math a level paper pure, Essays (high school) of Mathematics

math a level paper pure edexcel

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2025/2026

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Pearson Edexcel
Level 3
GCE Mathematics
Advanced Level
Paper 1 or 2: Pure Mathematics
Practice Set 6
Time: 2 hours
Paper Reference(s)
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.
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Pearson Edexcel

Level 3

GCE Mathematics

Advanced Level

Paper 1 or 2: Pure Mathematics

Practice Set 6

Time: 2 hours

Paper Reference(s)

9MA0/01 or

9MA0/

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.

___________________________________________________________________________________

6. Figure 1 shows a sketch of part of the graph y = f( x ) where Figure 1 (a) State the range of f. (1 mark) (b) Given that , where k is a constant has two distinct roots, state the possible values of k. **(7 marks)

7.** Show that f ( x ) can be written in the form , where A , B and C are constants to be found. (7 marks) ___________________________________________________________________________________

8. A ball is dropped from a height of 80 cm. After each bounce it rebounds to 70% of its previous maximum height. (a) Write a recurrence relation to model the maximum height in centimetres of the ball after each subsequent bounce. (2 marks) (b) Find the height to which the ball will rebound after the fifth bounce. (2 marks) (c) Find the total vertical distance travelled by the ball before it stops bouncing. (4 marks) (d) State one limitation with the model. **(1 mark)

9.** Solve in the range. Round your answer to 1 decimal place. **(4 marks)

10.** Use proof by contradiction to show that there is no greatest positive rational number. **(4 marks)

11.** The first three terms in the binomial expansion of are. (a) Find the values of a and b. (5 marks) (b) State the range of values of x for which the expansion is valid. (2 marks) (c) Find the value of c. (2 marks) ___________________________________________________________________________________

Figure 3 Figure 3 is a graph of the price of a stock during a 12-hour trading window. The equation of the curve is given above. (a) Show that the price reaches a local maximum in the interval. (5 marks) Figure 3 shows that the price reaches a local minimum between 9 and 11 hours after trading begins. (b) Using the Newton–Raphson procedure once and taking t 0 = 9.9 as a first approximation, find a second approximation of when the price reaches a local minimum. (6 marks)

____________________________________________________________________________

TOTAL FOR PAPER IS 100 MARKS