2025 A-level H2 Mathematics (9758) Paper 1 Suggested Solutions

By KS Teng

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. Click to expand.)

Question 1: u_2 = 3a + 5, u_3 = 9a + 20; a = 0.5
Question 2: d = -0.5, a = 8
Question 3: 1, \frac{\pi}{3}; iz
Question 4: \frac{dy}{dx} = \frac{1}{2}(3x - 4)(x+1)^{-1.5}, x = \frac{4}{3}; \frac{d^2y}{dx^2} = 0.421 > 0, minimum
Question 5: x \ge \ln 2; 2 \ln 2 + e + \frac{2}{e} - 4
Question 6: 1.21 \times 10^{-4}; 13300 years
Question 7: \pi(e - 2); 13.18
Question 8: \begin{pmatrix}-2\\1.5\\1.5 \end{pmatrix}; \begin{pmatrix}-1\\2\\3 \end{pmatrix}; 85.9^{\circ}
Question 9: y = px + \frac{p^3}{6}x^3 + \ldots; 1 + 4.5 x^2 + \ldots
Question 10: f^{-1}(x) = \frac{4-bx}{x+a}, R_{f^{-1}} = (-\infty, -b ) \cup ( - b, \infty); \frac{4-2a}{2+a}
Question 11: \frac{dy}{dx} = \frac{5(\sin \theta + \theta \cos \theta)}{7(\theta \sin \theta - \cos \theta)}; \theta = -0.86, 0.86; CD = 31.4; \theta = 0; \theta = \frac{\pi}{2}, - \frac{\pi}{2}; 31.4, does not satisfy given conditions
Question 12: 1-2i; p = -4, q = 9, \text{root} = 2; \frac{1}{5} + \frac{2}{5}i, \frac{1}{5} - \frac{2}{5}i, \frac{1}{2}

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2025 A-level H2 Mathematics (9758) Specimen Paper 2 Suggested SolutionsJC Mathematics, Mathematics
2025 A-level H2 Mathematics (9758) Paper 2 Suggested SolutionsJC Mathematics, Mathematics