question 9: Question 10: Question 11:

#### 2021 A-level H2 Mathematics (9758) Paper 1 Suggested Solutions

All solutions here are suggested. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions Numerical Answers (workings/explanations are after the numerical answers.) Question 1: Question 2: Question 3: Question 4: Question 5: Question 6: Smallest , Translate the graph of units in the negative direction Question 7: Question 8: Question […]

#### Removal of CLT topics (again) 2021

For students wondering the impact of removal of CLT. This picture should explain. 🙂 Below is a compiled list of topics removed for other subjects. H2 Mathematics: Correlation & Regression H2 Economics: International Trade & Globalisation H2 Chemistry: Transition Elements H1/H2 Physics: Nuclear Physics H2 Biology: Impact of Climate Change on Animals & Plants H1 […]

#### AY2021 June Revision J1 Revision Paper 1 Solutions

1. (a) 1. (b) is parallel to , where is a scalar. 2. Using partial fractions, we find that Using method of differences (DIY), we have that 3. differs from by less than 1 Plot the graph of and in the GC, sketch it out. * You can key in modulus by pressing (alpha)(window)(1). Observe […]

#### AY2021 June Revision P&C Solutions

1. The two empty seats have to be considered as two identical objects, hence ways. 2. 3. or 4. 5. (a) 5. (b) ; 6. (i) or 6. (ii) 6. (iii) Case 1: 4 distinct letters. Case 2: Exactly 3 distinct letters. Case 3: Exactly 2 distinct letters. Total number of ways 7. (a) He […]

#### 2020 A-level H2 Mathematics (9758) Paper 2 Suggested Solutions

All solutions here are suggested. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. Numerical Answers (workings/explanations are after the numerical answers.) Question 1: Question 2: Question 3: Question 4: Question 5: Question 6: Question 7: Question 8: Question 9: Question 10:

#### 2020 A-level H2 Mathematics (9758) Paper 1 Suggested Solutions

All solutions here are suggested. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. Sorry, due to copyrights issues, I cannot share the paper. Numerical Answers (workings/explanations are after the numerical answers.) Question 1: Question 2: Question 3: Question 4: Question 5: ; refer to solutions below for explanation.Question 6: […]

#### 2020 A-level H2 Mathematics (9758) Suggested Solutions

The following are the links to the 2020 A-level H2 Mathematics (9758) suggested solutions by Mr. Teng. All solutions here are suggested. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. 2020 A-level H2 Mathematics (9758) Paper 1 2020 A-level H2 Mathematics (9758) Paper 2 Relevant materials MF26

#### Impact of removal of common last topic (CLT)

It has been awhile since the last update and I hope all the students are well and studying hard for the upcoming preliminaries and A’levels. A handful of students have asked me about the impact of the removal of the common last topic (CLT). For H2 Mathematics, it will be Correlation & Regression. So I […]

#### 2019 A-level H2 Mathematics (9758) Suggested Solutions

The following are the links to the 2019 A-level H2 Mathematics (9758) suggested solutions by Mr. Teng. All solutions here are suggested. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. 2019 A-level H2 Mathematics (9758) Paper 1 2019 A-level H2 Mathematics (9758) Paper 2 Relevant materials MF26

#### 2019 A-level H2 Mathematics (9758) Paper 2 Suggested Solutions

All solutions here are suggested. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. Numerical Answers (workings/explanations are after the numerical answers.) Question 1: Question 2: Question 3: Question 4: Question 5: Question 6: Question 7: Question 8: ; orange bird & yellow bird, orange bird & white rider, white […]

#### 2019 A-level H2 Mathematics (9758) Paper 1 Suggested Solutions

All solutions here are suggested. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. Numerical Answers (workings/explanations are after the numerical answers.) Question 1: Question 2: Question 3: Question 4: Question 5: Question 6: Question 7: Question 8: Question 9: Question 10: Question 11: Question 12: Relevant materials MF26 KS […]

#### How to prepare for H2 Mathematics (9758) for 2019 and beyond

The last step is of course looking into how we can prepare for the papers in the upcoming years. It certainly will not be easy as Cambridge taught us not to predict and simply just be consistently ready. In class, I always stress to students about concept-learning. It is important to learn the concept well, […]

#### Expectations for H2 Mathematics (9758) 2019 and beyond

After looking at what 2018 had offered and taught us, we should now consider what we need to look forward to. The 2017 and 2018 paper both showed students that there WILL be unseen questions coming out during A’levels. Unseen questions are basically questions that expect students to be able to respond on the spot, […]

#### An analysis of the H2 Mathematics (9758) 2018 Paper

Let us do a breakdown and analysis of the H2 Math Paper. Paper 1 was in general quite manageable. A few questions stood out, i.e., question 9iii and 10ii. These two are in fact “knowledge” from H2 Further Mathematics. These are considered to be application questions in the eyes of SEAB, thus, it is fair […]

#### Aftermath of A’levels H2 Mathematics (9758) 2018

Some students proclaimed “I’m finally done with Math!”. Just fyi, be careful of the modules you take in University because chances are that Math will still be around. 🙂 The purpose of this post is to do a breakdown of the recent paper and of course what can be observed for the upcoming paper, i.e., […]

#### Complex Numbers with Graphings Problem

N95/II/12 Given that where , express the real and imaginary parts of in terms of . (i) Hence show that the point representing in an Argand diagram lies on the curve with Cartesian equation . (ii) Show that , and find a similar expression for . Deduce that .

#### What’s on my mind for H2 Mathematics Paper 2 2018?

This is just me talking to myself… With paper 1 over, seems like this time round, the paper is slightly imbalanced. Questions that were too easy at the front, and last three became rather hard. 9iii: Deviates from standard question, but a simple substitution, not that difficult if a student does not overthink it. Practice […]

#### A-level H2 Mathematics (9758) Suggested Solutions (2017 – 2021)

After teaching H2 Mathematics for so many years and sharing my suggested solutions post A-levels, I thought I collate them nicely and type them all neatly here in LaTeX. 🙂 Please let me know should I make any careless mistakes as I typed them all out and spell check does not work with math equations. […]

#### 2018 A-level H2 Mathematics (9758) Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. Paper 1 Paper 2 Relevant materials MF26 Comments on 2017 Paper

#### 2018 A-level H1 Mathematics (8865) Paper 1 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. Numerical Answers (click the questions for workings/explanation) Question 1: Question 2: Question 3: Question 4: Question 5: Question 6: 0.31104; 0.54432 (exact answers) Question 7: 3360; 40; Question 8: Question 9: , 0.18, Not independent, 0.189 […]

#### What’s on my mind for H2 Mathematics Paper 1 2018?

Firstly, everything here will just be me talking to myself and I am not spotting any trends. Functions, good to know how to do piecewise composite functions. Checking for inverse algebraically. And to use discriminant to find range or domain of functions. Conics, good to be familiar and spot them. Finding graph of f(x) from […]

#### Some tips on preparing for A’levels 2018

Personally, I find SEAB-Cambridge getting more and more creative these days. Looking at the recent practical exams, they seem to prefer students to think and perform on the spot. If we look elsewhere to O’levels, this seem to be the trend too. I will prefer to say that TYS are useful to get students used […]

#### How to improve our H2 Mathematics?

Many students of mine have asked me this question numerous times. Some lamented that they work really hard, finishing off the revision package timely. However, they still cannot improve from a C/B to an A or some are still fishing for a pass. I feel that many students have a misunderstanding about H2 Mathematics. The […]

#### Sampling & Survey #10 – Cluster Sampling

So today we discuss about Cluster Sampling. We will begin by looking at cluster sampling with equal probabilities. Firstly, a cluster is a grouping of the members of the population. Previously, we assumed that we can directly sample the elements of the population and these sampling units are the elements of the population. However, this […]

#### 2018 A-level H2 Mathematics (9758) Paper 1 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. Numerical Answers (click the questions for workings/explanation) Question 1: ; Question 2: or ; Question 3: Question 4: ; or *Question 5: , Question 6: Question 7: Question 8: ; ; Question 9: ; 8 units […]

#### 2018 A-level H2 Mathematics (9758) Paper 2 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. Numerical Answers (click the questions for workings/explanation) Question 1: Question 2: , other roots , Question 3: Question 4: Question 5: Question 6: Question 7: Question 8: Question 9: Question 10: Relevant materials MF26 KS Comments

#### Modal value & Expected value

Let us look at the difference between modal value and expected value. We shall start by saying they are different, albeit close. Modal value refers to the mode, that is, the value that has the highest probability (chance) of occurring. Expected value refers to the value, we expect to have, on average. Before we start, […]

#### Differential Equations (Applications)

When Mr. Teng retired on 1 January 2018, he put a sum of 500 at the start of each month for groceries. Denote the amount of money that Mr. Teng has at the time years by . (i) The differential equation relating and can be written in the form of . State the values of […]

#### DRV questions with a twist

I want to share a question that is really old (older than me, actually). It is from the June 1972 paper. As most students know, Maclaurin’s series was tested in last year A’levels Paper 1 as a sum to infinity. And this DRV did the same thing. Here is the question. A bag contains 6 […]

#### Solutions to Review 1

Question 1 (i) (ii) Using long division, we find that So the asymptotes are and Question 2 (i) This is a hyperbola with centre , asymptotes are , and vertices and . is a graph with asymptotes and . Use GC to plot. (ii) —(1) —(2) Subst (2) to (1), (iii) From graph, we observe […]

#### Scatter Diagrams

I was teaching scatter diagram to some of my students the other day. A few of them are a bit confused with correlation and causation. I gave them the typical ice cream and murder rates example, which I shared here when I discussed about the r-value. Think of correlation like a trend, it simply can […]

#### All the best for 2017 Release of A’levels Results!

Will like to take this opportunity to wish all students receiving your results tomorrow, all the best! And do not worry too much and feel free to ask for any advice! Students will find the following useful 🙂 The following are the grade profiles of local universities, NUS and NTU. NTU IGP NUS IGP Take […]

#### Release of Results for 2017 A’levels

Students should note that the release of A’levels 2017 is on 23rd Feb 2018. More details can be found here.

#### Getting ready for JC

Its been awhile since we last posted. And it is good to know that JC1s have all been well inducted or settled into their schools. Of course, I do hear that many schools are severely overcrowded recently. Anyway, I thought of sharing how students can get ready for JC. I contemplated sharing how to cope […]

#### JC Talk 2018

Over the weekends, Mr. Teng had the privilege to share his knowledge about JC with parents and students of O’levels 2017, at Newtonapple Learning Hub. The lessons for J1 2018 started on the first week of January and the schedules can be found here. The following are the grade profiles of local universities, NUS and […]

#### Call for Registration 2018!

Registration for classes in 2018 has been opened. You can find out more about the class schedules here. Do note that JC1 class will commence in first week of January as there are registrations from IP students. For O’levels students, you can treat it like a head-start! We will also be holding a workshop for […]

#### Solutions to December Holiday Revision

Hopefully you find your holidays meaningful. Take the time to unwind and relax. Also, if you have completed the Set A and Set B. The solutions can be found here. If you do have any questions, please WhatsApp me. 🙂 Solutions to Set A Solutions to Set B Relevant Materials: MF26

#### Solutions to Set B

Hopefully, you guys have started on the Set B. You will find the following solutions useful. Click on the question. Please do attempt them during this December Holidays. 🙂 If you do have any questions, please WhatsApp me. 🙂 Relevant Materials: MF26

#### Solutions to Set A

Hopefully, you guys have started on the Set A. You will find the following solutions useful. Click on the question. Please do attempt them during this December Holidays. 🙂 If you do have any questions, please WhatsApp me. 🙂 Relevant Materials: MF26

#### Thoughts on the H2 Mathematics (9758) Papers 2017

Solutions can be found here. Personal Thoughts: The paper isn’t tedious. Students can do them so long as they know their stuffs. There are several generalising of questions, like question 6 of paper 1. We also saw how conditional probability was actually tested subtly, this tests students’ abilities to reason with guidance (not sure if […]

#### A-level H2 Mathematics (9758) Suggested Solutions (2017)

Here is the suggested solutions for H2 Mathematics (9758). They are all typed in LaTeX, so if it does not render, please leave a comment and let me know. Thank you. The suggested solutions for H2 Mathematics (9740) is here. Students of mine should obtain the modified A’levels Paper, and the solutions to the additional […]

#### 2017 A-level H1 Mathematics (8865) Paper 1 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. Numerical Answers (click the questions for workings/explanation) Question 1: Question 2: Question 3: Question 4: Question 5: Question 6: Question 7: Question 8: Question 9: ; latex 0.0336; \bar{y}=0.64, s^2 = 0.0400latex \frac{48+x}{80+x}, \frac{32+x}{80+x}; x= 16; […]

#### 2017 A-level H1 General Paper (8807) Paper 1

Sharing the A-level H1 General Paper (8807) Paper 1… ‘The past is not dead; it is not even past.’ Discuss. Can the use of animals for scientific research ever be justified? In your society, to what extent is it acceptable for public money to be used for the acquisition of works of art? ‘Rehabilitation, […]

#### Thoughts on H2 Mathematics (9758) 2017 Paper 1

This is a new syllabus and this is the first time it will be tested. Personally, I don’t think it will be easy and students should not underestimate this upcoming A’levels. And I’m referring to the A’levels, on the whole. We saw how the Science Paper 4 were… unexpected. The new H2 Mathematics (9758) syllabus […]

#### 2017 A-level H2 Mathematics (9740) Paper 2 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. This is answers for H2 Mathematics (9740). H2 Mathematics (9758), click here. Numerical Answers (click the questions for workings/explanation) Question 1: Question 2: Question 3: Question 4: Question 5: Question 6: Question 7: ; Do not […]

#### 2017 A-level H2 Mathematics (9740) Paper 1 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. This is answers for H2 Mathematics (9740). H2 Mathematics (9758), click here. Numerical Answers (click the questions for workings/explanation) Question 1: ; Question 2: or Question 3: 2 Question 4: ; translate the graph 4 units […]

#### 2017 A-level H2 Mathematics (9740) Suggested Solutions

Please take note that this is the solutions for H2 Mathematics (9740) Click here for H2 Mathematics (9758) suggested solutions Paper 1 Paper 2 Relevant materials MF26 KS Comments:

#### Interesting Trigonometry Question

We know how A’levels like to combine a few topics across. We also know how bad trigonometry can be. I was coaching my International Bachelorette (IB) class last week and came across a fairly interesting question. It tests students on their abilities to manage double angle identities. Not a tough question, but definitely good practice […]

#### Solutions to the modified A’levels Questions

Students of mine who have been diligently doing the modified TYS I sent them, and have difficulties with the questions that were added in to make the paper a full 3 hour paper, will find the following solutions helpful. Please try to do them in a single 3 hour seating, these are modified to cater […]

#### 2017 A-level H2 Mathematics (9758) Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. Paper 1 Paper 2 Relevant materials MF26 Comments on 2017 Paper

#### 2017 A-level H2 Mathematics (9758) Paper 2 Suggested Solutions

All solutions here are suggested. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. This is answers for H2 Mathematics (9740). H2 Mathematics (9740), click here. Numerical Answers (click the questions for workings/explanation) Question 1: Question 2: Question 3: Question 4: Question 5: Question 6: Question 7: ; Do not […]

