KS Teng

Oct142017 by KS TengNo Comments

Last Hustle for A’levels 2017

JC General Paper, JC Mathematics, Mathematics

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.

Lessons will be held at:
Newton Apple Learning Hub
Blk 131, Jurong Gateway Road #03-263/265/267 Singapore 600131
Tel: +65 6567 3606

You may contact Tutor KS or Tutor Christine for further questions.

Details are as follow:

“Lets’ Hustle!”

Oct52017 by KS TengNo Comments

Some TYS Questions worth looking at

JC Mathematics

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 of syllabus. In general, we give ourselves 1.5min for every 1 mark.

So here, I’ll share a list of questions that Mr. Wee has compiled. Mr. Wee also wrote e-books recently on solving non-routine problems. They are very interesting and provides the learners a new perspective to solving problems.

Non-routine Problems (Click to link to the solutions)
N2016/P1/Q3
N2016/P1/Q8
N2016/P1/Q10(a)
N2015/P1/Q3
N2015/P1/Q11

Application Questions
N2016/P1/Q9
N2015/P1/Q8
N2014/P1/Q11
Specimen P1/Q9
Specimen P1/Q11
Specimen P2/Q9
Specimen P2/Q10

All the best for your revision!

Oct32017 by KS TengNo Comments

RVHS GP Prelims paper 1 2017

JC General Paper

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 what extent is this true in the workplace today?
Is increased military spending justifiable when countries are not at war?
Should we always be compassionate?
To what extent is renewable energy the solution for the world’s increasing need for energy?
Consider the relevance of patriotism in your society today.
Given that the global population is growing rapidly, should people be having more children?
To what extent are the needs of the marginalised met in your society?
‘There is no such thing as bad art.’ Discuss

Oct22017 by KS TengNo Comments

APGP Interest Rate Question

JC Mathematics, Mathematics

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 $ $x$ on 1 January 2000. From 1 January 2001 onwards, he makes a deposit of $ $x$ at the start of each year.

(i) Show that the total amount in the savings account at the end of the n $^{th}$ year is $ $\frac{k}{k-1} (k^n - 1)x$ , where $k = \frac{100 + r}{100}$ .

(ii) At the end of the year 2019, Mr. Scrimp has a total amount of $ $22x$ in the savings account. Find the value of $r$ , giving your answer correct to one decimal place.

Assume that the last deposit is made on 1 January 2019 and that the total amount in the savings account is $50000 on 1 January 2020.

For a period of $N$ years, where $1 \le N \le 20$ , Mr. Scrimp can either continue to keep this amount in the savings account to earn interest or invest this amount in a financial product. The financial product pays an upfront sign-up bonus of $2000 and a year-end profit of $200 in the first year. At the end of each subsequent year, the financial product pays $20 more profit that in the previous year.

(iii) Find the total amount Mr. Scrimp will have at the end of $N$ years if he invests in the financial product.

(iv) Using the value of $r$ found in (ii), find the maximum number of years Mr. Scrimp should invest in the financial product for it to be more profitable than keeping the money in the savings account.

(i)
$(1 + \frac{r}{100})x + (1 + \frac{r}{100})^2 x + (1 + \frac{r}{100})^3 x + \ldots + (1 + \frac{r}{100})^n x$

$= \frac{(1 + \frac{r}{100})x[(1 + \frac{r}{100})^n - 1]}{(1 + \frac{r}{100}) - 1}$

$= \frac{(\frac{100 + r}{100})x[(\frac{100 + r}{100})^n - 1]}{(\frac{100 + r}{100}) - 1}$

Let $k = \frac{100 + r}{100}$

$\Rightarrow \frac{k x[k^n - 1]}{k - 1}$

Total Amount $= \$ [\frac{k}{k-1}(k^n - 1 ) x ]$

(ii)

$\frac{k}{k-1}(k^{20} - 1 ) x = 22 x$

$\frac{k}{k-1}(k^{20} - 1 ) = 22$

Using GC, $k = 1.0089905$

$\Rightarrow \frac{100 + r}{100} = 1.0089905$

$\therefore r = 0.89905 \approx 0.9$ (1 decimal place)

(iii)

Total amount $= 50000 + 2000 + \frac{N}{2}[2(200) + (N-1)(2)]$

$= 52000 + N(200 + N-1)$

$= 52000 + 199N + N^2$

(iv)

With the savings account, he has $ $[50000(1.009)^N]$ at the end of $N$ years.

With the financial product, he has $ $[52000 + 199N + N^2]$ at the end of $N$ years.

For it to be more profitable,

$[52000 + 199N + N^2] > [50000(1.009)^N]$

Sep282017 by KS TengNo Comments

HCI GP Prelims paper 1 2017

JC General Paper

‘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 education, but few are educated.’ Discuss with reference to situations in your society today.
‘Tourism brings less developed countries more harm than good.’ Comment.
How worried should we be that recent advances in science and technology are creating new challenges and worsening old problems?
‘Looks matter, and much more than substance too.’ Would you agree with this claim?
‘The hallmark of a great country is not how prosperous it is, but how inclusive its people can be.’ Should your country work towards this ideal?
‘We must surrender our human rights to win the battle against terrorism.’ Do you agree?
‘Smart cities: innovative, but not necessarily better.’ What do you think?
‘Corporate social responsibility is bad for business and companies should not be expected to take it up. To what extent would you agree?
‘Let us read and let us sin, for what harm can these amusements bring?’ Comment.

