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

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: \frac{1}{x^2} (1 - \text{ln}x); 1 - \frac{2}{e}
Question 2: x= \frac{1}{2} or x=3; \frac{125}{6}\pi \text{units}^3
Question 3: y = 3 -x^2
Question 4: x = - 1 \pm \sqrt{3}, 0, -1; - 1 - \sqrt{3} \textless x \textless -1 or 0 \textless x \textless -1 + \sqrt{3}
*Question 5: b = -1, f^{-1}(x) = 1 + \frac{a+1}{x-1}, x \in \mathbb{R}, x \neq 1, a \neq -1
Question 6: \lambda = \pm 2 \sqrt{31}
Question 7: N(-\frac{1}{17}, 0)
Question 8: A = 5, u_3 = 40; a =7.5, b =-5, c = -5; 15(2^n - 1) - 7.5n - 2.5n^2
Question 9: k= 2; 8 units
Question 10: I = \frac{3A}{2e}
Question 11: 102.43;1215.71; first day of June 2018; b = \frac{4}{3}; b = 1.23

*Do note that question 5 is problematic as the domain of ff needs to be equal to the domain of g. I do not know the consequences of a faulty question.

Relevant materials

MF26

KS Comments

Fairly interesting paper. It was tedious at some point. It is good to note that some H2 Further Mathematics content or techniques were brought down and tested in this paper. Students should be comfortable with unseen questions and being in unfamiliar territories while applying known or learnt concepts well.

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