2019 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 (workings/explanations are after the numerical answers.)

Question 1: b = -a, c = -7a, d = 15a
Question 2: a = 0.682; ~b = 1.891
Question 3: f(x) = 2 \{(x - 1)^3 - 5 \}
Question 4: x \in [2, 4]
Question 5: f^{-1}(x) = \frac{1}{2} \ln (x + 4), D_{f^{-1}(x)} = (-4, \infty );~ x = \ln 3 - 2
Question 6: \frac{1}{2} \bigg( 1 - \frac{1}{2n+1} \bigg); ~\frac{1}{42}
Question 7: y = \frac{1}{e}, y = 2e x + e;~ 79.6^{\circ}
Question 8: k = 13;~ r = -1, f \in \mathbb{R}, f \neq 0, S_n = \frac{1}{2} f [1 - (-1)^n], f \in \mathbb{R}, f \neq 0;~ T_{11} = 63
Question 9: w + \frac{1}{w} = 2 \cos \theta;~ k = i;~ 1
Question 10: y = 0;~ \theta = 0, \pi, 2\pi;~ \theta_1 = 0, \theta_2 = \pi; 6 \pi a^2
Question 11: \frac{d \theta}{dt} = - k(\theta - 16), \theta = 16 + 64 \bigg( \frac{1}{4} \bigg)^{t/30};24^{\circ} C~ t = 540 \text{minutes}
Question 12: Q \bigg( \frac{8}{11}, \frac{1}{11}, \frac{2}{11} \bigg), R \bigg(- \frac{37}{11}, -\frac{39}{11},- \frac{23}{11} \bigg); ~\cos \theta = \frac{11\sqrt{3}}{21}, \cos \beta = \frac{11\sqrt{510}}{255}; ~\frac{10}{3}\sqrt{3};~ k = 1.86;~ k < 1

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