9MA0 01 Pure Mathematics 1 PDF

Preview

Summary

Mechanics and statisicsts questions to help you...

Description

Write your name here Surname

Other names

Pearson Edexcel Level 3 GCE

Centre Number

Candidate Number

Mathematics Advanced Paper 1: Pure Mathematics 1 Wednesday 6 June 2018 – Morning Time: 2 hours You must have: Mathematical Formulae and Statistical Tables, calculator

Paper Reference

9MA0/01 Total Marks

Candidates may use any calculator allowed by the regulations of the Joint Council for Qualifications. Calculators must not have the facility for symbolic algebra manipulation, differentiation and integration, or have retrievable mathematical formulae stored in them.

Instructions

black ink or ball-point pen. •• IfUsepencil is used for diagrams/sketches/graphs it must be dark (HB or B). in the boxes at the top of this page with your name, • Fill centre number and candidate number. all questions and ensure that your answers to parts of questions • Answer are clearly labelled. the questions in the spaces provided • Answer – there may be more space than you need. should show sufficient working to make your methods clear. Answers • You without working may not gain full credit. • 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 question paper. The total mark for this paper is 100. The marks each question are shown in brackets • – use this asfora 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

P58348A ©2018 Pearson Education Ltd.

1/1/1/1/1/

*P58348A0144*

Answer ALL questions. Write your answers in the spaces provided.

1 − cos 4θ 2θ sin 3θ

(3) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________

DO NOT WRITE IN THIS AREA

1. Given that θ is small and is measured in radians, use the small angle approximations to find an approximate value of

_____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________

DO NOT WRITE IN THIS AREA

_____________________________________________________________________________________

_____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________

2

*P58348A0244*

DO NOT WRITE IN THIS AREA

_____________________________________________________________________________________

DO NOT WRITE IN THIS AREA

Question 1 continued _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ DO NOT WRITE IN THIS AREA

_____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________

DO NOT WRITE IN THIS AREA

_____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ (Total for Question 1 is 3 marks)

*P58348A0344*

3

Turn over

2. A curve C has equation

(a) Find (i)

(ii)

x>0

dy dx d 2y d x2

(3)

(b) Verify that C has a stationary point when x = 4 (2)

DO NOT WRITE IN THIS AREA

y = x2 − 2x − 24 x,

(c) Determine the nature of this stationary point, giving a reason for your answer. (2) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________

DO NOT WRITE IN THIS AREA

_____________________________________________________________________________________

_____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________

4

*P58348A0444*

DO NOT WRITE IN THIS AREA

_____________________________________________________________________________________

DO NOT WRITE IN THIS AREA

Question 2 continued _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ DO NOT WRITE IN THIS AREA

_____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________

DO NOT WRITE IN THIS AREA

_____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ (Total for Question 2 is 7 marks)

*P58348A0544*

5

Turn over

3.

A

O

DO NOT WRITE IN THIS AREA

r cm θ r cm B Figure 1 Figure 1 shows a sector AOB of a circle with centre O and radius r cm. The angle AOB is θ radians. The area of the sector AOB is 11 cm2 Given that the perimeter of the sector is 4 times the length of the arc AB, find the exact value of r. (4) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________

DO NOT WRITE IN THIS AREA

_____________________________________________________________________________________

_____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________

6

*P58348A0644*

DO NOT WRITE IN THIS AREA

_____________________________________________________________________________________

DO NOT WRITE IN THIS AREA

Question 3 continued _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ DO NOT WRITE IN THIS AREA

_____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________

DO NOT WRITE IN THIS AREA

_____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ (Total for Question 3 is 4 marks)

*P58348A0744*

7

Turn over

4. The curve with equation y = 2 ln(8 − x) meets the line y = x at a single point, x = α. (2) y y=x 4

y = 2 ln(8 − x)

O

x

4

DO NOT WRITE IN THIS AREA

Figure 2 Figure 2 shows the graph of y = 2 ln(8 − x) and the graph of y = x. A student uses the iteration formula xn + 1 = 2 ln(8 − xn ),

DO NOT WRITE IN THIS AREA

(a) Show that 3 < α < 4

n∈

in an attempt to find an approximation for α. Using the graph and starting with x1 = 4 (b) determine whether or not this iteration formula can be used to find an approximation for α, justifying your answer. (2) _____________________________________________________________________________________ _________...