Exam (elaborations)
A level Mathematics Practice Paper E - Pure Mathematics Without Mark scheme
- Module
- Pure Mathematics
- Institution
- PEARSON (PEARSON)
A level Mathematics Practice Paper E - Pure Mathematics Without Mark scheme
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Pearson Edexcel Level 3GCE Mathematics
Advanced Level
Paper 1 or 2: Pure Mathematics
Practice Paper Paper Reference(s)
E Time: 2 hours 9MA0/01 or 9MA0/02
You must have:
Mathematical Formulae and Statistical Tables, calculator
Candidates may use any calculator permitted by Pearson regulations. Calculators must not
have the facility for algebraic manipulation, differentiation and integration, or have
retrievable mathematical formulae stored in them.
Instructions
• Use black ink or ball-point pen.
• If pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
• Answer all questions and ensure that your answers to parts of questions are
clearly labelled.
• Answer the questions in the spaces provided – there may be more space than you need.
• You should show sufficient working to make your methods clear. Answers without
working may not gain full credit.
• Inexact answers should be given to three significant figures unless otherwise stated.
Information
• A booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
• There are 14 questions in this paper. The total mark is 100.
• The marks for each question are shown in brackets – use this as a guide as to how
much time to spend on each question.
Advice
• Read each question carefully before you start to answer it.
• Try to answer every question.
• Check your answers if you have time at the end.
• If you change your mind about an answer, cross it out and put your new answer and
any working underneath.
, Answer ALL questions.
n(n+1)
1+ 2 + 3 +... + nº
1. Prove by exhaustion that 2 for positive integers from 1 to 6
inclusive. (3 marks)
1+ sin𝜃 + tan 2𝜃 1
2. (a) When θ is small, show that the equation 2cos3𝜃 - 1 can be written as 1- 3𝜃 .
(4 marks)
(b) Hence write down the value of
1+ sin𝜃 + tan 2𝜃
2cos3𝜃 - 1 when θ is small.
(1 mark)
3. A stone is thrown from the top of a building. The path of the stone can be modelled using the parametric
2
y =8t - 4.9t +10
equations x =10t , , t 0, where x is the horizontal distance from the building in metres
and y is the vertical height of the stone above the level ground in metres.
(a) Find the horizontal distance the stone travels before hitting the ground.
(4 marks)
(b) Find the greatest vertical height.
(5 marks)
x =sec 4 y
4. Given that , find
(a)
dy
dx in terms of y. (2 marks)
dy k
=
dx x , where k is a constant which should be found.
(b) Show that
x2 - (3 marks)
1
5
f x = 6 + 32 - 7 x2
x x
5.
f x dx
(a) Find ∫
. (3 marks)
9
f x dx
(b) Evaluate ∫ 4 , giving your answer in the form
numbers.
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