#### 2017 A-level H2 Mathematics (9758) Paper 1 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. This is answers for H2 Mathematics (9758). H2 Mathematics (9740), click here. Numerical Answers (click the questions for workings/explanation) Question 1: ; Question 2: or Question 3: ; Maximum point Question 4: ; translate the graph […]

#### Last Hustle for A’levels 2017

As we are all busy counting down to A’levels, The Culture SG Team will like to share the preparatory course that we have for students. The lessons will all be $70 for each session and the max class size will be 15 students. You may contact Tutor KS for further questions. Details are as follow: “Lets’ […]

#### Some TYS Questions worth looking at

Prelims Exams was scary. H2 Mathematics isn’t that easy. Students that had difficulties finishing their prelims exams, should consider working on their time management. The best way to do it, practice 3 hour paper… in a single sitting. And students should note to modify their TYS slightly as several questions in each paper are out […]

#### RVHS GP Prelims paper 1 2017

Is being innovative more desirable than keeping the status quo? ‘The promise of science and technology cannot be realised without the humanities.’ Do you agree? Is politics today nothing but a series of empty promises? ‘Education perpetuates rather than fights inequality.’ Comment. ‘Men only need to be good, but women have to be exceptional.’ To […]

#### APGP Interest Rate Question

This is a question from TJC Promotion 2017 Question 10. Thank you Mr. Wee for sharing. Mr. Scrimp started a savings account which pays compound interest at a rate of r% per year on the last day of each year. He made an initial deposit of latex x at the start of each year. (i) […]

#### HCI GP Prelims paper 1 2017

‘Nothing but provocation and self-centredness.’ Is this a fair description of the state of affairs in today’s world? ‘My life, my choice.’ How far can people expect to live life this way? Should historical monuments and objects be preserved when such an undertaking is very expensive or even a source of unhappiness? ‘Many receive an […]

#### 2017 A-level H2 Mathematics (9758) Specimen Paper Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. Paper 1 Paper 2 Relevant materials MF26

#### 2017 A-level H2 Mathematics (9758) Specimen Paper 2 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. Numerical Answers (click the questions for workings/explanation) Question 1: Question 2: Question 3: Question 4: Question 5: Question 6: Question 7: Question 8: Question 9: Question 10: Relevant materials MF26 KS Comments The specimen paper 2 […]

#### 2017 A-level H2 Mathematics (9758) Specimen Paper 1 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. Numerical Answers (click the questions for workings/explanation) Question 1: Question 2: Question 3: Question 4: 1277cm, 3400cmQuestion 5: is a maximum, 20Question 6: Question 7: Question 8: Question 9: Question 10: Question 11: Relevant materials MF26 […]

#### Random Questions from 2017 Prelims #4

Find the acute inclination of the reflected ray to the -axis when is inclined at to the -axis and to the -axis.

#### RI JC GP Prelims paper 1 2017

‘The protection of animals is an indulgence.’ Do you agree? ‘In an increasingly uncertain world, there is little point in predicting the future.’ Discuss Would the world be a better place without religion? ‘We should abolish state funding for the Arts.’ How far do you agree that this should be the case for your society? […]

#### Making Use of this September Holidays

This is a little reminder and advice to students that are cheong-ing for their Prelims or A’levels… For students who have not taken any H2 Math Paper 1 or 2, I strongly advise you start waking at up 730am and try some papers at 8am. I gave my own students similar advices and even hand […]

#### Anderson JC GP Prelims paper 1 2017

Should small countries be allowed to take the lead in global affairs? To what extent can the Arts effect positive social change today? ‘Experiences are more valuable than material possessions.’ Do you agree? ‘People in the workplace should embrace, rather than fear, technological advancements.’ Discuss. ‘The news today deals with what is popular, rather than […]

#### Trigonometry Formulae & Applications (Part 2)

I meant to share more on factor Formulae today. However, a few students are not so sure how to get the R-formulae correctly during their preliminary exams recently. So I thought that I’ll share how they can derive the R-Formulae from the MF26. The following is the R-Formulae which students should have memorised. It is […]

#### Temasek JC GP Prelim Paper 1 2017

Temasek Junior College 8807 H1 General Paper Paper 1 2017 Can government surveillance eradicate the threat of terrorism? Examine the claim that globalization creates equal opportunities for all. ‘The government is not doing enough to support local sportsmen in your society.’ What is your view? To what extent is a universal language desirable? Should people […]

#### Tampines GP Prelim Paper 1 2017

Tampines Junior College 8807 H1 General Paper Paper 1 2017 How realistic is it for your society to embrace diversity? Protecting the environment should be given greater priority than eradicating poverty. How far do you agree? ‘Appearance can be deceiving.’ To what extent is this true of the media today? Discuss the view that smart […]

#### Random Questions from 2017 Prelims #3

Here is another question that is from CJC H2 Mathematics 9758 Prelim Paper 1. Its a question on differentiation. I think it is simple enough and tests student on their thinking comprehension skills. This is question 6. A straight line passes through the point with coordinates (4, 3) cuts the positive x-axis at point P […]

#### Trigonometry Formulae & Applications (Part 1)

Upon request by some students, I’ll discuss a few trigonometry formulae here and also some of their uses in A’levels. I’ve previously discussed the use of factor formulae here under integration. I’ll start with the R-Formulae. It should require no introduction as it is from secondary Add Math. This formulae is not given in MF26, […]

#### Random Questions from 2017 Prelims #2

Today I’ll share a question that came out of CJC Prelim 2017 Paper 1 for H2 Mathematics 9758. I think some of my student would have seen this question before and we discussed it in class before. Very technical question. This is question 11, I’ll share only the first part which is on the application […]

#### ACJC Prelims paper 1 2017

ACJC 2017 H1 General Paper 8807 Prelim Paper 1 To what extent does education prepare the young for a world that is constantly changing? ‘Science imparts knowledge but not wisdom.’ Do you agree? Have we placed too much emphasis on work today? Is being original always beneficial? ‘It is better to be feared than to […]

#### Integration By Parts

Today, I’ll share a little something about Integration by Parts. I want to share this because I observe that several students are over-reliant on the LIATE to perform Integration by Parts. This caused them to overlook/ appreciate its use. Lets start by reviewing the formula for Integration by Parts I like to share with students […]

#### Random Questions from 2017 Prelims #1

Last year, I shared a handful of random interesting questions from the 2016 Prelims. Students feedback that they were quite helpful and gave them good exposure. I thought I share some that I’ve seen this year. I know, its a bit early for Prelims. But ACJC just had their paper 1. 🙂 This is from […]

#### H2 Mathematics (9740) 2016 Prelim Papers

So many students have been asking for more practice. I’ll put up all the Prelim Papers for 2016 here. Do note that the syllabus is 9740 so students should practice discretion and skip questions that are out of syllabus. 🙂 Here are the Prelim Paper 2016. Have fun! Here is the MF26. 2016 ACJC H2 […]

#### Population problems eventually solve themselves-government meddling only makes things worse. Discuss

This is a past year question that has been adapted from HCI. Pretty interesting topic… Let’s see how to unpack this question together… This question assumes that population problems (demographic issues are part of the natural process on earth, which would eventually balances itself over a long period of time). Government interference would merely make […]

#### Students, test your Vectors!

As the prelims examinations draw really close, many students were asking me to give questions to test their concepts for several topics. In class, I had the opportunity to explore several applications questions too. We saw several physics concepts mixed. We also have some conceptual questions that need students to be able to use the […]

#### The value of humility in modern society

Came across this question in class which stumps a lot of my students in answering this… It seems so contradictory right… to be humble in our modern day? Ok let’s see what are some characteristics of our modern society first. We are driven by our pursuit of material goals, increasingly status conscious and technologically driven. […]

#### The pursuit of happiness is making us sad?

Came across a very interesting topic from ACJC prelim past year paper…and this got me thinking. It was about the pursuit of happiness in SG society and whether it is making us sad. Sounds pretty paradoxical ya? So what exactly is happiness in SG society? I would dare to define it in tangible terms (just […]

#### Thinking [email protected]re #9

[email protected] is a series of questions that we, as tutors feel that are useful in helping students think and improve their understanding. Thinking [email protected] is curated by KS. More of him can be found here This is a standard summation question. I’m interested in the last part only. The answer to (ii) is written there by […]

#### Quick Summary (Probability)

University is starting for some students who took A’levels in 2016. And, one of my ex-students told me to share/ summarise the things to know for probability at University level. Hopefully this helps. H2 Further Mathematics Students will find some of these helpful. Random Variables Suppose is a random variable which can takes values . […]

#### Youth Unemployment (Argh!!!)

This post is a continuation of the previous blog post where we would examine the situation of youth unemployment in developed nations. But first let us understand a little bit of context of how youth unemployment comes about… Well, many have said that it is due to the structural changes of the economy, ie basically […]

#### Let’s talk about sense of belonging…

Recently I have been hooked on this youtube video: What caught me in my tracks was the lyrics of the song, other than the composition of the song. The lyrics go like this, “Who could bring me to fly high in the sky? … Maybe I don’t belong here and have to leave; enough with […]

#### Thinking [email protected] #8

[email protected] is a series of questions that we, as tutors feel that are useful in helping students think and improve their understanding. Thinking [email protected] is curated by KS. More of him can be found here This is a interesting Complex Number Question. The complex number satisfies . What is

#### Let’s talk about the environment

A rather boringgggg yet simple topic to handle for the A levels. Most of the environment questions are asking about whether economic growth conflicts with environmental preservation… Let’s talk a look at how this issue could be approached… No both growth and preservation could be handled together: citizens are getting more eco-conscious and could force […]

#### Let’s talk about terrorism!

Terrorism has been an ongoing threat in many parts of the world. Once in a while, we could hear of lone wolf attacks that are occurring overseas. Just yesterday Brussels was hit by an attempted terrorist attack, and recently there was a London Bridge attack as well. Gun shooting cases are also heard of once […]

#### Thinking [email protected] #7

[email protected] is a series of questions that we, as tutors feel that are useful in helping students think and improve their understanding. Thinking [email protected] is curated by KS. More of him can be found here This is an application question for hypothesis testing from the 9758 H2 Mathematics Specimen Paper 2 Question 10. The average time […]

#### Thinking [email protected] #6

[email protected] is a series of questions that we, as tutors feel that are useful in helping students think and improve their understanding. Thinking [email protected] is curated by KS. More of him can be found here This is a very interesting vectors question from a recent JC BT Shown in the diagram is a methane molecule consisting […]

#### Let’s talk about money!!! (arts funding)

We all know that arts is a common topic that comes out year after year for the A levels. Should you choose to specialize in this topic, you would need to understand the issues and complexity that come along with state funding of the arts. Of course, funding does come with tangible and intangible benefits […]

#### Let’s talk about our future! (the youths specifically)

Once in a while, A level questions would like to test something hypothetical, about the future and whether prospects are going to be more optimistic or pessimistic. Of course, most of the focus would be on the youths since they are the future. It would be advisable to attempt questions that are more general, as […]

#### Let’s talk about poverty

As we all know, essay questions on poverty are usually popular among students. It is an easy topic that usually asks about the reasons for poverty, whether this issue can be resolved, and whether people are poor due to their own personal failings. With that, let’s take a look at some of the reasons why […]

#### Thinking [email protected] #5

[email protected] is a series of questions that we, as tutors feel that are useful in helping students think and improve their understanding. Thinking [email protected] is curated by Aaron. More of him can be found here. Given a chance to counter Sir Isaac Newton’s famous quote of “What goes up must come down”, do you think it […]

#### Thinking [email protected] #5

[email protected] is a series of questions that we, as tutors feel that are useful in helping students think and improve their understanding. Thinking [email protected] is curated by KS. More of him can be found here. This is a very challenging trigonometry question from AJC Mid Years P1 Q10. Using the formula for , prove that . […]

#### June Crash Course

The team at The Culture SG has been really busy and we have a lot of things prepared to help you guys work for that A. First up! Crash course for June… And we know it is a bit late to be announcing this on the site now, but we have really been caught up […]

#### What distinguishes a truly great work of art from a merely average one?

A truly great work of art: ability to attract the attention of its audience, invoking passion and strong emotion in them while at the same time, allowing for artists to disseminate their message clearly through their work. It may not necessarily be in terms of pricing. An expensive piece of art may not be truly […]

#### Thinking [email protected] #4

[email protected] is a series of questions that we, as tutors feel that are useful in helping students think and improve their understanding. Thinking [email protected] is curated by Aaron. More of him can be found here. Can you explain how a privacy screen protector works on your smartphone?

#### Thinking [email protected] #4

[email protected] is a series of questions that we, as tutors feel that are useful in helping students think and improve their understanding. Thinking [email protected] is curated by KS. More of him can be found here. This is a question from 1993 Paper 1. The positive integers, starting at 1, are grouped into sets containing integers, as […]

#### Population problems eventually solve themselves-government meddling only makes things worse. Discuss

Government intervention solves population problems such as population decline, which will be left unresolved if left to the masses. With a preference for smaller families and a general unwillingness to start a family in today’s modern society, negative or zero population growth often ensues. These have detrimental impact on affected countries, such as a fall […]

#### Thinking [email protected] #3

[email protected] is a series of questions that we, as tutors feel that are useful in helping students think and improve their understanding. Thinking [email protected] is curated by Aaron. More of him can be found here. In designing a circuit, an engineer needs to use five 5KΩ resistors to design a resistors network of approximately 4.3KΩ. How should […]

#### Thinking [email protected] #3

[email protected] is a series of questions that we, as tutors feel that are useful in helping students think and improve their understanding. Thinking [email protected] is curated by KS. More of him can be found here. This is a question from 1976 A’levels Paper 2. I thought it is pretty interesting to discuss the question with a […]

#### Thinking [email protected] #2

[email protected] is a series of questions that we, as tutors feel that are useful in helping students think and improve their understanding. Thinking [email protected] is curated by Aaron. More of him can be found here. Assuming an object is moving in a circular motion in a polar coordinate system given by and . Can you derive […]

#### Thinking [email protected] #1

[email protected] is a series of questions that we, as tutors feel that are useful in helping students think and improve their understanding. Thinking [email protected] is curated by Aaron. More of him can be found here. Kepler’s Third Law states that the period of a planet’s orbit is directly proportional to the cube of the semi-major axis […]

[email protected] is a series of questions that we, as tutors feel that are useful in helping students think and improve their understanding. Thinking [email protected] is curated by Aaron. More of him can be found here. Why study Physics? I have questioned many students and getting answers ranging from “Just a subject that I have to take […]

#### Should increased automation be embraced by our society?

In this latest May day’s speech by PM Lee, a lot of focus has been given to the future of jobs and the changing economy of Singapore. For a summary of the speech, you could refer to this link <a href=”http://www.straitstimes.com/politics/jobs-jobs-jobs-8-highlights-from-pm-lee-hsien-loongs-may-day-rally”>http://www.straitstimes.com/politics/jobs-jobs-jobs-8-highlights-from-pm-lee-hsien-loongs-may-day-rally</a> This has got me thinking about the current trajectory of the economy and what the […]

#### Thinking [email protected] #2

[email protected] is a series of questions that we, as tutors feel that are useful in helping students think and improve their understanding. Thinking [email protected] is curated by KS. More of him can be found here. (i) Find the two possible values of such that , leaving your answer in exact form , where and are real […]

#### Junior College education: A path increasingly less traveled?

Following up from the previous blog post about JC merger, it seems that there are more interesting and candid responses from the public. Here is one example that could interest you: <a href=”http://mothership.sg/2017/04/ex-nmp-calvin-cheng-makes-the-point-about-the-jc-mergers-that-no-one-wants-to-talk-about/”>http://mothership.sg/2017/04/ex-nmp-calvin-cheng-makes-the-point-about-the-jc-mergers-that-no-one-wants-to-talk-about/</a> This begs the question whether the merger is an attempt to make JC education more exclusive/competitive, considering that 7 out of the 8 […]

#### Thinking [email protected] #1

[email protected] is a series of questions that we, as tutors feel that are useful in helping students think and improve their understanding. Thinking [email protected] is curated by KS. More of him can be found here. Each card in a deck of cards bear a single number from 1 to 5 such that there are cards […]

#### Meritocracy? Junior colleges merger and its implications

It’s pretty interesting that shortly after our post on meritocracy, we have news about the junior college (JC) mergers. For more information about the news, you could take a look at this weblink. This drastic move by MOE has sparked a lot of concerns among the public and has brought up a few issues for us […]

#### Understanding meritocracy in Singapore

Before we start off on the topic of meritocracy, let’s examine this particular news article about it. Based on the author’s argument, it is pretty clear that meritocracy is an esteemed principle of governance in Singapore. It is based on achieving equality of opportunities, rather than equality of outcomes. It is a system to filter candidates […]

#### Differentiation Question #1

Given that , find the approximate percentage change in when increases from 2 by 2%.

