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

JC Mathematics, Mathematics

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:
Question 11:


Relevant materials


KS Comments

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! 🙂

Random Questions from 2017 Prelims #1

Random Questions from 2017 Prelims #1

JC Mathematics

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 ACJC 2017 Prelims Paper 1 Question 7. And it is on complex numbers.

(a) Given that 2z + 1 = |w| and 2w-z = 4+8i, solve for w and z.

(b) Find the exact values of x and y, where x, y \in \mathbb{R} such that 2e^{-(\frac{3+x+iy}{i})} = 1 -i

I’ll put the solutions up if I’m free.

But for students stuck, consider checking this link here for (a) and this link here for (b). These links hopefully enlightens students.

Just FYI, you cannot \text{ln} complex numbers as they are not real…

H2 Mathematics (9740) 2016 Prelim Papers

H2 Mathematics (9740) 2016 Prelim Papers

JC Mathematics

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 Math Prelim P1 QP
2016 ACJC H2 Math Prelim P2 QP

2016 CJC H2 Math Prelim P1 QP
2016 CJC H2 Math Prelim P2 QP

2016 HCI JC2 Prelim H2 Mathematics Paper 1
2016 HCI JC2 Prelim H2 Mathematics Paper 2

2016 IJC H2 Math Prelim P1 QP
2016 IJC H2 Math Prelim P2 QP

2016 JJC H2 Math Prelim P1 QP
2016 JJC H2 Math Prelim P2 QP

2016 MI H2 Math Prelim P1 QP
2016 MI H2 Math Prelim P2 QP

2016 MJC H2 Math Prelim P1 QP
2016 MJC H2 Math Prelim P2 QP

2016 NJC H2 Math Prelim P1 QP
2016 NJC H2 Math Prelim P2 QP

2016 NYJC H2 Math Prelim P1 QP
2016 NYJC H2 Math Prelim P2 QP

2016 PJC H2 Math Prelim P1 QP
2016 PJC H2 Math Prelim P2 QP

2016 SAJC H2 Math Prelim P1 QP
2016 SAJC H2 Math Prelim P2 QP

2016 SRJC H2 Math Prelim P1 QP
2016 SRJC H2 Math Prelim P2 QP

2016 TJC H2 Math Prelim P1 QP
2016 TJC H2 Math Prelim P2 QP

2016 TPJC H2 Math Prelim P1 QP
2016 TPJC H2 Math Prelim P2 QP

2016 VJC H2 Math Prelim P1 QP
2016 VJC H2 Math Prelim P2 QP

2016 YJC H2 Math Prelim P1 QP
2016 YJC H2 Math Prelim P2 QP

Students, test your Vectors!

Students, test your Vectors!

JC Mathematics

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 entire topic to solve it.

So I’ll share one here. This involves several concepts put together. I’ll put the solution up once I find the time. Concepts that will be involved, will be

  1. Vector Product
  2. Equations of Plane
  3. Finding foot of perpendicular of point

The question in one a reflection of a plane in another plane. I think such questions will come out in a few guided steps in exams. But should a student be able to solve it independently, it shows that he has good understanding.

The plane p has equation x + y + z = 9 and the plane p_1 contains the lines passing through (0, 2, 3) and are parallel to (1, -1, 0) and (0, 1, 1) respectively. Find, in scalar product form, the equation of the plane which is the reflection of p_1 in p.

Thinking Math@TheCulture #4

Thinking [email protected] #4

JC Mathematics, Mathematics

[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 1, 2, 4, 8, \ldots integers, as indicated below, so that the number of integers in each set after the first is twice the number of integers in the previous set.

\{ 1 \}, \{ 2, 3 \}, \{ 4, 5, 6, 7 \}, \{ 8, 9, 10, 11, 12, 13, 14, 15 \}, \ldots

(i) Write down the expressions, in terms of r for

(a) the number of integers in the r^{th} set,

(b) the first integer in the r^{th} set,

(c) the last integer in the r^{th} set.

(ii) Given that the integer 1,000,000 occurs in the r^{th} set, find the integer value of r.

(iii) The sum of all the integers in the 20^{th} set is denoted by S, and the sum of all the integers in all of the first 20 sets is denoted by T. Show that S may be expressed as 2^{18}(3 \times 2^{19} - 1).

Hence, evaluate \frac{T}{S}, correct to 4 decimal places.


