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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


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


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