#### Common Errors for Application Question(AQ)

My previous posts have touched on the points that you would need to excel in your AQ. It is also important for you to understand what are some pitfalls so that you will not make these mistakes. 1. Rehash of the author’s argument/ summary of the author’s argument- did not go on to elaborate or […]

#### Probability Question #4

A gambler bets on one of the integers from 1 to 6. Three fair dice are then rolled. If the gambler’s number appears times (), he wins latex k1. Calculate the gambler’s expected winnings

#### Random Sec 4 Differentiations

B6 let Sub to Thus, it is a min point. C7 let (NA). There are no stationary points for this curve. C8 Let Evaluate with a calculator…

#### Vectors Question #4

Another interesting vectors question. The fixed point has position vector a relative to a fixed point . A variable point has position vector r relative to . Find the locus of if r (r – a) = 0.

#### Evaluation for Application Question (AQ)

Have you ever wonder what teachers mean by evaluation? Many students have asked me this during my classes. Well to put it simply, evaluation for the AQ is not just simply stating whether you agree or disagree. You would need to provide a reason to support your point. So how exactly should you evaluate? Well […]

#### Characteristics of Singapore’s society (Application Question)

This list is non-exhaustive and serves as a guide for you to expand on Singapore’s characteristics… Pls take a look at my previous post on Singapore’s characteristics, so that you would have a better overview. Highly globalized and connected city, with heavy focus on technological developments Highly educated High cost of living Pragmatic, concerns usually […]

#### Vectors Question #3

This is a question a student sent me a few days back, and I shared with my class. Find the Cartesian equation of the locus of all points (plane) that is equidistant of the plane and plane. The following should aid students to visualise. Sidenote: I think Vectors is a very important topic for 9758 […]

#### A little reminder to students doing Calculus now

When , it implies we have a stationary point. To determine the nature of the stationary point, we can do either the first derivative test or the second derivative. The first derivative test: Students should write the actual values of and in the table. We use this under these two situations: 1. is difficult to […]

#### Do’s and Don’ts For Application Question (AQ)

Are you interested to know what are the requirements of a good Application Question (AQ)? Well according to the examiner’s report, the best AQ responses are/demonstrate: “eloquent”, “mature”, “lively”, “well-informed personal voice”, “energetic”, “well-organized”, “fresh insights”, “evaluative”, ” written with clarity, confidence and conviction” On the other hand, mediocre marks are awarded to individuals who: […]

#### APGP Question #3

This is a question from a recent ACJC JC2 test. A philanthropist started a donation matching programme to encourage more people to donate regularly to a particular charity. (a) For a person who donates more than the previous month, the philanthropist will donate 20 in the third month, and ten times more than John in […]

#### Responsibility of Protecting the Environment

Environment is a common and easy essay question that could potentially come out for the exams… Students should always analyze their essays from a stakeholder’s perspective to give a more holistic evaluation. Developed countries Governments in developed countries have the necessary skills, influence and resources to aid the protection of the environment. They would have […]

#### Singapore Budget 2017- What it means for Singaporeans?

Future Economy: What is in store for all of us? Recently, news have been focusing on changes in technology that bring about new prospects for certain segments of the population but disenfranchises others. Some would call it the “Fourth Industrial Revolution”. This is a situation in which disruptive technologies streamline processes making work more efficient and […]

#### Vectors Question #2

If , where , and are all non-zero vectors, show that bisects the angle between and .

#### Post-Results 2016

Let’s face it. Some of us will not get the dream results we want. Don’t give up and let fear conquer you. For students unsure of the available courses, they can check out the following post. It contains the grade profile for local universities. Our Team will be here if you need help/ advice. Feel […]

#### In times of economic hardship, should a country still be expected to provide financial or material aid to others?

Students are expected to address the criteria of this question throughout the essay; it being in times of economic hardship. For a quality essay, the terms “should” and “expected” should be addressed as well. For instance, a country should still give aid, but perhaps not be expected at a time when its survival is in […]

#### Singapore Inclusive Policies- A reflection

“An Inclusive Society, A Stronger Singapore” Budget Plan 2012-2016: fulfilled promises, financial burden and new directions In 2012, the Singapore government introduced a 5-year budget plan aiming to make Singapore a fair, stronger and inclusive society. The main features of this ambitious project were: Restructuring to sustain growth Less dependency on foreign labour More grants […]

#### Things to note for 9758 H2 Mathematics

It has been awhile since the A’levels. We talked and met up with several of our students. Some students are working and some are preparing their Personal Statements for overseas University Applications. A few of them also remarked that they wish they put more efforts into studying A’levels. An advice to this year JC2 – […]

#### Release of A’levels Results 2016

For students who took A’levels in 2016, please note that information for the release of A’levels Results 2016 can be found in the following! Release of A’levels 2016 Grade Profile (i.e. Number of As you need to get into courses for) SMU NTU NUS P.S. Results does not define you. When one door closes, another opens.

#### Checklist for Vectors

Many schools have been doing vectors recently. Thought I’ll share a little summary/ checklist I have done for my students. Basic Concepts Operations on Vectors Addition & Subtraction Scalar multiplication Dot Product (Scalar) a • a = |a|2 If a ⊥ b, then a • b = 0 a • b = b • a Cross Product (Vector) a × a = 0 a × b = […]

#### “In your society, do the arts merit the vast sums of money spent on it?”

Between the 1960s and 1990s, there has been a strong perception that the arts were an abstract waste of time. More focus was invested on STEM – science, technology, engineering and mathematics – to boost the value of each worker and compensate for our geographical disadvantage. Recently, the Singapore government revealed that 822 million in 2003 to […]

#### A little history of e

Some students remarked on why I actually recognise e, that is, . Well, e is a rather unique constants. Firstly, for all JC students, we see it our daily algebra & complex numbers. Students exposed to university statistics will see e appearing in the formula for normal distribution, that is, . Secondly, the story of […]

#### How to maintain your self discipline to study?

Dear all, this is a general post on how to keep your study momentum up during this december holidays. As you already know, this december holidays is not only a time for you to rejuvenate yourself from the hectic JC life, it is also an important revision time for you! It is a time when […]

#### Commentary for 2016 A level paper

1. ‘Any adaptation of a novel for a film, television or the theatre is never as effective as the original.’ Discuss. (Media) 2. Assess the view that traditional buildings have no future in your society. (Arts and SG Society) 3. ‘Longer life expectancy creates more problems than benefits.’ Discuss. (S&T) 4. Considering the money involved, […]

#### Some questions that students ask recently.

I’ve been asked many times recently about what university course to take, and also what university to go too, etc. Some students ask me how does Financial Mathematics work? So I’ve come across an article here. This article illustrates how to be a quant, which is just one of the jobs available to someone who […]

#### 2016 A Level H2 Physics (9646) Paper 1 Suggested Solutions

All solutions here are SUGGESTED. Casey will hold no liability for any errors. Comments are entirely personal opinions. B C B D D C D D B C A D D C C A D A B D Question 21 is a flawed question. When unpolarised light goes through a polarizer, the I is halved […]

#### Thoughts on A’levels H2 Mathematics 2016 Paper 2

I’ll keep this short since we are all busy. One thing about paper 1 we saw, there were many unknowns. So topics which I think will come out… Differentiation – I think a min/max problem will come out, possibly with r and h both not given and asked to express r in terms of h. […]

#### How far has modern technology made it unnecessary for individuals to possess mathematical skills?

How far has modern technology made it unnecessary for individuals to possess mathematical skills? Argument 1: Modern technology has provided us with tools that automate mathematical operations for us, making possessing mathematical skills redundant. Elaboration: All we have to do are to insert the data we want to be processed into our modern technological tools, […]

#### ‘Everyone has an opinion, but not everyone’s opinion is of equal value.’ What is your view?

‘Everyone has an opinion, but not everyone’s opinion is of equal value.’ What is your view? Define opinion and its purpose. An opinion is a view or judgment formed about something, not necessarily based on fact or knowledge. Opinions are predicated on the individual’s current understanding and analysis of perceived phenomena, and its dynamic nature […]

#### ‘Countries experiencing conflict should be left to sort their own problems.’ How far do you agree?

‘Countries experiencing conflict should be left to sort their own problems.’ How far do you agree? Question analysis- definition of key terms Experiencing conflict: having issues dealing with domestic problems such as human rights; civil war; poverty Left to sort: They should be left on their own terms to deal and resolve their own problems. […]

#### Is competition always desirable?

Is competition always desirable? Defining competition The activity of striving to gain or win something by establishing superiority over others, competition is highly prevalent in today’s fast paced and at times seemingly unforgiving society. To do well for this question, there is a need to compare the benefits of competition to collaboration. Which one is […]

#### Assess the view that most natural disasters are the result of human activity.

Assess the view that most natural disasters are the result of human activity. Question analysis-definition of key terms Natural disaster: Floods, landslides, tsunami, Human activity: Deforestation, increasing urbanization, the pursuit of economic growth and the refusal to use environmentally friendly products Assumption: Natural disasters today are on a very frequent and common basis, so much […]

#### Evaluate the claim that equality of opportunity for females is a desirable, but unrealistic goal.

Evaluate the claim that equality of opportunity for females is a desirable, but unrealistic goal. Question analysis-definition of key terms Equality of opportunity: same chances to succeed in all aspects of life Desirable: beneficial not just to the women, but towards the larger society as a whole Unrealistic: impossible task to achieve; just a dream […]

#### ‘People who do the most worthwhile jobs rarely receive the best financial rewards.’ To what extent is this true in your society?

‘People who do the most worthwhile jobs rarely receive the best financial rewards.’ To what extent is this true in your society? Question analysis- Definition of Key Terms Most worthwhile jobs: occupations that are mostly serving the needs of the people for a very humanitarian and altruistic purpose. Such instances would be social workers, nurses, […]

#### ‘Any adaptation of a novel for film, television or the theatre is never as effective as the original’. Discuss

Thesis Some may argue that any adaptation of a novel for film, television or the theatre is never as effective as the original given that novels are able to deliver much more content in greater detail and that novels excel in communicating the character’s emotions and thoughts via various literary devices, developing a more intimate and deeper […]

#### ‘Human need, rather than profit, should always be the main concern of scientific research.’ Discuss

Human need, rather than profit should always be the main concern of scientific research. Discuss. Define scientific research and its purpose. Scientific research is the systematic investigation of scientific theories and hypotheses. This leads to a deeper understanding and knowledge of the mechanics behind physical world around us, which in turn empowers mankind to come […]

#### Considering the money involved, should developing countries be allowed to host major sporting events?

Considering the money involved, should developing countries be allowed to host major sporting events? Question Analysis: Definition of Key terms Developing countries: Nations that have not reached first world status yet, low Human Development Index (HDI) relative to other countries. Basic infrastructure could be missing from the nation, and the nation is riddled with poverty. […]

#### ‘Longer life expectancy creates more problems than benefits.’ Discuss

Longer life expectancy creates more problems than benefits. Discuss. Stand: Longer life expectancy creates more problems than benefits, unless we find a way to effectively redistribute our resources and find alternative sustainable energy resources. Argument 1: More people living in retirement can potentially be taxing on the economy Elaboration: Economic output will only be increased if […]

#### Assess the view that tradition buildings have no future in your society.

Assess the view that traditional buildings have no future in your society Question Analysis- Definition of Key Terms Traditional Buildings: Structures that have a historical significance to Singapore. These could be the old colonial buildings; buildings that reflect unique architecture that showcase a nation’s culture and identity or even a historical past. No Future: Possible […]

#### Singapore’s Characteristics for Application Question (AQ)

It is common for AQ to ask you to contextualize the issues to Singapore’s society. As such, there is a need for you to be familiar with certain features in Singapore. Listed below are just some features for you to brainstorm. They are not exhaustive. Singaporean’s behaviour (positive): Hardworking, ambitious, have high expectations, obedient, law-abiding, […]

#### Should business be ethical at the expense of company profits and staff welfare?

Question analysis: At the expense: at the cost of something, the opportunity cost. Please note that you have to address this criteria throughout the whole essay. Ethical: Relating to moral principles. Pls note that ethics are subjective and every individual has different moral codes. What is considered ethical to an individual may not be to […]

#### How to study for Gp?

Now that the A levels GP paper is drawing nearer and nearer, many students have asked about their revision strategies… Given the limited time left, I would advise students to : Consolidate their niche chosen topics for the exam- in terms of the arguments, content, evaluation and examples. Make a list of the past mistakes […]

#### 2016 A-level H2 Mathematics (9740) Suggested Solutions

All solutions here are SUGGESTED. KS will hold no liability for any errors. Comments are entirely personal opinions. Thoughts before 2016 A-level H2 Mathematics Paper 1 Paper 2 Relevant materials MF26 KS Comments: Strictly speaking, the last 9740 H2 Mathematics Paper. Personally, I feel this paper was rather challenging and it provided a bit of […]

#### Thoughts about 2016 A’levels H2 Mathematics Paper

I’ve covered some things in classes, with sufficient revisions and final lap papers set. So I thought we have a little breakdown. And of course, we should review what was weeded away in the 9740 H2 Mathematics Syllabus. After all, this is the very LAST time the can test them. Recurrence Relations. I’ve harped on […]

#### Random Questions from 2016 Prelims #13

NYJC/2/11 On a typical weekday morning, customers arrive at the post office independently and at a rate of 3 per 10 minute period. (i) State, in context, a condition needed for the number of customers who arrived at the post office during a randomly chosen period of 30 minutes to be well modelled by a […]

#### Random Questions from 2016 Prelims #12

HCI/1/6 A group of boys want to set up a camping tent. They lay down a rectangular tarp OABC on the horizontal ground with OA = 3 m and AB = 1.5 m and secure the points D and E vertically above O and B respectively, such that . Assume that the tent takes the […]