Singapore Inclusive Policies- A reflection

Singapore Inclusive Policies- A reflection

JC General Paper

“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:

  1. Restructuring to sustain growth
  • Less dependency on foreign labour
  • More grants and support for SMEs
  1. Building a fair and inclusive society
  • Improving the social mobility of lower income families through improved financial and educational subsidy and/or grant schemes
  • Helping seniors live long and well by offering housing purchase schemes, credit incentives for hiring aged workers, increased retirement savings and more affordable healthcare
  • Supporting those with disabilities and special needs through subsidies for employing caretakers, providing educational and skills support facilities and building elder-friendly infrastructure
  • Sharing the fruits of Singapore’s economic growth by giving out GST vouchers in cash, Medisave and U-save

(taken from http://www.singaporebudget.gov.sg/budget_2012/download/FY2012_Budget_in_Brief.pdf)

It is not difficult to understand why the government initiated such a plan. In the words of PM Lee “We all have something to contribute,” (channelnewsasia.com, 31 Oct 2015) hence maximising the potential of our human resource: young, old, poor, rich, abled and disabled, and keeping them healthy and happy is a strategic move to support Singapore’s future economic growth.

It is now 2017 and the government has indeed delivered most of what was promised in the budget plan. To highlight a few of these achievements, our neighbourhoods and transport systems are now more elder-friendly, we receive our GST cash vouchers as promised, we have two spanking-new hospitals in the West and are currently in the midst of integrating our healthcare groups to streamline operations and make healthcare more affordable, we built a $25million Enabling Village to help those with disabilities and special needs and we have decreased the local to foreign worker dependency ratio. However no success story is without sacrifice and just who or what were the sacrificial lambs in this budget plan? Moreover, which areas should the government focus on in the next one?

Tax payers are once again not spared from funding Singapore’s progressive aspirations and why should they? The money is redistributed and re-invested to make Singapore a fairer and stronger society. However tax rates have gone up again for YA2017 for the rich and upper middle classes, from a range of 17-20% to a range of 18-22% and with the addition of two new income tiers (www.iras.gov.sg). The question is, is this really fair? I heard that little “Yes!” go up in your head. Truth be told, it depends on how the rich make their money. For those who own successful local businesses, the new tax hikes are going to hurt and might even discourage further business growth or expansion. For those who make their riches through stocks and shares, guess what? These are not declared when filing income tax! Perhaps we should work towards minimising the number of those who profit from loopholes in the system if we truly wish to build a fairer – also towards the rich— and more inclusive society.

Finally, what new directions might we find in the AY2017 budget? The Committee on the Future Economy (CFE) of Singapore recently released a report highlighting key growth sectors and proposed seven strategies to sustain Singapore’s economy in the coming years.

Key growth sectors: finance, hub services, logistics, urban solutions, healthcare, the digital economy and advanced manufacturing

Seven strategies:

  • Deepen and diversify international connections
  • Acquire and utilise deep skills
  • Strengthen enterprise capabilities to innovate and scale up
  • Build strong digital capabilities
  • Develop a vibrant and connected city of opportunity
  • Develop and implement Industry Transformation Maps (ITMs)
  • Partner each other to enable innovation and growth

(taken from https://www.gov.sg/microsites/future-economy/the-cfe-report)

One can therefore expect more money in the AY2017 budget to be channelled into re-skilling the workforce, encouraging innovation and improving digital infrastructure and technology i.e. building a Smart Nation. Support for the elderly, disabled and those with special needs might take on a minor role in the budget this year because it was the focus of AY2012-16’s budget plan.

Nonetheless, there is so only so much money can do in helping a country to survive. As pointed out by PM Lee, Singaporeans need to practice active citizenship. This means making the effort to keep oneself fit and healthy, using the incentives and support systems in place to reskill or retrain oneself to meet with changing labour demands, revising educational content to ensure our students are prepared for the future by the time they graduate and managing ones expectations and demands in times of economic difficulty. Policies, systems and budget plans will change but the brunt of it can be softened by adopting the right attitude and mentality. Thus when the AY2017 budget comes out, hold your tongue for a moment, understand the changes and safety nets in place and learn to embrace them. If not, a corner of Hong Lim Park beckons you.

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

JC Physics

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

  1. B
  2. C
  3. B
  4. D
  5. D
  6. C
  7. D
  8. D
  9. B
  10. C
  11. A
  12. D
  13. D
  14. C
  15. C
  16. A
  17. D
  18. A
  19. B
  20. D
  21. Question 21 is a flawed question. When unpolarised light goes through a polarizer, the I is halved while the A is reduced by a factor of root 2. But based on the information Cambridge provides, the answer is C.
  22. D
  23. D
  24. C
  25. C
  26. B
  27. C
  28. A
  29. B
  30. B
  31. A
  32. C
  33. D
  34. B
  35. B
  36. B
  37. D
  38. C
  39. C
  40. C

Note to all: Casey will not respond to most of the comments as he is busy. You may contact him by SMS at  +65 9474 5005 if you have a burning question.

Feel free to explain the answers, if you are confident. Many thanks.