Solutions to Set B

Solutions to Set B

JC Mathematics, Mathematics

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

Solutions to Set A

JC Mathematics, Mathematics

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

Thoughts on the H2 Mathematics (9758) Papers 2017

JC Mathematics, Mathematics

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 after this first trial year, will they still guide the students.) Application questions were not tough and well guided. Students can solve it easily if they read it well. Statistics was well crafted and neat.

To be blunt, I’ll give credit to the 9740 H2 Mathematics paper that run concurrently, since it is too tough to set two sets of papers. Its easy to acknowledge that the 9740 (2016) paper was way harder than 9740 (2017). Next year won’t be the same.

Advice: Students should be careful when you revise, make sure you learn, and not do. Understand what you’re doing. The 2017 paper was an inquisitive paper, examiners were watching closely if you pay attention to details, and know your definitions well.

I’ll do an analysis for the paper, you can click on the individual question and read. For students that took the paper, I hope it doesn’t demoralise you.

Paper 1

Paper 2

 

 

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

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

JC Mathematics

Sharing the A-level H1 General Paper (8807) Paper 1…

 

  1. ‘The past is not dead; it is not even past.’ Discuss.
  2. Can the use of animals for scientific research ever be justified?
  3. In your society, to what extent is it acceptable for public money to be used for the acquisition of works of art?
  4. ‘Rehabilitation, not punishment, should be the purpose of the justice system.’ Discuss.
  5. Is regulation of the press desirable?
  6. Do events, rather than politicians, shape the future?
  7. How far is science fiction becoming fact?
  8. Examine the role of music in establishing a national identity in your society.
  9. To what extent are people judged more by their physical appearance than by their abilities?
  10. ‘Practical ability is just as important as intellectual skills.’ How far is this true in your society?
  11. Assess the view that attempts to control climate change can never be truly effective.
  12. The quality of written language is being destroyed by social media.’ What is your view?
  13.  

Thoughts on H2 Mathematics (9758) 2017 Paper 1

Thoughts on H2 Mathematics (9758) 2017 Paper 1

JC Mathematics, Mathematics

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 has several topics removed, and these were mostly topics that were “drill-able”, aside from complex numbers. The new syllabus added in mainly, new integration forms, focus on parametric Equations with Cartesian equations, and of course, Discrete R.V. But let us leave the statistics out.

Students should familiarise themselves with the trigonometry Formulae in MF26. There are several topics that can be linked up with trigonometry, makes me wonder why it isn’t a chapter by itself. Complex numbers has a trigonometry form too, so make sure students know how to manipulate it, given the trigonometry Formulae.

Next, students should understand the use of Maclaurin’s. What does it mean for x to be small, and the implications when they say h is small compared to R… And also finding the general term of a Maclaurin’s Expansion.

It won’t hurt to review how to find the Area using Shoe-lace method. And not forgetting our Sine Rule and Cosine Rule.

Do know how to prove a one-one function… Non-graphically. (i.e. not using the Horizontal Line Test)

Do know that the oblique asymptote of f(x) becomes y=0 when we do the y = \frac{1}{f(x)} transformation too.

Lastly, students must READ really carefully and discern every information. Having marked many scripts, many students do not read carefully and lose marks here and there. And they do add up… Be alert and read, take note of the forms that they want. Here are 10 little things to take note when you read the question.

  1. Cartesian/ Polar/ Exponential for complex
  2. Scalar/ Parametric/ Cartesian for vectors
  3. Set/ range/ interval of values
  4. Algebraically => show all the workings without a GC.. usually discriminant, completing the square or maybe some differentiation will be involved.
  5. Without using a calculator => show your workings and check with a GC (secretly)
  6. Decimal places, etc…
  7. Rounding off when you’re dealing with an inequality
  8. Units used in the questions, (ten thousands, etc)
  9. Rate of change; leaking means the rate is negative…
  10. All answers should be in 3 SF UNLESS OTHERWISE STATED. Degrees to 1 DP. RADIANS to 3 SF.

Have fun and all the best!

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

2017 A-level H2 Mathematics (9740) 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 (9740). H2 Mathematics (9758), 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: 2
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{1}{a}, \frac{1}{ae}); \frac{1}{a^2}
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})

 

Relevant materials

MF26

KS Comments

To be honest, this paper is really the same as the H2 Mathematics (9758). They just rephrased everything. You can see for yourself here.

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