#### ‘The young lack drive.’ Do you agree?

Question Type: Simple Polarity (no conditional words present in the question) Key Words: The young; drive Minimum Requirements: Students will need to unpack the key words and explore the reasons why one can argue that the young lack drive. Similarly, they must be able to also highlight why some may disagree with this claim. Better […]

#### Sportsmanship is irrelevant in today’s society. Discuss.

Question type: Simple Polarity Focus word: irrelevant Topic word: Sportsmanship – playing fair, following the rules of the game, respecting the judgment of authority (referees and officials), treating opponents with respect – can refer to more than sports Context: Today’s society (Scope can extend beyond sports.) P: Sportsmanship breeds healthy competition, builds and promotes bonds […]

#### Random Questions from 2016 Prelims #11

TPJC/P2/4 (a) The complex number w is given by (i) Find the modulus and argument of w, giving your answer in exact form. (ii) Without using a calculator, find the smallest positive integer value of n for which is a real number. (b) The complex number z is such that (i) Find the value of […]

#### GP 2016 Prelim trends

This post is going out to all students that are taking their A levels GP 2016 this year: the listed topics are just some of the common questions that schools have set in this prelim. You may want to take note of it and prepare for these issues just in case. Being prepared beats being […]

#### Random Questions from 2016 Prelims #10

PJC P2 Q1 The complex numbers a and b are given by and respectively. (i) On a single Argand diagram, sketch the loci (a) (b) (ii) Find the range of where is the complex number that satisfies the relationships in part (i)

#### 2016 A-level H1 Mathematics (8864) Paper 1 Suggested Solutions

All solutions here are SUGGESTED. KS will hold no liability for any errors. Comments are entirely personal opinions. As these workings and answers are rushed out asap, please pardon me for my mistakes and let me know if there is any typo. Many thanks. I’ll try my best to attend to the questions as there […]

#### 2016 A-level H1 General Paper (8807) Paper 1 Suggested Solutions

All solutions here are SUGGESTED. Christine will hold no liability for any errors. Comments are entirely personal opinions. Read more about Christine’s Pre-A’levels 2016 thoughts here. Read more about Christine’s Post-A’levels 2016 thoughts here. Please leave a comment/ reply here if you need to discuss with anything with me. Try not to spam the number. […]

#### 2016 A-level H2 Mathematics (9740) Paper 2 Suggested Solutions

All solutions here are SUGGESTED. KS will hold no liability for any errors. Comments are entirely personal opinions. Numerical Answers (click the questions for workings/explanation) Question 1: Question 2: Question 3: Question 4: Question 5: Question 6: Question 7: Question 8: Question 9: Question 10: Relevant materials MF15 KS Comments

#### 2016 A-level H2 Mathematics (9740) Paper 1 Suggested Solutions

All solutions here are SUGGESTED. KS will hold no liability for any errors. Comments are entirely personal opinions. Thoughts about Paper 2. Numerical Answers (click the questions for workings/explanation) Question 1: Question 2: Question 3: Question 4: Question 5: Question 6: Question 7: Question 8: Question 9: Question 10: Question 11: Relevant materials MF15 KS […]

#### 2016 A’level Suggested Solutions

Congratulations on the completion of A’levels for the 2016 batch! As for those who still, are taking A’levels 2017, we hope you find this site helpful. Read the comments (ignore the trolls who have yet grown up) and learn from our mistakes. It has been a pleasure for all us to interact with you guys. […]

#### Random Questions from 2016 Prelims #9

HCI P1 Q2 Solve the inequality Hence find , leaving your answer in exact form.

#### Random Questions from 2016 Prelims #8

ACJC P2 Q3 The function g is defined by (ii) Explain why the composite function exist. (iii) Sketch the graph of .

#### Random Questions from 2016 Prelims #7

VJC P1 Q9 (i) Sketch the graph with equation , where and A hemispherical bowl of fixed radius cm is filled with water. Water drains out from a hole at the bottom of the bowl at a constant rate. When the depth of water if cm (where ). (ii) Use your graph in (i) to […]

#### Random Questions from 2016 Prelims #6

HCI P1 Q5 Sketch on a single Argand diagram, the loci defined by and (i) Find the minimum value of (ii) Find the minimum value of (iii) Given that , state the minimum value of

#### ‘Religion divides rather than unites.’ Discuss. (RI 2016 Prelims)

I realized that I have not done a post about religion, so here is a basic outline for this essay. This question requires students to compare whether religion is more divisive or more unifying in nature. The world’s major religions preach love, peace, tolerance, kindness, forgiveness and reconciliation. However in reality, religion often divides rather […]

#### Random Questions from 2016 Prelims #5

NYJC P1 Q4 Referred to the origin , the points A and B have position vectors a and b respectively. A point C is such that OACB forms a parallelogram. Given that M is the mid-point of AC, find the position vector of point N if M lies on ON produced such that OM:ON is […]

#### Random Questions from 2016 Prelims #4

VJC P1 Q6 A curve has equation and a line has equation as shown above. is a fixed point on C and A is an arbitrary point on . State the geometrical relationship between the line segment AB and is the distance from B to A is the least. Taking the coordinates of A as […]

#### Random Questions from 2016 Prelims #3

AJC P1 Q7 The function f is defined by . (i) State the greatest value of for which exists. (ii) Define in similar form.

#### 6 weeks left to A levels!!!

Dear students, I’m sure most of you are already done with your prelims or nearly done… In fact, some of you have already gotten back your GP papers. How did you fare? I’m sure most of your teachers would have told you that Prelim results are usually quite an accurate indication of your final A […]

#### Random Questions from 2016 Prelims #2

NYJC P1 Q10b The function (i) Use an algebraic method to find the range of g. (ii) State a sequence of transformations which transform the graph of to the graph of

#### Random Questions from 2016 Prelims #1

YJC P1 Q4 Given for . If and , sketch the graph of for .

#### Applications of modern world

Dear students, I’m sure you have come across the phrase “modern world” in your essay and application question especially. Are you aware that features of the modern world are the most important component to scoring in the AQ? So what exactly constitute these modern society features? Competitive society: goal to be better than the rest; […]

#### So why do I chose to take A’levels annually?

So I can discuss with my students. Having taken the paper allows me to observe pitfalls quickly. At times, I do wonder how many students will fall for these tricks when I am doing the paper too, and chuckle at it. I can also understand the anxiety and anxiousness that the students have, so having […]

#### Do I really take A’levels H2 Mathematics?

Yes, I have 8 As from H2 Mathematics Paper to date already. Many students still are bewildered by why I do that and wonder what it is like for me. It is fun. Some closer students have done mock/ practice papers with me before. This is an interesting and good exercise, which I’m still studying […]

#### Hit Hard by the Preliminaries?

As some Preliminary exams have begun, I’ve heard from students that they are severely defeated after the papers. Several subjects were so difficult that they are having second thoughts about taking A’levels. To be frank, I know some schools intentionally set out of the world paper just to scare the students and make their students […]

#### National boundaries make little geographical or economic sense nowadays. Discuss.

This question assumes that as the world gets more and more globalized, there is greater freedom of movement of ideas, trades and people, so much so that our lives are intertwined. The increasing globalization of the world is also made more astute with the pervasiveness of social media. As such, it makes little sense for us to […]

#### Problem Solving Tips #1

So these past months, I have been focusing on harnessing students’ abilities to interpret questions properly. Every line in a question is there for a reason and hold little pieces of information. As a student, you need to piece these information together. Take the following question as an example: We have a, b and c=a+2b. […]

#### GP Crash Course Content

Dear Readers, I have received some calls regarding a rerun of GP crash course on content. We have done this twice during June, and we have given our students 8 sets of content notes. If u are interested and would like us to do a re-run, pls comment below or contact us at 90050181. We […]

#### Special Post for A levels Students GP

Dear students, This is a special post going out to all of you. Considering that your A levels are drawing near and you are already in the midst of your prelims, what are some topics that you are still struggling with? What are some essays that you would like to see a post on? The […]

#### H2 Mathematics Crash Course Sept

Our team at “theculture.sg” have been really busy the past few weeks, which explains the lack of posts. We have really exciting news to share with our reads. While we are busy preparing our students for the preliminary exams on all levels such as time management and exam preparedness, we received many queries regarding the […]

#### General Paper Crash Course Sept- Skills focused

Dear readers, In view of your upcoming examinations and to help you better prepare for them in this final stretch, we are pleased to announce that we are having a crash course for General paper this September holidays. We will be focusing on imparting our skills to you to help you ace your examinations. Our […]

#### Getting what one wants in life is what matters. Discuss.

Getting what one wants in life is what matters. Discuss. This is a very deep philosophical question that requires students to answer in a mature way on what do they think life is about. What are the things that matter to us? Do they hold any meaning at all at the end? Is it even […]

#### Is it necessary for a country to invest in its artists?

In today’s society where globalization has led to a world that has become heterogeneous, countries can use their artists to not only articulate their own culture but to establish an identity through art. Local artists often would base their artistic efforts on the experience of being a citizen and living in the country, thereby providing […]

#### History matters in shaping the future of a country. To what extent is this true?

History matters in shaping the future of a country because it allows counties to understand changes and developments that had taken place to create the present society. In this highly globalized world we live in today, there is a need for developed countries to maintain the fast pace lifestyle while developing counties play catch up. […]

#### How important is it for people in your society to retain a sense of tradition?

Traditions are important because it provides people with a way to govern themselves in a world where moral standards are now often being compromised. Most traditions have moral and ethical messages embedded within them, and these serve as guidelines as to how people should govern themselves and, therefore, gain a degree of control over their […]

#### Can nuclear research be justified?

Nuclear research, despite its usefulness in benefitting the populace, can also be used as a form of weaponry to destroy, with catastrophic results. Nuclear technology is extremely harmful in its natural form, even if stored within a power plant. Its destructive potential, when fully unleashed, makes it an excellent choice as a missile or a […]

#### 5 Golden Rules for your Application Question (AQ)

How do you handle the application question (AQ) effectively? Here’s 5 golden nuggets for you to remember. Work on your timing! Always complete your AQ under timed conditions! You should allocate a maximum of 30 minutes to complete it. The biggest trap to avoid is messing your timing and spending too much time on the […]

#### 100 days more…

So the Midyear results are all out and Prelims are known to be in 4-5 weeks’ time. Many students are frantically searching for help and attempting to salvage their results. We are sorry to say that we aren’t able to take any more private students due to time constraints, and only the group classes are […]

#### Is the elimination of global poverty a realistic aim?

Poverty as defined by the UN is “the denial of choices and opportunities, a violation of human dignity”. What this essentially means is that a person suffering from poverty lacks the ability to participate actively in society; having no capability to feed and clothe a family. It also means that this individual is insecure and […]

#### Reimagining mathematical notations

Maths notation is often overly complex. Let’s see how this can be better:

#### Advice for JC1 students

Dear JC1 students, This post is reaching out to all of you to encourage you to study well and to prepare for your upcoming promotional examinations. I’m sure by now most of you would have received your mid year results back, and should have a clearer picture on whether you are going to get promoted […]

#### How to get an A for General Paper

Many students have always wondered how to score an A for General Paper especially leading up to their examinations. Besides knowing your basic content for the essay question that you are attempting, it is also critical for students to have some basic examination skills. The aim of this post is to highlight some important examination and […]

#### Advice for J2 students who are still failing at this stage

Dear J2 students, This coming week should be when your examination results are being released to you. After a month of intensive studying in June, how do you think you will fare? Based on my years of tutoring, I can safely say that if you are aspiring for straight As for the A levels, you […]

#### Environmental Conservation is solely the responsibility of the government. Do you agree?

Environmental Conservation is solely the responsibility of the government. Do you agree? Environmental questions are possibly the simplest to tackle in the examination given the predictability of the type of questions that come out. This question is asking about who are the actors that should be responsible in the protection and conservation of the environment. […]

#### Is it ever justifiable to break the law?

Is it ever justifiable to break the law? “Ever justifiable”: set a criteria for such a question. Possible criteria that you can set: 1) law implemented is unlawful/ unreasonable e.g. when the punishments outweigh the crime 2) breaking the law suffices as the last hope/action and it actually benefits society as a whole. Law: A […]

#### GP Fun Fact Poverty #2

Here is a continuation of our post on poverty. Take a look at these figures and think about the glaring divide between the haves and the haves-not. What are some of your feelings and thoughts? #1: US families living in extreme poverty, living with less than USD$2 a day has doubled to 1.6 million since […]

#### Fun Facts #1: Poverty

This is going to be a very somber post about poverty around the world today… While considering the posts and the stats, please also consider some issues like income inequality; why is poverty concentrated only in some particular regions; Are richer nations obligated to help the poorer nations? Could this issue on poverty be resolved? […]

#### Is there any point in trying to predict future trends?

Yes there is a point in predicting future trends Predicting future trends is not pointless especially when the lives and livelihoods of millions of people are ultimately at stake. This applies to anything from the economy of the world, to business trends for companies and even the potential of a natural disaster to occur. For […]

#### June Revision Exercise 4 Q1

(a) Using cover-up rule, we find that (b) Back to June Revision Exercise 4

#### June Revision Exercise

You can find the solutions of all ten sets of the June Revision Exercise we did in class. Have fun! June Revision Exercise 1 June Revision Exercise 2 June Revision Exercise 3 June Revision Exercise 4 June Revision Exercise 5 June Revision Exercise 6 June Revision Exercise 7 June Revision Exercise 8 June Revision Exercise […]

#### June Revision Exercise 3 Q11

(i) When When Using GC, When time interval between the first and second alarm. (iii) As which is impossible as the canal has only a fixed capacity of . Thus, the model is not valid for large values of (iv) Assume that the weather condition remain unchanged. Back to June Revision Exercise 3

#### June Revision Exercise 3 Q6

(a)(i) Consider is a circle with centre Origin and radius . Thus, required area is the area of a quadrant with radius (ii) (b) Back to June Revision Exercise 3

#### June Revision Exercise 3 Q3

(a)(i) Let (a)(ii) *Students are expected to prove that gives the maximum area. (b)(i) latex xlatex \Rightarrow \frac{dy}{dx}=0latex y=-x^2latex y=-x^2latex x^3 + 2y^3 +3xy=klatex x^3 + 2(-x^2)^3 +3x(-x^2)=klatex 2x^6 + 2x^3 + k=0latex y=-1latex -1=-x^2latex x =\pm xlatex x = 1, k=-4latex x = -1, k=0$ Back to June Revision Exercise 3

#### June Revision Exercise 3 Q2

(i) When Equation of tangent: Equation of normal: (ii) Hence, tangent cuts curve again at (iii) At Q, At R, Back to June Revision Exercise 3

#### June Revision Exercise 3 Q1

(i) For tangents to be parallel to the -axis, Sub into Thus, equations of tangents which are parallel to -axis are (ii) units per second. Back to June Revision Exercise 3

#### June Revision Exercise 3

Please do check through the solutions on your own, especially for questions that we did not have chance to properly discuss during class. You may whatsapp me too if you have a burning question. Note: You should not spend more than 180mins on the entire exercise. June Revision Exercise 3 Q1 June Revision Exercise 3 […]

#### June Revision Exercise 8 Q5

(i) If they intersect, then for some Solving with GC, we have . Thus, the lines intersect. (ii) Equation of plane: (iii) Required distance (iv) Area of quadrilateral Back to June Revision Exercise 8.

