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, but do not fully rely on these as examinations are surprising always.
Vectors algebra, planes, APGP, DE with substitution, Complex Conjugates and Functions (Piece wise with conics). All the best.

Showing 19 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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