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# OCR A LEVEL MATHEMATICS A (H240/01)
PURE MATHEMATICS – PRACTICE PAPER 1
**Time allowed:** 2 hours
**Total marks:** 100
**Instructions to candidates**
- Use black ink. HB pencil may be used for graphs and diagrams.
- Answer all questions in the spaces provided.
- Show all working – marks may be given for correct methods even if
the final answer is wrong.
- Give non-exact answers to 3 significant figures unless otherwise stated.
---
## Section A (Short Answer) – 50 marks
**1.** State the value of \(\int \frac{1}{x} \, dx\).
[1 mark]
---
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**2.** Solve the equation \(e^{2x} - 5e^{x} + 6 = 0\), giving your
answers in exact logarithmic form.
[4 marks]
---
**3.** The curve \(C\) has equation \(y = x^3 - 3x^2 + 2\). Find the
coordinates of the stationary points and determine their nature.
[5 marks]
---
**4.** Find \(\int (2x + 1)(x - 3) \, dx\).
[3 marks]
---
**5.** A geometric progression has first term \(a = 4\) and common
ratio \(r = \frac{1}{2}\).
Find the sum to infinity.
[2 marks]
# OCR A LEVEL MATHEMATICS A (H240/01)
PURE MATHEMATICS – PRACTICE PAPER 1
**Time allowed:** 2 hours
**Total marks:** 100
**Instructions to candidates**
- Use black ink. HB pencil may be used for graphs and diagrams.
- Answer all questions in the spaces provided.
- Show all working – marks may be given for correct methods even if
the final answer is wrong.
- Give non-exact answers to 3 significant figures unless otherwise stated.
---
## Section A (Short Answer) – 50 marks
**1.** State the value of \(\int \frac{1}{x} \, dx\).
[1 mark]
---
, 2|Page
**2.** Solve the equation \(e^{2x} - 5e^{x} + 6 = 0\), giving your
answers in exact logarithmic form.
[4 marks]
---
**3.** The curve \(C\) has equation \(y = x^3 - 3x^2 + 2\). Find the
coordinates of the stationary points and determine their nature.
[5 marks]
---
**4.** Find \(\int (2x + 1)(x - 3) \, dx\).
[3 marks]
---
**5.** A geometric progression has first term \(a = 4\) and common
ratio \(r = \frac{1}{2}\).
Find the sum to infinity.
[2 marks]