#### June Revision Exercise 8 Q6

(a) (b) If the plane contains the line , the is parallel to : and the point lies in the plane : Alternatively, you may consider that : — (1) — (2) Solving, Back to June Revision Exercise 8.

#### June Revision Exercise 8

Below are the solutions for the June Revision Set 8 (Vectors) Do let me know if you don’t understand the solutions. Thanks Question 1 Question 2 Question 3 Question 4 Question 5 Question 6 Question 7 Question 8 Question 9

#### Is aging population a necessarily bad thing?

Topics on ageism have been coming out recently in many schools prelim papers. Perhaps its worth taking a look at this topic on aging population. Who are we referring to in an aging population? Usually it refers to elderly aged 65 years and above. Aging population has been the concern of many developed nations since […]

#### The role of artificial intelligence in our lives

There seems to be increasingly interest in artificial intelligence in the area of science and technology today. As such, I have decided to create a post to address this just in case it comes out for the A levels. What is artificial intelligence? Artificial intelligence is the combination of computer science, physiology and philosophy. In the […]

#### Arts and Literature Questions

Dear readers, I’m sure some of you have realized that I have been posting essay outlines for arts and literature questions. Based on my teaching experience, many students do not like to attempt such questions because they are deemed to be difficult and boring. Most students do not even have an interest in the arts, […]

#### Are certain types of writing superior to others?

Define writing- information rich articles in newspapers; formal writing in contracts; aesthetic and expressive forms such as poetry, music composing and narratives. All types of writing specialize in their own genre and niche and would definitely not be as effective or applicable in other categories. It would be too simplistic to base a writing’s significance […]

#### ‘Unlike the Arts, such as writing or music, Mathematics lacks the capacity for creativity.’ How far do you agree with this statement?

‘Unlike the Arts, such as writing or music, Mathematics lacks the capacity for creativity.’ How far do you agree with this statement? Agree: Arts allows individuals the space to explore and create possibilities based on their own imaginations. Multiple viewpoints can congregate and amalgamate to form new ones. Arts is often seen to be the […]

#### Inequality question

So lets see how to resolve inequalities that a bit longer than usual. and or and . Thus,

#### Fun Facts #2: Marriage

#1: Couples who cohabit before marriage are more likely to divorce than those who wait. #2: There are 100 divorces every hour in the US. #3: A law in 2013 in Iran allows men to marry their 13 year old adopted daughters. #4: Inter-racial marriage is banned in the US from 1776 to 1967. #5: […]

#### Fun Facts #1: Marriage

This is personally one of my favourite topics for the essays: Marriage and Family. While taking a look at these figures, we must also know what are the implications of these facts… Here are some interesting facts that I have found: #1: 75% of people who marry partners from an affair eventually divorce. #2: 80% […]

#### The man who knew infinity

Previously, I shared a post on the golden nugget. It relates a bit about the movie The Man Who Knew Infinity. I finally found time to watch it while I’m overseas. Usually in Singapore, I’m too overwhelmed with work and tuitions. So yes, I actually watch movies and gym/ swim when I’m overseas. So the […]

#### Fun Facts #2: Climate Change

#1: The golden toad is the first species to go extinct due to climate change. #2: Around 15% of the carbon released in the environment is due to deforestation and change in use of land. #3: Climate change enhances the spread of pests that causes life threatening diseases like dengue, malaria, Lyme disease etc. #4: Due to the greenhouse […]

#### Should we embrace the advances of life science?

Should we embrace the advances of life science? This question assumes that the advances of life science should be met with some level of skepticism, for fear that there are harmful drawbacks from the pursuit of life science. What are some of these implications? Life sciences here could refer to cloning; stem cell research; bioengineering; […]

#### Importance of June Holidays

June holidays are coming and JC2 students should really grab this last opportunity that you have to study. This is effectively your time you have a full month to study for your upcoming A’levels. Through the years, we see many students who have their efforts paid off for working hard during June Holidays. So make […]

#### Animal rights is a futile pursuit. Discuss.

Animal rights is a futile pursuit. Discuss. 1.At this current moment, humans have difficulty even preserving humans rights, to ask us to fight for animal rights seem a too far distant dream. Also, it questions the credibility of our fight for animal rights since we are already exploiting the humans of our kind. It does […]

#### Golden Nugget!!!

My brother shared this interesting video with me a few days back when he was at the screening for The Man Who Knew Infinity. I’m looking forward to watching this movie too! Back to the video! It focuses on the sum that is written above. And interestingly, this sum that should not be defined (as […]

#### Format for Application Question (AQ)

Here’s the format for the Application Question (AQ): Intro- Brief summary of the author’s point; your overall stand + justification. Your justification should be in terms of Singapore’s related examples. Requirements a. Main Sentence/ Idea (identified from the passage). You can either quote directly from the author or to paraphrase his ideas. b. Your view/ stand. […]

#### Fun Facts #2: Crime and Punishment

This is a continuation from our first post on Crime and Punishment… #1: In ancient Rome, the preferred method of execution was crucifixion. Although largely abandoned as a method of execution by nearly every country in the world, at least one country still uses the method: Sudan. Crucifixion results in a slow, agonizing death, which is […]

#### Introduction to Stochastic Calculus

Back in undergraduate days, when I took my first module on financial mathematics, my professor introduced us by that the most important things are the following This is a probability triple where 1. is the ‘true’ of physical probability measure 2. is the universe of possible outcomes. 3. is the set of possible events where […]

#### Fun Facts #1: Crime and Punishment

Some interesting stats that you can use for the topic on Crime and Punishment… Most of these facts touch on the death penalty. Students should consider the goals of punishment, and assess for themselves whether the death penalty goes against their own ethical and moral beliefs. Death penalty is largely used for the goal of […]

#### Fun Fact #1 Climate Change

Students who love to do topics on environment, you can take a look at the next few series on climate change and global warming examples. For the rest, perhaps taking a look at such figures, will incite you to do your part to make the Earth a more sustainable place for living. #1: 37% of […]

#### Question of the Day #18

Here is a very very interesting question involving probability that a student saw in her tutorial and asked me. Here it is 🙂 A student is concerned about her car and does not like dents. When she drives to school, she has a choice of parking it on the street in one space, parking it […]

#### Fun Facts #2 Money

Hello all, This is a second post on money. I will just keep this to the last post, as money and business is usually not a very popular question for students attempting the A level paper. Take a look at some of the guiding questions in order to understand why I have selected these facts. […]

#### Fun Facts #1 Money

Dear Readers, Our next series will be on money. This is to help you for the GP topic on money and business. Take a look at them, have some fun and learn something new. #1: If you have 75 trillion is in circulation in the world, if we were to distribute this amount, each person […]

#### List of Great and Helpful Math Articles

Here is a compilation of all the Math articles/ opinions KS has done. Students should read them when they are free to improve their mathematics skills. They will come in handy! 🙂 For ease of navigation, some bigger topics sorted according to topics. Trigonometry Integrations Permutations & Combinations (Combinatorics) Vectors Complex Numbers APGP, Sequences & […]

#### Fun facts #4 Women

Dear Readers, This will be the last series about fun facts for women. I’m sure you are getting bored with this series, we will be moving on to the next one soon! #1: only 2% of the women consider themselves as beautiful. (what does this say about the media portrayal of women? Does it have […]

#### Fun Facts #3 Women

For this series of fun facts for women, you can take a look at these examples and use them in a sports essay, gender and even prejudice and discrimination essays. #1: Women were first allowed to participate in the Olympics Games in 1900. #2: Iran recently held its first marathon, but women were excluded from […]

#### Fun Facts #2 Women

Dear Readers, This is a continuation of our fun facts on women. You can use the examples provided here for your essay topics of gender; prejudice and discrimination. #1: Every 90 sec, one woman dies during pregnancy or childbirth. (what does this say about healthcare in the world?) #2: All of the 20 richest women […]

#### Python related articles

Here is a compilation of all the Python articles KS has done. Students should read them when they are free to improve their mathematics skills. They will come in handy! 🙂 Learning Python #1 Learning Python #2 Python Codes

#### APGP, Sequence & Series related articles

Here is a compilation of all the APGP, Sequence & Series articles KS has done. Students should read them when they are free to improve their mathematics skills. They will come in handy! 🙂 1. Will it ever converge? 2. Intuition of Mathematical Induction 3. Things you might want to know when making a conjecture

#### Statistics related articles

Here is a compilation of all the Statistics articles KS has done. Students should read them when they are free to improve their mathematics skills. They will come in handy! 🙂 1. What does unbiased in Math mean? 2. What is r-value? 3. Why is the r-value independent of translation and scaling? #1 4. Why […]

#### Complex Numbers related articles

Here is a compilation of all the Complex Numbers articles KS has done. Students should read them when they are free to improve their mathematics skills. They will come in handy! 🙂 1. Scary Complex Numbers 2. Cool trick to solve questions in polar form. 3. Brute forcing simultaneous equations involving Complex Numbers 4. Deriving […]

#### Integration related articles

Here is a compilation of all the Integration articles KS has done. Students should read them when they are free to improve their mathematics skills. They will come in handy! 🙂 1. Integrating Trigonometric Functions (1) 2. Integrating Trigonometric Functions (2) 3. Integrating Trigonometric Functions (3) 4. Integrating Trigonometric Functions (4) 5. Integrating Trigonometric Functions […]

#### Vectors related articles

Here is a compilation of all the Vectors articles KS has done. Students should read them when they are free to improve their mathematics skills. They will come in handy! 🙂 1. To Draw or Not to Draw? 2. Cross vs. Dot Product 3. Finding area of quadrilateral in vectors

#### Challenging A’levels Questions

Below is a list of questions that students should take note of! The questions are not there due to copyright issues. But linked are the suggested solutions by KS. 🙂 2016 P1: 3, 10, 11 2016 P2: 4b 2015 P1: 3, 9 2015 P2: 9, 11 2014 P1: 3, 7, 9 2014 P2: 1, 4, […]

#### Brute forcing simultaneous equations involving Complex Numbers

So I have many students coming up to me and saying, “Mr Teng, How do you know which to substitute away or when to introduce when doing simultaneous equations for complex numbers?” Here is a lesser method that will give you the answers. It is definitely a clearer method that involves less pitfalls. This method […]

#### Combinatorics related articles

Here is a compilation of all the Combinatorics articles KS has done. Students should read them when they are free to improve their mathematics skills. They will come in handy! 🙂 1. Why is 0! = 1? 2. The Birthday Paradox

#### Trigonometric related articles

Here is a compilation of all the trigonometry articles KS has done. Students should read them when they are free to improve their mathematics skills. They will come in handy! 🙂 1. How to derive the sum to produce formula 2. Integrating Trigonometric Functions (1) 3. Integrating Trigonometric Functions (2) 4. Integrating Trigonometric Functions (3) […]

#### Science versus Arts – which is better?

Science Versus Arts- Which is more useful/valuable to society? In pragmatic and materialistic Singapore, science subjects have always taken a greater prominence and value in our society. Science subjects are seen to be able to offer one a better standard of living compared to popular belief that arts subjects are unable to accord one a […]

#### 2010 A-level H2 Mathematics (9740) Paper 1 Question 11 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. KS Comments:

#### 2010 A-level H2 Mathematics (9740) Paper 1 Question 10 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. (i) Direction vector of Normal vector of Since is parallel to the normal vector of is perpendicular to . (ii) Point of intersection . (iii) — (1) — (2) — (3) Since satisfies all 3 equations, […]

#### 2010 A-level H2 Mathematics (9740) Paper 1 Question 9 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. Total Volume Total Surface Area, Thus, gives a minimum total surface area. (ii) (iii) (iv) If the box has square ends, then KS Comments:

#### 2010 A-level H2 Mathematics (9740) Paper 1 Question 8 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. (i) (ii) (iii) (iv) From (iii) Since Thus, locus meets the positive real axis when x=2. KS Comments: The first two parts requires both students to be able to apply your knowledge of complex numbers formulas, […]

#### 2010 A-level H2 Mathematics (9740) Paper 1 Question 7 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. where k is a positive constant. When Since When When KS Comments: Not a tough question, just be care when you draw the graph, consider only the positive t values. Students can omit the module too […]

#### 2010 A-level H2 Mathematics (9740) Paper 1 Question 6 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. (i) Using GC, (ii) Using GC, Area (iii) Area (iv) Thus, KS Comments: Take note to give (i) to 3 decimal places! For (iii), students can use GC to check their answers too! (iv), Students might […]

#### 2010 A-level H2 Mathematics (9740) Paper 1 Question 5 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. (i) When When Coordinates are (ii) KS Comments: Some students wasted time to find the expression , which shows they have poor knowledge. Students should label the axial intercepts coordinates, .

#### 2010 A-level H2 Mathematics (9740) Paper 1 Question 4 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. (i) Differentiating the given equation by , (ii) Tangent parallel to x-axis Then, Therefore, coordinates are and . KS Comments: Quite straight forward with the implicit differentiations at (i). Students should understand what it means when […]

#### 2010 A-level H2 Mathematics (9740) Paper 1 Question 3 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. (i) (ii) KS Comments: Formulas!!! Every simple questions involving formulas!

#### 2010 A-level H2 Mathematics (9740) Paper 1 Question 2 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. (i) (ii) Since the first two terms are equal, Third term KS Comments: Students should know how to find coefficient of terms efficiently. Refer here if they don’t. This is rather simple since they only expect […]

#### 2010 A-level H2 Mathematics (9740) Paper 1 Question 1 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. (i) Since since (ii) since KS Comments: A very straight forward question coming out of Vectors I. Students should be well versed with the expansions.

#### 2010 A-level H2 Mathematics (9740) Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. Please kindly comment at the specific questions should you have any questions.

#### Question of the Day #17

This is a pretty cool and interesting question from AMC. There are four lifts in a building. Each makes three stops, which do not have to be on consecutive floors on include the ground floor. For any two floors, there is at least one lift which stops on both of them. What is the maximum […]

#### List of Great and Helpful GP Articles

Here is a compilation of great articles. Interpreting GP essay Questions How to write a good essay Introduction? How to craft a good essay body paragraph? How to write a good essay conclusion? How to write an essay that will get you an A? How to tackle GP Summary (1) How to tackle GP Summary […]

#### The Value of Arts

Dear Readers, Here’s some lessons on the arts. You may use them for your arts essay in General Paper. 10 LESSONS THAT THE ARTS TEACH 1. The arts teach children to make good judgments about qualitative relationships. Unlike much of the curriculum in which correct answers and rules prevail, in the arts, it is judgment […]

#### Question of the Day #15

This question was sent in by a student, which I think is rather interesting given 2015 A’levels P1 Q3 had something similar. Use a definite integral to evaluate , given your answer correct to 5 decimal places. Hint: Recall that the sum of area under the graph can be found using integration.

#### Fun Facts about Women (Gender topic)

Dear Readers, We will be starting a series of Fun facts weekly on various topics, to help you for your examples in your exams. We have come to realize that many students lack specific examples to support their arguments in their essays, and our job is to help you out in your revision process! For […]

#### Question of the Day #14

All possible straight lines joining the vertices of a cube with mid-points of its edges are drawn. At how many points inside the cube do two or more of these lines meet?