Sep132017 by KS TengNo Comments

Random Questions from 2017 Prelims #4

JC Mathematics, Mathematics

Find the acute inclination of the reflected ray $d$ to the $z$ -axis when $d$ is inclined at $60^{\circ}$ to the $x$ -axis and $45^{\circ}$ to the $y$ -axis.

Hint

Sep132017 by KS Teng3 Comments

RI JC GP Prelims paper 1 2017

JC General Paper

‘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?
‘Business should have no place in politics.’ Do you agree?
‘Scientific knowledge cannot be trusted because it is unreliable.’ Is this a fair statement?
‘Celebrities today do little that is worth of celebration.’ Discuss.
Are machines making humans obsolete?
Consider the importance of non-conformity in your society.
‘Achieving greater income equality for all is a desirable but unrealistic goal.’ Do you agree?
How effective is technology in making us healthier?
‘History is just set of lies.’ Discuss.

Sep42017 by KS TengNo Comments

Making Use of this September Holidays

JC Mathematics, Mathematics

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 them 4 sets of 3 hours practice papers. Students need to grind themselves to be able to handle the paper at 8am. It is really different. Not to mention, this September Holidays is probably your last chance to be able to give yourself timed practices.

For students who took H2 Math Paper 1, you might be stunned with the application questions that came out. For NJC, its Economics. For YJC, its LASER. For CJC, a wild dolphin appeared. And more. These application questions are possible, due to the inclusion of the problems in real world context in your syllabus. You can see the syllabus for yourself. I’ve attached the picture below. So for Paper 2, expect these application questions to be from statistics mainly, as suggested in your scheme of work below.

For students that have took H2 Math paper 1 & 2, and this is probably ACJC. The paper was slightly stressful, given the mark distributions, but most of the things tested are still technically “within syllabus”. For one, the directional cosine question, is a good reminder to students that they should not leave any pages un-highlighted. AC students should be able to properly identify their weaknesses and strengths this time round. If its time management, then start honing that skill this holidays – by having timed practice. A quick reminder that the TYS papers are not 3 hours, since some of the questions are out of H2 Mathematics 9758 syllabus. Students can consider the ratio of 1 mark to 1.5 min to gauge how much time they have for each paper.

R-Formulae seems to be popular about the prelims exams this time round, making waves in various schools. Perhaps it was because it appeared in the specimen paper, and if you’re keen on how it can be integrated or need a refresher. I did it recently here.

Lastly, for the students that are very concerned on application questions. Check the picture below. It contains some examples that SEAB has given. Students should also be clear about the difference between a contextual question and an application question.

With that, all the best to your revision! 🙂

Aug292017 by KS Teng1 Comment

Trigonometry Formulae & Applications (Part 2)

JC Mathematics, Secondary Math

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 under assumed knowledge, just saying…

$a \text{cos} \theta \pm b \text{sin} \theta = R \text{cos} (\theta \mp \alpha)$

$a \text{sin} \theta \pm b \text{cos} \theta = R \text{sin} (\theta \pm \alpha)$

where $R = \sqrt{a^2 + b^2}$ and $\text{tan} \alpha = \frac{b}{a}$ for $a > 0, b > 0$ and $\alpha$ is acute.

So here, I’ll write the addition formulae that’s found in MF26.

$\text{sin}(A \pm B) \equiv \text{sin}A \text{cos} B \pm \text{cos} A \text{sin} B$

$\text{cos}(A \pm B) \equiv \text{cos}A \text{cos} B \mp \text{sin} A \text{sin} B$

I’ll use an example I discussed previously.

$f(x) = 3 \text{cos}t - 2 \text{sin}t$

Write $f(x)$ as a single trigonometric function exactly.

Lets consider the formulae from MF26.

$\text{cos}(A \pm B) \equiv \text{cos}A \text{cos} B \mp \text{sin} A \text{sin} B$

$R\text{cos}(A \pm B) \equiv R \text{cos}A \text{cos} B \mp R \text{sin} A \text{sin} B$

We can let

$3 = R \text{cos} B ---(1)$

$2 = R \text{sin} B ---(2)$

$\Rightarrow \sqrt{ 3^2 + 2^2 } = \sqrt{ R^2 \text{cos}^2 B + R^2 \text{sin}^2 B}$

$\Rightarrow \sqrt{13} = R$

$\Rightarrow \frac{R \text{sin} B}{R \text{cos} B} = \frac{2}{3}$

$\Rightarrow \text{tan} B = \frac{2}{3}$

Putting things together, we have that

$f(x) = \sqrt{13} \text{cos} ( t + \text{tan}^{\text{-1}} (\frac{2}{3}))$

Aug272017 by KS TengNo Comments

Random Questions from 2017 Prelims #3

JC Mathematics

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 and positive y-axis at point Q. It is given that $\angle PQO = \theta$ , where $0 < \theta < \frac{\pi}{2}$ and O is the origin.

(i) Show that equation of line PQ is given by $y = (4-x) \text{cot} \theta +3$ .

(ii) By finding an expression for $OP + OQ$ , show that as $\theta$ varies, the stationary value of $OP + OQ$ is $a + b \sqrt{3}$ , where $a$ and $b$ are constants to be determined.

Solution