2021 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: a = 4, b, -6, c = 0, d = 7
Question 2: x = -1 + \sqrt{7}, \quad x = 1 + \sqrt{5}
Question 3: y =0.5x + 3.5
Question 4: |z| = 1, \text{arg}(z) = \frac{\pi}{4}, z^2 = i; 0
Question 5: \frac{x}{(x+2)(x+3)(x+4)} = - \frac{1}{x+2} + \frac{3}{x+3} - \frac{2}{x+4}, \quad \frac{1}{6} + \frac{1}{n+3} - \frac{2}{n+4}, \quad \frac{1}{6}
Question 6: Smallest y = \frac{1}{2a}, Translate the graph of C 2a units in the negative x direction
Question 7: y = 1 + x + \frac{1}{2}x^2 + \frac{1}{3}x^3
Question 8: -x + 2z =  -3; \lambda = -1, \mu = 1, \begin{pmatrix}1\\5\\-1\end{pmatrix}, \begin{pmatrix}-3\\3\\1\end{pmatrix}; 2 \sqrt{6}
Question 9: (\frac{\pi}{4}, \frac{1}{\sqrt{2}}e^{\frac{\pi}{4}}) is maximum; V = \frac{\pi}{2}(\frac{1}{4}e^{\pi} - \frac{3}{4})
Question 10: \frac{dN}{dt} = kN, k = \frac{1}{2}\ln3, t = 4.19; N = \frac{2}{\ln 3} [(50 \ln 3 - d) e^{0.5 \ln 3 t} + d]; d > 50 \ln3; t = 5.35
Question 11: PS = 2a(\pi - \beta + \sin \beta); \beta = 1.90; 22.9, 15.1

Things that have yet to come out… Sequences and series/ definite integral/ functions, and more… All the best for paper 2!

Showing 20 comments
  • jimmy

    question 6 should be -2a in positive x-axis

  • celia

    can u do h1 math pls!!

  • Kelvin Soh

    Q4: Should z^2 be i instead?

    • KS Teng

      yes, you are right. I believe it is below in the solutions. I probably missed it out in the final numeric section. Will add in. Thank you for pointing it out.

  • tan

    do u hv the qns ppr

    • KS Teng

      so sorry, I don’t as I believe there is copyright laws involved. 🙁 But I believe reddit has it circulating.

  • Dion

    Is it possible to state the marks allocation for each part

    • KS Teng

      Hi, I believe you can go reddit and find the question paper circulating and it should help. I can’t share it as there are copyright laws involved.

  • jack

    11.b what if i did the integration correctly but put the limits wrongly? how manyy marks would i lose?

    • KS Teng

      I would say a maximum of 3 marks since it is a 6 marks question.

  • Lead

    Is there ecf for stats

    • KS Teng

      there is no ecf in mathematics, simply method and answer mark.

  • Bona

    If I didn’t simplify my expression in q2, how much marks I lose?

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