#### JC2 Statistics 2016

Most JCs by now should be embarking on their Statistics Journey. I know a school that is finishing up really fast, and I think they will easily finish the syllabus by May. So I notice many students are thrown off the track with Statistics. It is slightly out of their comfort zone, especially Permutation and […]

#### AHOY! The Pirate Story Solution

So I posted up a question titled “AHOY! The Pirate Story Problem” which can be found here. Here is the solution! We begin with a more intuitive idea. Consider only 2 pirates. Pirate 2 can easily propose that he gets all the 100 gold coins. Since he constitutes 50% of the pirates (his vote will […]

#### Question of the Day #13

A student asked me this question recently. I think this is from AMC. There are 42 points placed on a straight line so that each distance from to is where . What is the sum of the distances between every pair of these points? Note: EVERY PAIR.

#### ‘The world would be a better place if more political leaders were women.’ What is your view?

‘The world would be a better place if more political leaders were women.’ What is your view? Question Analysis: Female stereotype- more emotional; more nurturing and caring Male stereotype: Stronger; more aggressive to push through policies; less emotional Better place- economic prosperity; technological advancement; greater peace and prosperity for all; increased medical advancement to ensure […]

#### 2002 A-level H2 Mathematics Paper 2 Question 30 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. (a) (i) Alternatively, (ii) When , required probability (b) Key GC with either sequence or use table functions. We want to solve Plot and check for the x that gives a corresponding value that is less […]

#### 2010 A-level H2 Mathematics (9740) Paper 2 Question 7 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. (i) (ii) (iii) P(B’|A) (iv) since A and C are independent (v)

#### 2015 A-level H2 Mathematics (9740) Paper 2 Question 12 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. (i) Let X and Y denote the mass of a apple and pear in grams respectively. (3 SF) (ii) (3 SF) (iii) Let A and B denote the mass of a peeled apple and peeled pear […]

#### 2015 A-level H2 Mathematics (9740) Paper 2 Question 11 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. (i) Number of ways ways (ii) Number of ways ways (iii) Number of ways ways (iv) Case 1: 2 A’s together and B’s separated Case 2: 2 B’s together and A’s separated Case 3: 2 A’s […]

#### 2015 A-level H2 Mathematics (9740) Paper 2 Question 10 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. (i) Graph to be inserted (ii) (a) (4 DP) (b) (4 DP) (c) (4 DP) (iii) Using GC, (3 SF) (iv) (3 SF)

#### 2015 A-level H2 Mathematics (9740) Paper 2 Question 9 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. (i) since A and B are independent. (ii) (iii) If , (maximum) If , (minimum)

#### 2015 A-level H2 Mathematics (9740) Paper 2 Question 8 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. Let X denote the mass of pineapple tarts and denote the population mean mass of pineapple tarts. Unbiased estimate of population mean = 0.8825 (3 SF) Under Test Statistic, at 10% level of significance. Using GC, […]

#### 2015 A-level H2 Mathematics (9740) Paper 2 Question 7 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. (i) Firstly, the average number of errors per page is constant. Secondly, the number of errors in a page is independent of the number of errors in another page. (ii) Let X denote the number of […]

#### 2015 A-level H2 Mathematics (9740) Paper 2 Question 6 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. (i) Let X denote the number of red sweets in a small packet of 10 sweets. (3 SF) (ii) Let Y denote the number of red sweets in a large packet of 100 sweets. Since n […]

#### 2015 A-level H2 Mathematics (9740) Paper 2 Question 5 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. (i) Manager is unable to obtain an appropriate sampling frame. (ii) Manager can consider taking equal number of respondents from adults and aged first. Then, he can stand outside the supermarket, interview whoever walks in, based […]

#### 2015 A-level H2 Mathematics (9740) Paper 2 Question 4 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. (a) Let P(n) be the statement When n=1, LHS RHS Since LHS = RHS, P(1) is true. Assume P(k) is true for some k, Want to show P(k+1) is true, LHS = RHS Since P(1) is […]

#### 2015 A-level H2 Mathematics (9740) Paper 2 Question 3 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. (a) (i) for all Since is increasing function, it has no turning points, f is 1-1, its inverse will exist. (a) (ii) Let Reject since (b) Let We need for all real values of g.

#### 2015 A-level H2 Mathematics (9740) Paper 2 Question 2 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. (i) (ii) Let be point on L that makes from P. for some So when , L is minimum. (iii) KS Comments:

#### 2015 A-level H2 Mathematics (9740) Paper 2 Question 1 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. (i) (ii) When When years. KS Comments: Straightforward question.

#### 2011 A-level H2 Mathematics (9740) Paper 2 Question 9 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. (i) (a) P(faulty) = P(made by A and faulty) + P(made by B and faulty) = 0.6(0.05) + 0.4(0.07) = 0.058 (b) P(made by A | faulty) = = = (ii) (a) P(exactly one of them […]

#### GP Crash Course

Dear all faithful readers of Theculture, We are pleased to announce that we will be having a General Paper Crash Course this coming May to help you better prepare for your upcoming Mid-year Exams and A levels. To better cater to students who may be having exams before or after the June holidays, we will […]

#### AHOY! The Pirate Story Problem

So here is an interesting question. This actually appeared in a job interview at Google too. 🙂 So give it a shot if you’re keen. There are many ways to solve this, one can solve it mathematically using optimisation, or using Game Theory’s Backward Induction. There are five pirates who have to split 100 gold […]

#### Question of the Day #7

$latex \int \frac{1}{\sqrt{3x+4} - \sqrt{3x+1}}dx$ Answer$latex \frac{2}{27}[(3x+4)^{\frac{3}{2}} + (3x+1)^{\frac{3}{2}}] + C$

#### Question of the Day #6

$latex \int \frac{1 + e^x}{1 - e^x}dx$ Answer$latex -2 \mathrm{ln}|e^{-\frac{x}{2}} - e^{\frac{x}{2}}| + C$

#### To what extent is it possible to make the punishment fit the crime?

To what extent is it possible to make the punishment fit the crime? This question is on the topic Crime and Punishment, and this is a pretty simple question for the A levels. Students need to be aware of the different goals of punishment such as for retribution, reformation and in extreme situations to incapacitate […]

#### Question of the Day #5

$latex \int e^x \frac{x^2 + 1}{(x+1)^2} dx$ Answer$latex e^x - 2 \frac{e^x}{x+1} + C$

#### Question of the Day #4

$latex \int \frac{1}{(3\mathrm{sin} 2 \theta - 4\mathrm{cos} 2 \theta)} dx$ Answer$latex \frac{1}{10}\mathrm{ln}|\mathrm{cosec}u - \mathrm{cot}u| + C$

#### Question of the Day #3

$latex \int \frac{\mathrm{sec}x}{\mathrm{ln}(\mathrm{sec}x + \mathrm{tan}x)} dx$ Answer$latex \mathrm{ln}|\mathrm{ln}(\mathrm{sec}x + \mathrm{tan}x| + C$

#### Question of the Day #2

$latex \int {\mathrm{tan}}^4 x dx$ Answer$latex \frac{1}{3} {\mathrm{tan}}^3 x - \mathrm{tan}x + x + C$

#### Question of the Day #1

So it was suggested in class that I start a little Integration of the Day thing, so students can have practice. We might just change the topic a bit, but for the time being, let’s stick with Integration.

#### Differential Equations Problem #1

To solve a DE with substitution, we first observe that we are given an equation with and variables, that is then we introduce . Here, our intention is to remove our variables and replace it with instead. So we should proceed to find . Since , we have that . All we need to do […]

#### All the best for your results!

All of us from theculture.sg would like to wish all the readers or ex-students the best of luck to the release of A’levels results 2015! Enjoy the open houses and do read up a bit on all the available university courses. Narrow some choices down and clear up as much doubts during the open houses […]

#### Consider the view that spoken language is more important than the written form.

Consider the view that spoken language is more important than the written form. This is one of the easier questions to attempt for this year, as it is just a simple comparison between the spoken language and the written form. So what are some of the benefits of the spoken language? We are able to […]

#### Why should we be concerned with current affairs when most of them will soon be forgotten?

Why should we be concerned with current affairs when most of them will soon be forgotten? This question requires students to think and assess about the importance of current affairs – whether there is any point in knowing and even being affected by them since these news will be outdated soon. After all, we live […]

#### A’levels Results 2015

It is FINALLY here! The day that students have been patiently expecting is fixed on 4 March 2016, a week from now. Link All the best too all the readers and my students for your results! A food for thought for all students: courses you need to apply for. Students can check up the indicative […]

#### How far, in your society, should unpopular views be open to discussion?

How far, in your society, should unpopular views be open to discussion? Students should consider whether it is possible to censor off these unpopular views given how advanced technology is nowadays. Even if it is possible for the state to monitor and censor off these views, it is going to be a very tedious process […]

#### Education should only be concerned with what is useful in life. Discuss.

Education should only be concerned with what is useful in life. Discuss. I would expect that this is a very popular examination question for this year. Education has always been a favourite topic for the cohort. Define terms Education: seen as a route to have a better life, to make more money. Usually Asian parents […]

#### How far is increased prosperity for all a realistic goal in your society?

How far is increased prosperity for all a realistic goal in your society? For the examination of this question, students will have to consider 3 main points: increased prosperity, realistic, your society (Singapore context). Students should also note that there is an absolute term “for all” which has to be carefully considered and evaluated at the […]

#### 2013 A levels H1 General Paper (8807) Paper 1 Suggested Solutions

For the benefit of our students and their revision, here’s the questions for the 2013 paper. Stay tune for our short outlines on these questions. The aim of our outlines is to create discussions online on possible arguments or perspectives on the questions. Feel free to comment on these questions when we have them up. […]

#### 2014 A levels H1 General Paper (8807) Paper 1 Suggested Solutions

For the benefit of our students and their revision, here’s the questions for the 2014 paper. Stay tune for our short outlines on these questions. The aim of our outlines is to create discussions online on possible arguments or perspectives on the questions. Feel free to comment on these questions when we have them up. […]

#### 2016 A’levels Timetable

So on the last day of CNY, SEAB announced the A’levels 2016 timetable! Below is the link. 2016 A’levels Timetable A little note: Students should take note that BOTH H2 Mathematics Paper will be a MORNING paper. So if you aren’t so much of a morning person, then you need to start doing Mathematics in […]

#### Integrating Trigonometric Functions

Trigonometric functions can be difficult to handle. So here is some intuition and idea on what to do when dealing with certain trigonometric functions. Integrating Trigonometric Function #1 Integrating Trigonometric Function #2 Integrating Trigonometric Function #3 Integrating Trigonometric Function #4 Integrating Trigonometric Function #5

#### Financial Engineering (I)

Before attempting to read what we have here, students should revise their basic probability and linear algebra first. Financial Engineering (I) #1 – Overview Financial Engineering (I) #2 – Introduction to No Arbitrage Financial Engineering (I) #3 – Interest rates and fixed income instruments Financial Engineering (I) #4 – Floating Rate Bonds and Term Structure […]

#### Welcome J1 to your new academic life 🙂

We at The Culture have been receiving calls recently since the start of the J1 orientation program about our tuition program. This post is a shoutout to those students who are interested in the services that we provide. Currently, all tutors of The Culture are working only with Newton Apple Learning Hub @ Jurong East […]

#### Arithmetic Problem #7

I came across this interesting algebra/ arithmetic problem the other day. … Do you think this will always work? Hint: We can use algebra to prove this cool sequence easily. Arithmetic Problem #7 Arithmetic Problem #6 Arithmetic Problem #5 Arithmetic Problem #4 Arithmetic Problem #3 Arithmetic Problem #2 Arithmetic Problem #1

#### Geometric Brownian Motion

This is really important for anyone interested in Finance Modelling. As what the movie Wolf on Wall Street says: They are referring to a geometric brownian motion. Firstly, we will begin with the definitions. We say that a random process, , is a geometric Brownian motion (GBM) if for all where is a Standard Brownian […]

#### Complex Number Problem #2

Show that . Hence show that For the first part, we can simply apply Euler’s Formula, that is The next part is a little more tricky, and since its hence, we will use what we solved previously to help us. Just for fun… Complex Number Problem #1

#### Introduction to Brownian Motion

Lets look at brownian motion now. And yes, its the same as what our high school teachers taught about the particles moving in random motion. Here, we attempt to give it a proper structure and definition to work with. A Brownian Motion is a random process with parameters if For , are mutually independent. This […]

#### Sampling & Survey # 9 – Regression Estimation

Today, we shall look at regression estimation. We will begin by looking at the usual & simple straight line regression model: . Let and by the ordinary least squares (OLS) regression coefficients of the slope and intercept. = = Precision is increase, that is Different estimators for population total We conclude here by observing that […]

#### Review of Basic Probability

So I understand that I lost many readers for the Sampling uploads.It is a bit difficult to the intensive use of notations and also the need for statistics knowledge. So here I’ll review a bit of basic probability. The contents here will be basic, and will involve some H2 Mathematics Statistics too. Discrete Random Variables […]

#### Sampling & Survey (Home)

Sampling & Survey #1 – Introduction Sampling & Survey #2 – Simple Probability Samples Sampling & Survey #3 – Simple Random Sampling Sampling & Survey #4 – Qualities of estimator in SRS Sampling & Survey #5 – Sampling weight, Confidence Interval and sample size in SRS Sampling & Survey #6 – Systematic Sampling Sampling & […]

#### Introduction to Martingales

This is a rather important topics for anyone interested in doing Finance. Lets look at their definition first. A Martingale is a random process with respect to the information filtration and the probability distribution , if for all for all Martingales are used widely and one example is to model fair games, thus it has […]

#### Sampling & Survey # 8 – Ratio Estimation

So last time we saw STR and here is a quick recap. Set the stratification scheme Set the stratum design Implement the sampling methods for each stratum independently Pool the strum estimates to estimate the population parameters Estimate their respective variances Construct CI, if necessary. Today, we look at ratio estimation. For starters, we will […]

#### Multivariate Distributions

Let be an n-dimensional vector of random variables. For all , the joint cumulative distribution function of X satisfies Clearly it is straightforward to generalise the previous definition to join marginal distributions. For example, the join marginal distribution of and satisfies If and is a partition of X then the conditional CDF of X_2 given […]

#### Some things that JC students should know.

In all these years of teaching, I realised that many JC students still do not know a handful of things. So I will list down a few random ones that I can recall off-hand, and of course expand a lot the way. You have MF26 formula booklet given. It contains your double angle formulas, some […]

#### Conditional Expectations and Variances

Here we look at an important concept that is an extension from Bayes Theorem, which we discussed briefly. The condition expectation identity says The condition variance identity says Here both and are both functions of Y and are therefore random variables themselves. With this, we start by considering a random sum of random variables. Let […]

#### Problem of Over-generalization in General Paper

Problem of Over-generalization in General Paper “Women are always subservient to men.” “Everyone uses Instagram nowadays.” These statements are glaring examples of over-generalization that are often too frequent in students’ essays. What is wrong with these statements? Well, to say that these statements are accurate would be akin to committing a crime for General Paper […]

#### Sampling & Survey #7 – Stratified Sampling

SRS form the basis of sampling and survey methods as it is easy to design and analyse, but it is rarely the best design. We may adopt systematic sampling or cluster sampling but we often are limited by the availability of sampling from. Thus, we need to look at stratified sampling to increase the precision. […]

#### Continuous Random Variables

We look at the definitions first. A continuous random variable, X, has a probability density function (PDF), if and for all events A The CDF and PDF are related by It is good to know that we have We X has a normal distribution, , and . And while We also have the log-normal distribution, […]

#### O’levels Results 2016!

All of us wish the students receiving the O’levels Results 2016 the best! And do not let grades define you. 🙂 If you’re keen to meet up with us for the JC Talk, you may contact Newtonapple Learning Hub at +65 9222 3423 for more details. This talk will be opened freely to the public […]

#### Financial Engineering (I) #2 – Introduction to No Arbitrage

Consider the following contract 1. Pay the price p at t=0. 2. Receive at time t=k, k = 1, …, T *Cash flow can be negative So what does the above contract mean? One pays a price p at time in order to receive this contract and get this cash flow. Thus at , and […]

#### Discrete Random Variables

As usual, definitions first. The cumulative distribution function (CDF), of a random variable, X, is defined by A discrete random variable, X, has probability mass function (PMF), , if and for all events A we have The expected value of a discrete random variable, X is given by The variance of an random variable, X, […]

#### Sampling & Survey #6 – Systematic Sampling

For today, it is going to be a short and simple session on Systematic Sampling, We can effectively consider systematic sampling as a proxy for simple random sampling. We start by taking (rounding up, if necessary), then draw a random number R from 1 to k. Then proceed to draw a systematic sample in periodic […]

#### 30 Free Awesome Resources for Students

New year, new you. Be ready to tackle on the new academic year with these awesome resources curated by Donut.sg You’re welcome. Did we miss anything out? Let us know by leaving a comment below.

