Some TYS Questions worth looking at

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)

Application Questions
Specimen P1/Q9
Specimen P1/Q11
Specimen P2/Q9
Specimen P2/Q10

All the best for your revision!

RVHS GP Prelims paper 1 2017

RVHS GP Prelims paper 1 2017

JC General Paper
  1. Is being innovative more desirable than keeping the status quo?
  2. ‘The promise of science and technology cannot be realised without the humanities.’ Do you agree?
  3. Is politics today nothing but a series of empty promises?
  4. ‘Education perpetuates rather than fights inequality.’ Comment.
  5. ‘Men only need to be good, but women have to be exceptional.’ To what extent is this true in the workplace today?
  6. Is increased military spending justifiable when countries are not at war?
  7. Should we always be compassionate?
  8. To what extent is renewable energy the solution for the world’s increasing need for energy?
  9. Consider the relevance of patriotism in your society today.
  10. Given that the global population is growing rapidly, should people be having more children?
  11. To what extent are the needs of the marginalised met in your society?
  12. ‘There is no such thing as bad art.’ Discuss
APGP Interest Rate Question

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.

(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 ]


\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)


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

= 52000 + N(200 + N-1)

= 52000 + 199N + N^2


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]

HCI GP Prelims paper 1 2017

HCI GP Prelims paper 1 2017

JC General Paper
  1. ‘Nothing but provocation and self-centredness.’ Is this a fair description of the state of affairs in today’s world?
  2. ‘My life, my choice.’ How far can people expect to live life this way?
  3. Should historical monuments and objects be preserved when such an undertaking is very expensive or even a source of unhappiness?
  4. ‘Many receive an education, but few are educated.’ Discuss with reference to situations in your society today.
  5. ‘Tourism brings less developed countries more harm than good.’ Comment.
  6. How worried should we be that recent advances in science and technology are creating new challenges and worsening old problems?
  7. ‘Looks matter, and much more than substance too.’ Would you agree with this claim?
  8. ‘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?
  9. ‘We must surrender our human rights to win the battle against terrorism.’ Do you agree?
  10. ‘Smart cities: innovative, but not necessarily better.’ What do you think?
  11. ‘Corporate social responsibility is bad for business and companies should not be expected to take it up. To what extent would you agree?
  12. ‘Let us read and let us sin, for what harm can these amusements bring?’ Comment.
Making Use of this September Holidays

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.

Scheme of Examination Source: SEAB

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.

Integration & Applications Source: SEAB

With that, all the best to your revision! 🙂

Anderson JC GP Prelims paper 1 2017

JC General Paper
  1. Should small countries be allowed to take the lead in global affairs?
  2. To what extent can the Arts effect positive social change today?
  3. ‘Experiences are more valuable than material possessions.’ Do you agree?
  4. ‘People in the workplace should embrace, rather than fear, technological advancements.’ Discuss.
  5. ‘The news today deals with what is popular, rather than what is important.’ How far do you agree with this statement?
  6. Evaluate the claim that a more connected world has resulted in greater divisions.
  7. ‘Public figures today are overly concerned about what people think of them.’ What is your view?
  8. Consider the view that there is no value in slowing down in today’s competitive world.
  9. Discuss the appeal and value of creativity in your society.
  10. Considering the increasing threat of terrorism, are governments justified in limiting people’s rights?
  11. To what extent is animal testing acceptable in scientific research?
  12. ‘Economic development is favoured at the expense of the welfare of people.’ How true is this of your society?
Random Questions from 2017 Prelims #3

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.

Trigonometry Formulae & Applications (Part 1)

Trigonometry Formulae & Applications (Part 1)

JC Mathematics, Secondary Math

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, although students can derive it out using existing formulae in MF26.

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.

Here is a quick example,

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

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

Here, we observe, we have to use the R-Formulae where

R = \sqrt{3^2 + 2^2} = \sqrt{13}

\alpha = \text{tan}^{\text{-1}} (\frac{2}{3})

We have that

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

I’ll end with a question from HCI Midyear 2017 that uses R-Formulae in one part of the question.

A curve D has parametric equations

x = e^{t} \text{sin}t, y = e^{t} \text{cos}t, \text{~for~} 0 \le t \le \frac{\pi}{2}

(i) Prove that \frac{dy}{dx}  = \text{tan} (\frac{\pi}{4} - t).

I’ll discuss about Factor Formulae soon.  And then the difference and application between this two formulae.

Random Questions from 2017 Prelims #2

Random Questions from 2017 Prelims #2

JC Mathematics, Mathematics, Secondary Math

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 of ratio theorem or mid point theorem. The second part is on application: Ray Tracing which I’ll discuss in class.

A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side. For the triangle show below, O, A and B are vertices, where O is the origin. \vec{OA} = a and \vec{OB} = b. The midpoints of OB, OA and AB are M, N and T respectively.

It is given that X is the point of intersection between the medians of triangle OAB from vertices A and B.

(i) Show that \vec{OX} = \frac{1}{3} (a +b)

(ii) Prove that X also lies on OT, the median of triangle OAB from vertex O.