Pearson Edexcel Level 3 GCE

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Candidate surname

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Centre Number

Candidate Number

Pearson Edexcel Level 3 GCE

Wednesday 6 October 2021 ? Afternoon

Time 2 hours

Paper reference

Mathematics

Advanced

PAPER 1: Pure Mathematics 1

9MA0/01

You must have: Mathematical Formulae and Statistical Tables (Green), calculator

Total Marks

Candidates may use any calculator allowed by Pearson regulations. Calculators must not have the facility for symbolic algebra 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). ?? Fill in the boxes at the top of this page with your name, ? centre number and candidate number.

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 15 questions in this question paper. The total mark for this paper 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.

Turn over

P68731A

?2021 Pearson Education Ltd.

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1.

f(x) = ax3 + 10x2 - 3ax - 4

Given that (x - 1) is a factor of f(x), find the value of the constant a.

You must make your method clear. (3)

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2

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Question 1 continued _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________

(Total for Question 1 is 3 marks)

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3

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2. Given that

f(x) = x2 - 4x + 5x

(a) express f(x) in the form (x + a)2 + b where a and b are integers to be found. (2)

The curve with equation y = f(x) ? meets the y-axis at the point P ? has a minimum turning point at the point Q

(b) Write down

(i) the coordinates of P

(ii) the coordinates of Q (2)

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4

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Question 2 continued _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________

(Total for Question 2 is 4 marks)

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3. The sequence u1, u2, u3,... is defined by 24

un+1 = k - un u1 = 2 where k is an integer.

Given that u1 + 2u2 + u3 = 0 (a) show that

3k2 - 58k + 240 = 0 (3)

(b) Find the value of k, giving a reason for your answer. (2)

(c) Find the value of u3 (1)

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Question 3 continued _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________

(Total for Question 3 is 6 marks)

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4. The curve with equation y = f(x) where

f(x) = x2 + ln(2x2 - 4x + 5)

has a single turning point at x =

(a) Show that is a solution of the equation

2x3 - 4x2 + 7x - 2 = 0 (4)

The iterative formula

1 xn+1 = 7 (2 + 4xn2 - 2xn3)

is used to find an approximate value for .

Starting with x1 = 0.3 (b) calculate, giving each answer to 4 decimal places,

(i) the value of x2 (ii) the value of x4

(3)

Using a suitable interval and a suitable function that should be stated,

(c) show that is 0.341 to 3 decimal places. (2)

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