#### New Year, New Syllabus!

Happy 2016 to everyone! I’ve a really exciting news to share now with regards to H2 Mathematics. As I mentioned in a post before, I felt that the current H2 Mathematics can do some upgrading. And yes, the long wait is over, the new syllabus is here. Brace yourself JC1 of 2016 (especially those receiving […]

#### H2 Math Thur 5pm

This page contains all questions and answers asked by students from this class. The most recent questions will be at the top. MF26

#### H2 Math Tue 7pm

This page contains all questions and answers asked by students from this class. The most recent questions will be at the top. MF26 10. (i) 11. (i) Since P is on l, for some t perpendicular to l

#### H2 Math Tue 5pm

This page contains all questions and answers asked by students from this class. The most recent questions will be at the top. MF26 Differentiate with respect to t. Substitute into given differential equation, Since Using the product to sum formula as shown here, we have Note: and — (1) — (2) — (3) Using GC, […]

#### H2 Math Mon 430pm

This page contains all questions and answers asked by students from this class. The most recent questions will be at the top. MF26

#### H2 Math Sun 2pm

This page contains all questions and answers asked by students from this class. The most recent questions will be at the top. MF26 … Since the is a constant, the series convergences. The sum to infinity Let denote the term of the AP. Since they are consecutive terms of a GP, , thus its not […]

#### H2 Math Sun 1130am

This page contains all questions and answers asked by students from this class. The most recent questions will be at the top. MF26 Vectors Q7 [Homework] (i) Using ratio theorem, Since is perpendicular to (ii) To be a parallelogram, (iii) Let Since — (1) — (2) Solving, Vectors Q8 [Homework] (i) (ii) Let R be […]

#### H2 Math Sun 930am

This page contains all questions and answers asked by students from this class. The most recent questions will be at the top. MF26 Vectors Q7 [Homework] (i) Using ratio theorem, Since is perpendicular to (ii) To be a parallelogram, (iii) Let Since — (1) — (2) Solving, Vectors Q8 [Homework] (i) (ii) Let R be […]

#### H2 Math Sat 330pm

This page contains all questions and answers asked by students/ discussions from this class. The most recent questions will be at the top. MF26 Recall the If the angle is obtuse , then . Thus, Vectors Q7 [Homework] (i) Using ratio theorem, Since is perpendicular to (ii) To be a parallelogram, (iii) Let Since — […]

#### Class Q&A

The following contains questions that students from each class asked. Feel free to discuss further. It is not a tuition schedule, just a mode of communication. H2 Math Sat 130pm H2 Math Sat 330pm H2 Math Sun 930am H2 Math Sun 1130am H2 Math Sun 2pm H2 Math Mon 2pm H2 Math Mon 430pm H2 […]

#### Financial Engineering (I) #1 – Overview

As some of you observe, I’ve been posting a handful of undergraduate and postgraduate materials or courses here. Some close students also asked me to share more on financial engineering. So here, I’ll start on a simple series on Financial Engineering, and will finish up the analytics materials before I finish this definitely. I’m quite […]

#### H2 Math Sat 130pm

This page contains all questions and answers asked by students from this class. The most recent questions will be at the top. MF26 We have that or or This is a worksheet from class. There is a slight typo, we need to show that So for all proof/ show questions, it is important that we […]

#### H2 Math Mon 730pm

This page contains all questions and answers asked by students from this class. The most recent questions will be at the top. MF26 Vectors Q7 [Homework] (i) Using ratio theorem, Since is perpendicular to (ii) To be a parallelogram, (iii) Let Since — (1) — (2) Solving, Vectors Q8 [Homework] (i) (ii) Let R be […]

#### H2 Math Mon 2pm

#### Sampling & Survey #5 – Sampling weight, Confidence Interval and sample size in SRS

So let us now continue study SRS. Recall in part 3, we introduced the idea of unit inclusion probability. Subsequently, we introduced , which is the sampling weight. The sampling weight of unit i can be interpreted as the number of population units represented by unit i. It is the reciprocal of the inclusion probability […]

#### Happy Holidays!

Merry Christmas and Happy New Year to all the visitors! Thanks for following or reading. 🙂 Personally, Mr Teng has been really busy pursuing his personal interests. On a side note, I thought of sharing this link with fellow readers, be it current or ex students who are interested in Mathematics! Good news, cos Springer […]

#### Sampling & Survey #4 – Qualities of estimator in SRS

So we formally introduced the estimators used in SRS previously. Now, we are interested in how good our estimators are, and if you recall, by good, I refer to accuracy (MSE), Precision (Variance) & Bias (Expectation). Let us look at these qualities of our estimators now. Estimator of population mean – Unbiased, this implies that […]

#### Number Theory Question #1

So here is a cheeky question with regards to cryptography, its the basis of public key encryption in Cryptography. I had a student asked about cryptography once, its a really interesting and exciting field. Many students who watched the Imitation Game, should be greatly intrigued by it. 🙂 So here is the question What is […]

#### Sampling & Survey #3 – Simple Random Sampling

Today we shall look at the first sampling method we introduced: Simple Random Sampling. Recall that we mentioned that this is the most basic form of probability sampling since it provides the theoretical basis for the more complicated forms. Here we will look at how to select a simple random sample (SRS) and also estimate […]

#### Sampling & Survey #2 – Simple Probability Samples

So recall that we are interested on the statistical aspects of taking and analysing a sample, and a good sample will be representative in the sense that characteristics of interest in the population can be estimated form the sample with a known degree of accuracy. Here, we will use Probability Sampling to conduct surveys. Probability […]

#### Customer Analytics #1 – Introduction

I’ll dive straight into what is customer analytics using an example. Consider that Pixar calls me and says about a Disney film, that they want to for instance, predict how many people are going to watch Inside Out in every state of United States. This is a really interesting problem, but this isn’t customer analytics. […]

#### Vectors Question #1

Since I’m at the topic of Vectors for most of my JC1 classes, I thought I share an interesting question regarding it. Yes, some students do tell me the questions aren’t really A’levels, but I think it does make you think and this is very important in learning. Question: Can you place 5 points in […]

#### Sampling & Survey #1 – Introduction

This is a new series (this is essentially post-graduate materials, meaning you need strong statistical background at university level) on Sampling and Survey. I know many JC students will think, I thought its just a simple 2-4 marks questions in A-levels. You are correct, but here, i’ll concentrate on the statistical aspects of taking and […]

#### Application Question (Philosophy)

The Application Question (AQ) has always been a struggle for many students who were first introduced to this in J1. Many students perhaps accustomed to scoring 2-3 marks for this section (out of 10 marks) have given up on it totally from what I have heard. As such, this post is to dispel the belief […]

#### Types of Science and Technology Questions

Science and Technology has always been a popular topic among students taking the A levels. Students always think that they know a lot about this topic given their association with technology on a day to day basis but do they really? As recent trends in the A levels have shown, Science and Technology questions are […]

#### Algebra Question #1

Here is a simple and interesting algebra question for the weekend and to chase the monday blues away 🙂 Suppose How many possible pairs of m & n are there?

#### Python Codes

The following is a collection of simple codes I wrote for Python while doing a Rice University Course on Coursera. 🙂 Rock, Paper, Scissors, Spock Guess The Number Game Stopwatch: The Game Pong Memory Blackjack Spaceship Ricerocks!(Asteroids) Will upload more if I do some more interesting ones. 🙂

#### 2015 A Level H1 Chemistry (8872) Paper 1 Suggested Solutions

All solutions here are SUGGESTED. Mr. Lee will hold no liability for any errors. Comments are entirely personal opinions. Many thanks to the student who sent us the question paper. 🙂 You can post any questions regarding the answers but please do not ask me how many marks to secure an A for the […]

#### 2015 A Level H2 Chemistry (9647) Paper 1 Suggested Solutions

All solutions here are SUGGESTED. Mr. Lee will hold no liability for any errors. Comments are entirely personal opinions. Question 1: B The element must be from Group IV so the electronic configuration must be either 1s22s22p2 or 1s22s22p63s23p2. The four electrons of highest energy refer to the electrons at shells with higher principal […]

#### Why study Mathematics?

So the A’levels is coming to an end. Good job to all the JC2s! I did receive a few questions on studying Mathematics at undergraduate level. So I thought the following article might just answer it. https://plus.maths.org/content/how-maths-can-make-you-rich-and-famous A few (living) mathematicians you can google are, Jim Simons, Edward Thorp and James Stewart too. The article […]

#### 2015 A Level H2 Physics (9646) Paper 1 Suggested Solutions

All solutions here are SUGGESTED. Casey will hold no liability for any errors. Comments are entirely personal opinions. 1.A 2.D 3.C 4.A 5.C 6.A 7.D 8.C 9.A 10.C 11.B 12.A 13.D 14.A 15.A 16.A 17.C 18.A/ C ;I am not sure of Q18 though. Cos in reality, there is a phase change of pi on […]

#### 2015 A Level H2 Chemistry (9647) Paper 3 Suggested Solutions

All solutions here are SUGGESTED. Mr. Lee will hold no liability for any errors. Comments are entirely personal opinions. [Please do not ask me how many marks for A. The bell curve is something that is out of your control so there is no point in estimating your grade based on the number of marks […]

#### Game Theory #2

To illustrate another similar example from last post, now supposed ALL the A-level Candidates met up in the town square. Prior to meeting up, they were all told by the head examiner that if everyone gets the same grade, all of you get an A. Else, the highest will have an A while the rest […]

#### Game Theory #1

Over the past two months, I’ve been reading up on Game Theory extensively. It has always been a subject of interest for me since undergraduate days. And I’m glad that I found time to read a bit on it. Students that are keen, can also follow the open courseware provided by Yale University for free. […]

#### 2015 O Level Chemistry (5073) Paper 1 Suggested Solutions

For those of you who just completed your GCE O Level Chemistry (5073) Paper 1, here are the suggested answers for the 40 MCQ questions. The paper was relatively straightforward so I hope that everyone is careful in answering the questions and you did not make careless mistakes. A good MCQ score is 38/40 if you […]

#### Importance of Mathematics in Finance

Students over the years do ask me, why do I take Mathematics? Like whats the use other than becoming a teacher. So here is a video with Jim Simons. In this interview, he shares how he cracked wall street. Mathematics is being used widely in the world. And in this video, Jim Simons shared how […]

#### Functions Questions #2

I am currently thinking of how to solve this following question, and will encourage any undergraduates to discuss this problem together. I’ll share a bit of what I’ve thought. If is a bijective function that satisfies and , what is the minimum value of So here the definition of means that is an automorphism of […]

#### Integration Question #2

I came across the integral a few days ago. Pretty interesting, many ways to solve this integral, be it graphically or by substitution. ? Answer: Hint: Consider the graph of , it should give a semicircle which centre is

#### Post- 2015 H2 Mathematics Paper 1 Thoughts

Easier than 2014. Tricky. Very tricky. Tedious. When I did it, it felt a bit like a AJC paper slightly, so I believe AJC students might find the paper quite comfortable. Paper is not super conceptual. Highlights: Question 3 which test students on the definition of integration, not a difficult question, but some may struggle […]

#### “Human actions should be based on scientific fact, not religious faith.” How far do you agree with this statement?

“Human actions should be based on scientific fact, not religious faith.” How far do you agree with this statement? Define Scientific fact- based on logic, rational, proven Religious faith- spiritual belief, morality guides actions Human actions- developments in science and technology, business decisions, personal decisions in our lives This question requires students to discuss if […]

#### When a government’s finances for social welfare are limited, should they be directed towards the young or the old?

When a government’s finances for social welfare are limited, should they be directed towards the young or the old? This question requires students to understand that all governments have limited funds for social spending and there is a need for governments to decide if more funds should be directed towards the young or the old. […]

#### “Parents have no right to impose their own values and beliefs on their children.” Discuss.

“Parents have no right to impose their own values and beliefs on their children.” Discuss. Define Impose- to force; dictate Values and beliefs- religion, sexual orientation, lifestyle etc This question wants students to discuss whether parents have the right and authority to impose their own lifestyles and values on their children, just because they […]

#### How effectively is public health promoted and managed in your society?

How effectively is public health promoted and managed in your society? Define Effectively- What is effective? To decide if something is effective, one has to measure the results against the intended objective. In this case, what is the state’s objective with regards to public health? Promoted- to raise awareness about public health Managed- suggests […]

#### A little on bell curve

Since many students were asking, I thought I’ll roughly explain the bell curve and its distribution properties. Before that, I thought I should mention that I’m not really sure myself if Private Candidates and School Candidates share a different bell curve. I doubt so, since all take the same subject code, there should be no […]

#### 2015 A-level H2 Mathematics (9740) Paper 2 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions.

#### “No cause is ever worth dying for.” Discuss

“No cause is ever worth dying for.” Discuss Define Cause- fighting for freedom, ideologies, rights, status, wealth, power etc Dying- Can interpret in both the literal and metaphorical manner. What exactly can constitute dying in the metaphorical manner? Dying in the sense of not living the life that an individual desires and wants? This question […]

#### 2015 A-level H1 Mathematics (8864) Paper Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. Students are highly encouraged to discuss freely for alternative solutions too. I typed this, so pardon me if got errors. There should be a handful of errors as I just type and solve as I go. […]

#### 2015 A-level H2 Mathematics (9740) Paper 1 Question 11 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. (i) (ii) Let (reject since When , using trigonometry identity, we find From For since and for principal values of We have that when , its is a maximum point. (iii) Using GC, Area (iv) At […]

#### Skewes’ Massive Number

Heard of Skewes’ Number? It is the number above which must fail (assuming that the Riemann hypothesis is true), where is the prime counting function and is the logarithmic integral. Isaac Asimov featured the Skewes number in his science fact article “Skewered!”

