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9709/23

Mathematics 9709/23 — May/June 2021

Cambridge AS Level · Pure Mathematics 2 · worked solutions for every part, with the mark scheme

7
questions
50
marks
75
minutes

Topics Logarithmic and Exponential Functions · Trigonometry · Algebra · Differentiation · Integration · Numerical Solution of Equations

Q1Logarithmic and Exponential FunctionsTrigonometryFree sample
(a)

Solve the equation ln⁡(2+x)−ln⁡x=2ln⁡3\ln(2 + x) - \ln x = 2 \ln 3.

3M
(b)

Hence solve the equation ln⁡(2+cot⁡y)−ln⁡(cot⁡y)=2ln⁡3\ln(2 + \cot y) - \ln(\cot y) = 2 \ln 3 for 0<y<12π0 < y < \frac{1}{2}\pi. Give your answer correct to 4 significant figures.

2M

The rest of this paper

6 more questions
  • Q2Algebra5M
  • Q3Trigonometry6M
  • Q4Integration8M
  • Q5Algebra · Logarithmic and Exponential Functions7M
  • Q6Differentiation · Logarithmic and Exponential Functions8M
  • Q7Numerical Solution of Equations · Differentiation11M
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