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4037/23

Additional Mathematics 4037/23 — October/November 2023

Cambridge O-Level · Calculator · worked solutions for every part, with the mark scheme

10
questions
80
marks
120
minutes

Topics Calculus · Quadratic functions · Logarithmic and exponential functions · Trigonometry · Functions · Simultaneous equations · +2 more

Q1FunctionsLogarithmic and exponential functionsFree sample

The functions f\mathrm{f} and g\mathrm{g} are defined as follows, for all real values of xx.

f(x)=2sin⁡x+3cos⁡x\mathrm{f}(x) = 2\sin x + 3\cos x g(x)=e3x−1\mathrm{g}(x) = \mathrm{e}^{3x} - 1
(a)

Find fg(0)\mathrm{fg}(0).

2M
(b)

Find gg(x)\mathrm{gg}(x).

1M
(c)

Solve the equation g−1(x)=13ln⁡5\mathrm{g}^{-1}(x) = \frac{1}{3}\ln 5.

3M

The rest of this paper

9 more questions
  • Q2Quadratic functions4M
  • Q3Logarithmic and exponential functions · Simultaneous equations9M
  • Q4Calculus6M
  • Q5Calculus8M
  • Q6Calculus · Quadratic functions9M
  • Q7Trigonometry7M
  • Q8Trigonometry · Quadratic functions10M
  • Q9Calculus · Straight-line graphs11M
  • Q10Series10M
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