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2016-h2-math-paper-1-solutions

Here’s my personal review of paper 1.

Overall:

The paper is a balanced paper, there several questions reused from previous years and there are a few questions that are phrased differently and requires some thinking. Scoring A may not be that easy but to get B is not difficult either.

I will gauge around 14 marks are from the difficult questions, which will not cause one to lose the A grade. It is about how careful one is with the remaining 84 marks.

By Question:

- Straightforward easy question.
- Straightforward easy question.
- This questions on the surface looks difficult but it is actually about recognising the coordinates of the power 4 eqn which is the same concept as quadratic eqn which is covered in O levels, hence I would consider this question of medium difficulty.
- Part (i) can be challenging if students do not plan on how to obtain powers of r, mainly using the equations of common ratio and make “a” the subject and substitute back to the equation(s). This is considered difficult. Part (ii) is straightforward, just that students may not realise it involves sum to infinity.
- Again this question may look difficult with cross product or dot product of several vectors but it is considered easy straightforward. Just follow the instructions and carry out the computation.
- Question 6 (i) may be a little tedious, especially when showing that P(k) is true implies P(k+1) is true. Students who do some factorisation may ease the amount of algebraic manipulation. Part (ii) and Part (iii) are basically “give away” marks.
- Question 7(a) can be tricky if students blindly memorise the “concept” that the conjugate is a root. In this case the coefficients are not real so that “concept” would result in 0 marks. Similarly for 7(b) one needs to use the idea of a “root” rather than using the “concept” mentioned above blindly again. So this question is tedious but not difficult as long as one is careful.
- Question 8 is considered straightforward. Part (iii) has multiple methods to solve as the question allows the freedom to do by differentiation, or double angle formula or using Binomial expansion by converting to sine and cosine.
- Question 9 is also considered straightforward as long as one knows the basic concept of substitution.
- Question 10(ai) is considered easy, Q10(aii) requires a little thinking but one just needs to follow the instruction and evaluate ff(x). Students who straightaway conclude that f is self inverse will find themselves stuck. 10(bi) is giveaway as long as one is careful with calculation, 10(bii) is considered more difficult as one has to “invent” examples to illustrate the function g is not one to one.
- Question 11 is a little unusual as many students are used to finding intersection between line and plane through scalar product or cartesian format but not often in parametric format. 11(b) can be difficult if one does not use the concept of distance between origin and a plane.