2020 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. Sorry, due to copyrights issues, I cannot share the paper.

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

Question 1: \begin{pmatrix}-2\\2\\-6 \end{pmatrix}; 49.2^{\circ}
Question 2: a = 5, b = 9, c = 14
Question 3: k=-9; f(x) = 3x - 4.5x^2 +4.5x^3 + \ldots
Question 4: \frac{z_1}{z_2 z_3} = \frac{\sqrt{2}}{2} \big( \cos \frac{5\pi}{12} + i \sin \frac{5 \pi}{12} \big) ; z_4 = \sqrt{2} \big( \cos \frac{\pi}{12} + i \sin \frac{\pi}{12} \big) \text{~and~} z_4 = \sqrt{2} \big( \cos -\frac{11\pi}{12} + i \sin - \frac{11\pi}{12} \big)
Question 5: \textbf{a} = k \textbf{b}; 3x -5y+2z = -5; refer to solutions below for explanation.
Question 6: t = - 8, k = 2; \text{root~} = -0.4 + 1.2i
Question 7: 2x + \frac{1}{4} \cos 4x + c; \frac{\pi^2}{4} + \frac{\pi}{8}; \frac{9}{4} \pi
Question 8: U_{30} = 47.5; 1672.5; S_{\infty} = 20; n = 18
Question 9: \{ k \in \mathbb{R}, 0 < k \le 4.5 \}; \frac{\pi}{2} - \frac{4}{3} \ln 2
Question 10: \frac{dP}{dt} = -0.03 P; P = Ae^{-0.03t} ; 0; \frac{dP}{dt} = n - 0.03P; P = \frac{100}{3} ( n - A e^{-0.03t}) ; n = 15
Question 11: x = \sqrt{4a+a^2}; \frac{\pi}{4}; 0.0801 \text{~rads} \le \theta < \frac{\pi}{2} \text{~rads}

Showing 8 comments
  • Annwj
    Reply

    I wanna read the comment

    • KS Teng
      Reply

      you will have better luck at reddit

  • Mohamed
    Reply

    For the DE question, if i got the equation wrong but the steps in ii correct and deduced that overtime population approaches 0, will i get any mark.

    • KS Teng
      Reply

      you should. But the model will probably be wrong since math in general does not carry ecf.

      • Orange94
        Reply

        does a wrong DE but correct way of solving DE get marks, thanks!

        • KS Teng
          Reply

          Given the marks distribution for the question, quite tough.. :/ Since the method to solve the DE was variable separable.

  • esther
    Reply

    regarding question 2, if i did all steps correctly just during differentiation i carelessly left out the dy dx on the product side of the equation, will there be ecf? or will the 6 marks just fly away like that 🙁 thank you for your reply and the answers!

    • KS Teng
      Reply

      i won’t just fly away. if your method to find tangents, etc are correct. there will be marks.

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