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.

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