2017 A-level H2 Mathematics (9758) Specimen 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: 0.7854 \text{cm}^2/s; 1.1781 \text{cm}^2/s
Question 2: y = \frac{1}{2}(x+2)^3 + 1,  x = 7.722
Question 3: x < -2 \text{~or~} 0 < x < 4
Question 4: 1277cm, 3400cm
Question 5: x=e^3 is a maximum, 20
Question 6: \textbf{b}+\textbf{c}=k\textbf{a}, k \in \mathbb{R};~ \bigg\{ \textbf{v} \in \mathbb{R}^3: \textbf{v} = \begin{pmatrix} 0\\0\\2 \end{pmatrix} + \lambda \begin{pmatrix}1\\0\\-3 \end{pmatrix}, \lambda \in \mathbb{R} \bigg\}
Question 7: w=0.6 + 0.2i, z = 0.5-1.5i;~-2iu\sin \theta, 2\sin \theta, \frac{\pi}{2} + \theta
Question 8: y + x \tan p = a \sin p; x^{2/3} + y^{2/3} = 1
Question 9: x = (2hR)^{0.5} \bigg( 1 + \frac{h}{2R} \bigg)^{0.5}; ~(2\alpha)^{0.5} \bigg( 1 -  0.75 \alpha \bigg);~h=3.886 \text{km}
Question 10: 2x - 3y + z = -9;~ P(-2,2, 1);~ \frac{x+2}{6} = \frac{y-2}{-11}= \frac{z-1}{-3}
Question 11: t = 14.13;~ A= 9.65;  A = \frac{10e^{at}}{4+e^{at}}

Relevant materials


KS Comments

The specimen paper 1 was useful to provide us with a glimpse of what is to be expected of the upcoming syllabus. The last two questions, in particular, showed us the extent of applications. It is definitely different from the old 9740 H2 Mathematics Syllabus as the questions are more intuitive and seek to push students’ imaginations more.

In this paper, Question 9 and Question 11 serve to be the application questions. Question 4 is a contextual/ application question that involves modelling solution. Question 8 test students on application of Mathematics and generally involves a brief statement to test the application.

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