2018 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 (click the questions for workings/explanation)

Question 1: f(x) = 3 (\frac{2}{9}x + 4)^{3/2} + 45, (54, 237)
Question 2: s = 69, t = 13, other roots = 2 + 3i, 0.5, w = - \frac{3}{2} \pm \frac{3\sqrt{3}}{2}i, w_1 w_2 w_3= 27, w_1 + w_2 + w_3= 0
Question 3: D(-5, -4, 3), 4x + 45y + 20z = 200, 58.6^{\circ}, 6.88 \text{units}
Question 4: \text{ln}(\text{cos}2x) = -2x - \frac{4}{3}x^4 - \frac{65}{45}x^6, x \neq \frac{\pi}{4}, -1.0644, -1.0670
Question 5: k \ge 9430000
Question 6: \frac{5}{9} \textless p \textless \frac{2}{3}, 0.43046721
Question 7: \text{P}(A' \cap B') = 1 - a - b + ab, \text{P}(A' \cap C') = 1 - a - c, \frac{2}{15} \le \text{P}(A \cap B) \le\frac{1}{3}
Question 8: \text{P}(S=10)=0; g(n) = 22n^2 + 78n +36
Question 9: r = 0.969, r = 0.993; P = 2.85 \times 10^{-8} R^2 - 0.283, R = 6450 \text{~revolutions~per~min}, P = 0.0273 \text{~watts}, P =1.02 \times 10^{-4} R^2 - 0.283
Question 10: 0.605, 0.773,  0.126, 136, 0.185

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