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

JC Mathematics

Post will be updated again on 9th November 2018.

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

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

JC Mathematics, Mathematics

Post will be updated again on 14th November 2018.

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

Solutions to the modified A’levels Questions

Solutions to the modified A’levels Questions

JC Mathematics

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 to the 9758 syllabus…

The rest of the solutions (that are questions from the original TYS) can be found here.

2012/P1/Q10

2012/P2/Q2

20112/P2/Q7

2012/P2/Q7

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

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

JC Mathematics, Mathematics

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: 2 \sqrt{15}; xy=6
Question 2: d = 1.5;~ r \approx 1.21 \text{~or~} r \approx -1.45;~n=42
Question 3: (\frac{1}{2}a, 0), (0,b);~ (a+1, 0,);~ (\frac{a+1}{2}, 0);~ (0, a), (b, 0);~ a = 1;~ gg(x) = x, x \in \mathbb{R}, x \neq 1  , ~ g^{-1}(x) = 1 - \frac{1}{1-x}, x \in \mathbb{R}, x \neq 1;~b= 2 \text{~or~}0
Question 4: 15.1875;~ \frac{\pi}{2a(a-1)};~ b = \frac{1}{2} + \frac{1}{2}\sqrt{1-a+a^2}
Question 5: \frac{5}{12}, \frac{5}{14}, \frac{5}{28}, \frac{1}{21};~ \mathbb{E}(T) = \frac{20}{7}, \text{Var}(T) = \frac{75}{98};~ 0.238
Question 6: 955514880;~ 1567641600;~ \frac{1001}{3876}
Question 7: 31.8075, 0.245;~ p = 0.0139; Do not reject h_0, Not necessary.
Question 8: Model (D); a \approx 4.18, b \approx 74.0;~ r \approx 0.981
Question 9: 0.632;~ 1.04 \times 10^{-4};~ 0.458;~ 0.421;~ 0.9408
Question 10: 0.345;~ 0.612;~ \mu = 12.3, \sigma = 0.475;~ k \approx 55.7

 

Relevant materials

MF26

KS Comments

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

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

JC Mathematics, Mathematics

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: ax + (2a - \frac{a^2}{2})x^2 + (\frac{a^3}{3} + 2a - a^2) x^3; a = 4
Question 2: x \textgreater \frac{1}{\sqrt{b}} + a or x \textless a
Question 3: x = \pm \frac{1}{\sqrt{2}} ; Maximum point
Question 4: a = 4, b =1; translate the graph 4 units in negative y-direction and translate the graph 2 units in positive x-direction.
Question 5: a = -1.5, b = 1.5, c = 7; x \approx -1.33; x \approx -0.145 or x \approx 1.15
Question 6: r = a + (\frac{d - a \cdot n}{b \cdot n}) b
Question 7: \frac{\text{sin}(2mx-2nx)}{4m-4n} - \frac{\text{sin}(2mx+2nx)}{4m+4n} + C; \pi
Question 8: z = -1 + 2i or z = 2 - i; p =-6, q=-66; (w^2 - 2w+2)(w^2-4w+29)
Question 9: U_n = 2An - A +B; A = 3, B =-9; k=4; \frac{1}{4} (n^4 + 2n^3 + n^2) ; e^x
Question 10: a = -4.4; R(1.5, 0.5, -1); \frac{1}{2}\sqrt{10}
Question 11: \frac{dv}{dt}=c; v = 10t +4; v = \frac{1}{k}(10- 10 e^{-kt}); 9.21s

 

Relevant materials

MF26

KS Comments

Firstly, to do well in this paper, student has to be quite intuitive, to be comfortable with the levels of unfamiliarity.