#### 2015 A-level H2 Mathematics (9740) Paper 1 Question 10 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. (i) (ii) Vol (iii) When When Vol Back to 2015 A-level H2 Mathematics (9740) Paper 1 Suggested Solutions KS Comments:

#### 2015 A-level H2 Mathematics (9740) Paper 1 Question 9 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. (a) For to be purely imaginary, (bi) for (bii) and By Cosine Rule, Back to 2015 A-level H2 Mathematics (9740) Paper 1 Suggested Solutions KS Comments: The first part of the question is rather interesting, since […]

#### 2015 A-level H2 Mathematics (9740) Paper 1 Question 8 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. (i) Let and denote the total time A & B take respectively, in seconds. (ii) (3 SF) (iii) For A: Time taken For B: Time taken Difference (nearest seconds) Back to 2015 A-level H2 Mathematics (9740) […]

#### 2015 A-level H2 Mathematics (9740) Paper 1 Question 7 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. (i) (ii) (iii) At E, Solving with GC, and Back to 2015 A-level H2 Mathematics (9740) Paper 1 Suggested Solutions KS Comments: Students that faced difficulties with ratio (like me) might struggle a bit here. But […]

#### 2015 A-level H2 Mathematics (9740) Paper 1 Question 6 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. (i) From MF15, (ii) Comparing coefficients, Coefficient of Back to 2015 A-level H2 Mathematics (9740) Paper 1 Suggested Solutions KS Comments: Hopefully you didn’t copy the formula wrongly. The next parts, just need to be really […]

#### 2015 A-level H2 Mathematics (9740) Paper 1 Question 5 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. (i) First, translate 3 units in the positive x-direction. Then scale by a factor of units parallel to the y-axis. (ii) (iii) Explanation: Back to 2015 A-level H2 Mathematics (9740) Paper 1 Suggested Solutions KS Comments: […]

#### 2015 A-level H2 Mathematics (9740) Paper 1 Question 4 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. Perimeter Area, Let Since , A is maximum when Back to 2015 A-level H2 Mathematics (9740) Paper 1 Suggested Solutions KS Comments: One important point here is that student must leave the exact answers as it […]

#### 2015 A-level H2 Mathematics (9740) Paper 1 Question 3 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. (i) Width of each rectangle Total area of rectangles When , we have the exact area instead. (ii) where Back to 2015 A-level H2 Mathematics (9740) Paper 1 Suggested Solutions KS Comments: (i) needs some explanations […]

#### 2015 A-level H2 Mathematics (9740) Paper 1 Question 2 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. (i) *please label graph and asymptote clearly. The app I used can’t do it. sorry (ii) Using Graphing Calculator, . (3SF) Back to 2015 A-level H2 Mathematics (9740) Paper 1 Suggested Solutions KS Comments: Students need […]

#### 2015 A-level H2 Mathematics (9740) Paper 1 Question 1 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. (i) At At Using GC, (to 3 decimal place) (ii) Using GC, (to 3 decimal place) (iii) (to 3 sig fig) Back to 2015 A-level H2 Mathematics (9740) Paper 1 Suggested Solutions KS Comments: Students should […]

#### Should there be any controls over the production of energy when the need for it is so great?

Should there be any controls over the production of energy when the need for it is so great? Define Production of energy: refers to the production of petroleum (crude oil), natural gas, coal and other alternatives such as electricity and even nuclear energy etc. Controls- what kinds/methods of controls? Controls over the quantity of production? […]

#### How far is it possible for one country to forgive another for its past actions?

How far is it possible for one country to forgive another for its past actions? Define Past actions: war time atrocities, political feuds, economic conflicts, social and ideological conflicts Forgive: the ability to “forget” and to move on with past historical animosities and collaborate with one another on international matters or even domestic affairs. What […]

#### In your society, how well are the demands of the economy and the environment balanced?

In your society, how well are the demands of the economy and the environment balanced? Define: demands of the economy- increasing productivity for Singaporeans, increasing economic growth of the country, being highly competitive and to have a cutting edge in the global world. This question requires students to consider if there is conflict between environment […]

#### To what extent should the arts in your society focus on local rather than foreign talent?

To what extent should the arts in your society focus on local rather than foreign talent? This question is indeed interesting considering how Singapore has stated her explicit aims of being a global arts hub on one hand, and the recent online Youtube controversy on the other hand about Stephanie Koh proclaiming that she is […]

#### “Books serve little purpose in education as technological developments become more sophisticated.” How far do you agree?

“Books serve little purpose in education as technological developments become more sophisticated.” How far do you agree? Define Sophisticated- to be more complex, challenging, makes learning easier and faster, almost instanteously Technological developments- wiring the world closer together, overload of new information, may lead to information paralysis Little purpose- losing relevance, especially in view of the […]

#### 2015 A’level Suggested Solutions

Congratulations on the completion of A’levels for the 2015 batch! As for those who still, are taking A’levels 2016, we hope you find this site helpful. Read the comments (ignore the trolls who have yet grown up) and learn from our mistakes. It has been a pleasure for all us to interact with you guys. […]

#### Consider the argument that the main purpose of television should be to educate rather than simply to entertain.

Consider the argument that the main purpose of television should be to educate rather than simply to entertain. This is a comparison question on the role of television- whether it should be of an educational role or an entertainment role. So what is exactly an educational or even entertainment role? Define- Educate: to impart values […]

#### “There is no such thing as bad publicity.” To what extent is this true?

“There is no such thing as bad publicity.” To what extent is this true? Define: Bad publicity- negative images and news about an individual and/or company making the headlines repeatedly. It could also possibly refer to controversial news. This phrase is commonly used in by businesses and individuals especially if they want to acquire fame […]

#### 2015 A levels H1 General Paper (8807) Paper 1 Suggested Solutions

As predicted correctly, this year’s paper has a fair mix of topics that we have proudly identified for students! We have kindly highlighted the questions whose topic we have correctly predicted. “There is no such thing as bad publicity.” To what extent is this true? (Media) How far is it possible for one country to […]

#### 2015 A-level H2 Mathematics (9740) Suggested Solutions

All solutions here are SUGGESTED. KS will hold no liability for any errors. Comments are entirely personal opinions.

#### KS’ thoughts on H2 Math 2015

After Christine shared what will likely pop up in the upcoming H1 GP paper, I thought I can share some thoughts too. Just to clarify, I am not spotting as I never believe in spotting for a Mathematics paper, the thought is pretty ambiguous. Let us first look at the effect of having the papers […]

#### Programming, why not?

As some of my closer students know, my brother is a web developer (I think that is the best I can do to introduce his job). And yes, you might have guessed that he is also the creator of this site, maintaining it haha. He shared the follow link awhile ago, and I thought I […]

#### Arithmetic Problem #6

Try this question! Hint: Simplify it first! 🙂 Arithmetic Problem #7 Arithmetic Problem #6 Arithmetic Problem #5 Arithmetic Problem #4 Arithmetic Problem #3 Arithmetic Problem #2 Arithmetic Problem #1

#### 2015 A Level General Paper Essay Predictions

Dear students, as we all know, you have currently less than 2 weeks to D-day (ok, just kidding, your GP paper). As most of you are stressing out over what to study, how to study for this remaining week, I hope this post will shed some light on what are the possible essay topics that […]

#### Learning Python #2: Object-oriented programming

Past couple of weeks, I’ve been really busy with preparation for A-levels. Over the weekends, I had enough time to spare to read up a bit on object-oriented programming while doing my Python course on Coursera. Object-oriented programming is a programming language model that revolves around objects rather than actions, and data rather than logic. […]

#### Arithmetic Problem #5

Saw this question on the internet and thought its rather interesting. A-levels students should be all buried other their workload, amidst the mock papers and ten year series. Hopefully this might help. Hint: try and group the number together. Arithmetic Problem #7 Arithmetic Problem #6 Arithmetic Problem #5 Arithmetic Problem #4 Arithmetic Problem #3 Arithmetic […]

#### Bayesian vs Frequentist Statistics

Some of you will probably hear of this two terms and wonder what’s the difference. Both of them are a statistical approach/ inference method. Personally, I am a Bayesian and use more of Bayesian Methods to do my stuffs. Firstly, the frequentist approach is a much simple model and does not consider prior knowledge. This […]

#### 2011 A-level H2 Mathematics (9740) Paper 2 Question 10 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. (i) Let be the population mean time taken to install an electronic component. (ii) Under Test Statistic, At 5% level of significance, we reject if (iii) At 5% level of significance, we do not reject if […]

#### 2011 A-level H2 Mathematics (9740) Paper 2 Question 11 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. (i) (ii) Since r is an integer, KS Comments: (ii) is honestly not easy. Some students didn’t know the formula which is puzzling as the formal is given in MF15. I think it is important that […]

#### H3 Mathematics

As the Promotional Examination Results are all released gradually for most schools, a few Year 5 students have came up to me to ask about H3 subjects. I can’t really comment for other subjects as I have to experience in them. Here, I’ll share more on H3 Mathematics. Firstly, there are two types of H3 […]

#### 2011 A-level H2 Mathematics (9740) Paper 2 Question 12 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. (i) Let X denote the number of people joining the queue in 4 minutes. (ii) Let Y denotes number of people joining the queue in t seconds. Using the Graphing Calculator, t = 55 (iii) Let […]

#### Real Business Cycle Theory

Today, we shall look at a really brief idea of Real Business Cycle (RBC) Theory. I decided to touch a bit on this, since some students have asked me about financial mathematics and mathematical modelling topics. So I thought I can do a brief introduction of them. Business cycle theory aims to explain the fluctuations […]

#### What are stochastic and deterministic processes?

During class, I occasionally mention to students that the calculus you learnt is deterministic and they go uh huh. So like what is non deterministic?! I’ll attempt to give some simple definitions and example and also touch on stochastic process. First, a deterministic process is one that given at a particular state and an action, […]

#### Learning Python #1

I’ve been playing around with Python these days, and even participate in an online course with Coursera. I’ve previously shared that Python is a good starting point for any student that are interested in picking up mathematical programming. Here, we use codeskulptor which is an online cloud that allows us to code, run, and even […]

#### 2011 A-level H2 Mathematics (9740) Paper 2 Question 7 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. (i) Firstly, the number of different friends is a fixed constant. Secondly, the probability of successfully contacting a friend is constant. (ii) The probability of contacting a friend will vary from friend to friend, as some […]

#### 2011 A-level H2 Mathematics (9740) Paper 2 Question 6 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. (i) Stratify the residents of the city suburb into different age groups. Stand on a street corner and ask people who walk past until the required number of people in each age group have been interviewed. […]

#### 2011 A-level H2 Mathematics (9740) Paper 2 Question 5 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. Solving, and KS Comments: A very straightforward question here, as it didn’t even try to trick unsuspecting students who often forget to change the signs before applying inverse norm function. Please use a Graphing Calculator to […]

#### 2011 A-level H2 Mathematics (9740) Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. Please kindly comment at the specific questions should you have any questions.

#### 2011 A-level H2 Mathematics (9740) Paper 2 Question 3 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. (i) Let (ii) (iii) Using Graphing calculator, KS Comments: Students should be careful to draw the curves according to the given domain. And since the question requests for equations of asymptotes, we should have label them […]

#### 2011 A-level H2 Mathematics (9740) Paper 2 Question 2 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. (i) (ii) Let Since We reject since Required stationary value of KS Comments: Students do not need to carry out the second derivative test since question only ask for the stationary value, instead of maximum of […]

#### 2011 A-level H2 Mathematics (9740) Paper 2 Question 8 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. (i) (ii) Using the Graphing Calculator, The product moment correlation coefficient measures the strength and direction of a linear relationship between two variables. Thus, the r-value only indicate correlation, but not causality. It is possible for […]

#### Complex Number Problem #1

I’ve come across many questions from students regarding complex numbers, and here is one thats quite fun to deal with! Now this is really interesting, but can be solved with a bit of manipulation. We all know this is akin to We know that Now our end result is a real number! Like mentioned with […]

#### What is a Markov Process?

A few students that have great interest in going into financial mathematics, be in JC students or Uni students that were taught by me before, asked me where to start. So I often recommend them to read on Markov Process first. Of course, you need a certain knowledge for statistics here to be able to […]

#### Trick to squaring numbers

Many students go wow when I evaluate workings, without a GC. I’m not showing off, but it is because I don’t really carry a calculator with me. haha. So some students do ask me how I evaluate the square of numbers so quickly. I thought, in light of A-level’s coming, I should share something interesting. […]

#### Let’s talk about Zipf’s Law

Zipf’s law /ˈzɪf/, an empirical law formulated using mathematical statistics, refers to the fact that many types of data studied in the physical and social sciences can be approximated with a Zipfian distribution, one of a family of related discrete power law probability distributions. The law is named after the American linguist George Kingsley Zipf […]

#### Pascal’s Triangle

This is a really good video that introduces students to Pascal Triangle’s. A-levels Students should be able to relate to the binomial expansion coefficients that are found in the triangle! There are much more uses to Pascal Triangle’s. I will share more when the A-levels end.

#### 2010 A-level H2 Mathematics (9740) Paper 2 Question 11 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. (i) Let number of calls in a period of 4minutes. (ii) Let length of time Let number of calls in a period of minutes. minutes seconds (iii) Let number of calls in a working day of […]

#### 2010 A-level H2 Mathematics (9740) Paper 2 Question 10 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. (i) (ii) (a) (b) (iii) Since the product moment correlation coefficient is close to 1 for (ib), the model is the better model. (iv) From GC, the regression line of F on is (3SF) When Since […]

#### 2010 A-level H2 Mathematics (9740) Paper 2 Question 8 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. (i) Required Probability (ii) Required Probability (iii) Case 1: The first digit is 3 or 5 Case 2: The first digit is 4 Required Probability

#### 2010 A-level H2 Mathematics (9740) Paper 2 Question 6 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. Unbiased estimate of population mean Unbiased estimate of population variance Let be the population mean time required by an employee to complete a task. against at 10% level of significance Reject if p-value Test Statistic, Applying […]

#### 2010 A-level H2 Mathematics (9740) Paper 2 Question 5 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. (i) In order to use stratified sampling, we need to know the sampling frame. Since we do not have access to this information, it will be difficult to use a stratified sample. (ii) We line all […]

#### 2010 A-level H2 Mathematics (9740) Paper 2 Question 4 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. (i) (ii) For to exist must be one-one, thus least value of (iii) (iv) Since (v) Range of

#### 2010 A-level H2 Mathematics (9740) Paper 2 Question 9 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. (i) (ii) (iii) Let number of peak rate calls over the two three-month periods.

#### 2010 A-level H2 Mathematics (9740) Paper 2 Question 3 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. (i) For the curve to have a turning point, (ii) (a) When (b) (iii)

#### 2010 A-level H2 Mathematics (9740) Paper 2 Question 2 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. (i) Let be the statement: When is true. Assume that is true for some , i.e. Want to prove that is true, i.e. LHS Since is true and is true, hence by Mathematical Induction, is true […]