2019 A-level H2 Mathematics (9758) Paper 2 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions.

Numerical Answers (workings/explanations are after the numerical answers.)

Question 1: - \frac{2}{3} x (1-x)^{3/2} - \frac{4}{15}(1-x)^{5/2} + C_1;~ - \frac{2}{3} (1-x)^{3/2} + \frac{2}{5}(1-x)^{5/2} + C_2
Question 2: x < - \frac{8}{3} \text{~or~} 1 < x < 2;~ - \frac{8}{3} < x < 1 \text{~or~} x >2
Question 3: r = \sqrt{\frac{150}{\pi}}, V = \frac{1500 \sqrt{6 \pi}}{\pi};~ r: h = 1:2
Question 4: f(x) \approx 1 + 2x^2;~ 0.02001;~0.02001
Question 5: \vec{OX} = \textbf{b} + \frac{5}{4} \textbf{a};~ \vec{OY} = \frac{10}{3} \textbf{a} + \frac{8}{3} \textbf{b};~ 3: 8
Question 6: 7.24 \times 10^{18}
Question 7: 0.102;~0.991;~ 45p^2 (1-p)^8;~ p = 0.0689
Question 8: \frac{23}{56};~\frac{13}{28};~\frac{1}{55};~\frac{21}{110}; orange bird & yellow bird, orange bird & white rider, white horse & white rider, white horse & yellow bird
Question 9: H_0: \mu = 750, H_1: \mu \neq 750;~ \bar{x} =756, p \approx 0.0897
Question 10: \frac{4}{3};~ (50, 18.6);~ y = -0.3x + 33.6;~ r \approx -0.985;~24.6 \text{km/l}
Question 11: 0.970; ~0.802;~M \approx 381;~0.846

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