Q1. Simple expansion using MF26. If you used it carefully, it should provide some guidance to Q9(c) actually.
Q2. Simple graphings, using secondary school modulus function knowledge.
Q3. Students have to know how to use y = 5x to find back the y-coordinate.
Q4. (a) is even easier if you simply did long division.
Q5. Remainder Theorem from Secondary School for (i). (ii), students need to be alert that when the gradient is ALWAYS positive, the function is strictly increasing, not just increasing.
Q6. Interesting question, that is similar to the Specimen Paper.
Q7. Use of Factor Theorem form MF26 will make this integration much comfortable. By parts work too.
Q8. Standard complex number practice question.
Q9. Very interesting questions. Especially (c), but like mentioned a keen student who did Q1 well, will realise the sum to infinity is simply from MF26.
Q10. Standard vectors questions. Just read carefully and it will be manageable.
Q11. Simple DE too. For the terminal velocity, just need to read that its “after a long time”.

Overall, a manageable paper.
Now things that have yet to come out…
Reciprocal Graph, Area/ Volume, Parametric Equations, Min/Max Problem, APGP, Function, Integration Techniques, Complex Number (Polar Form, Modulus, Argument), Vectors (Planes, Ratio Theorem), Small angle approximation

Integration By Parts

Integration By Parts

JC Mathematics

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

\int v \frac{du}{dx} ~dx = uv - \int u \frac{dv}{dx} ~dx

I like to share with students that Integration by Parts have two interesting facts.

  1. It allows us to integrate expression that we cannot integrate. Eg. \text{ln}x or inverse trigonometric functions. This is also closely related to how LIATE is established.

  2. This is closely related to point 1. That is, instead of trying to integrate the expression, we are differentiating it instead. And that itself, is a very important aspect.

Next, I like to point out to students that LIATE is a general rule of thumb.
GENERAL – because it does not work 100% of the times. And today, I’ll use an example to illustrate how LIATE actually fails.

\int \frac{te^t}{(t+1)^2} ~ dt

Here we observe two terms \frac{t}{(t+1)^2} and e^t. Going by LIATE, we should be differentiating \frac{t}{(t+1)^2} and integrating e^t.

\int t^2 e^{t} ~ dt
= \frac{t}{(t+1)^2} e^{t} - \int \frac{(1)(t+1)^2 - t(2)(t+1)}{(t+1)^4} e^t ~dt

Now observe what happened here, after applying integration by parts, it got “worst”. We are stuck to integrating \frac{(1)(t+1)^2 - t(2)(t+1)}{(t+1)^4} with an exponential… This should raise some question marks. But we did follow LIATE.

I’ll leave students to try out this on their own. And feel free to ask questions here. Have fun!

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

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

JC General Paper

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 question, and it does not have a healthy budget balance.

Financial aid- capital/loans/money

Material aid- manpower/distribution of basic goods and necessities

  • Provision of aid during economic hard times could be a political statement and commitment to the recipient country, helping to foster greater political relations in the long term. Giving of aid should be expected especially if the recipient country needs it more than the donor country. Such circumstances could be when the recipient country is facing civil war and there is urgent need of aid to cease the fighting etc. Another possible instance could be during times of natural disasters/emergencies. Also, for most of the donor country, aid takes up a small portion of their budget, hence it should not affect the current economy severely even if the country continues to give out aid during hard times. Aid accounts for 0.5% of the US budget yearly.
  • Governments should be responsible and accountable to their citizens first especially during hard times, hence aid should be allocated domestically rather than elsewhere. The dollar votes of the citizens and their voices are important, and it is only right that countries should be concerned with their own self-preservation before others. After all, an economically prosperous country will then be able to contribute more to the international community, rather than a slow and stagnate economy that is facing difficult times.
  • Perhaps a country should look at other means of support, rather than the provision of aid during bad times. It is presumptuous to assume that aid helps to alleviate the problems faced by the recipient countries. Often, aid may actually harm local industries and foster this sense of self-entitlement and dependency on the donor nations.
  • Legal obligations under international law could possibly bind countries to continue giving aid to another country. A short term economic difficulty does not suffice to repudiate this commitment, especially when contracts have been signed beforehand, and the donor country may risk ruining their legitimacy and international standing.

In dire situations, countries should still continue to give aid to one another. However, expectations to scale down in terms of aid is definitely reasonable and justifiable.

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.