Exam (elaborations)

Compilation Booklet of Past Papers for Paper 3 - Pure Mathematics 2 & 3

31 views 0 purchase

Course
Unit 3 - Pure Mathematics 3

Institution
CIE

Book
Cambridge International AS and A Level Mathematics: Pure Mathematics 2 & 3 Coursebook

Cambridge International AS & A Level Mathematics 9709: Pure Mathematics 2 & 3 Compilation book of Past Papers for Paper 3 All past papers from 2019 to 2022

[Show more]

Preview 10 out of 796 pages

View example

Uploaded on January 25, 2023
Number of pages 796
Written in 2022/2023
Type Exam (elaborations)
Contains Answers

past papers
book
booklet
2019
2020
2021
2022
9709
cie
as level
a level
pure math 3
math
mathematics

Book Title:Cambridge International AS and A Level Mathematics: Pure Mathematics 2 & 3 Coursebook

Author(s):Sue Pemberton, Julianne Hughes

Edition:2018
ISBN:9781108407199
Edition:Unknown

Exam (elaborations)
PEARSON EDEXCEL AS AND A LEVEL MATHEMATICS PURE MATHEMATICS YEAR 1-2/AS TEXTBOOK + E-BOOK (A LEVEL MATHS AND FURTHER MATHS 2024) FORMULAS COMBINED
Interview
Quadratic Functions

Study Level
A/AS Level
Examinator
CIE
Subject
Mathematics
Unit
Unit 3 - Pure Mathematics 3

SKH392

Member since 1 year 315 documents sold

$5.37

Add to cart

Add to wishlist

100% satisfaction guarantee
Immediately available after payment
Both online and in PDF
No strings attached

Cambridge International Examinations
Cambridge International Advanced Level

CANDIDATE
NAME

CENTRE CANDIDATE
*0123456789*

NUMBER NUMBER

MATHEMATICS 9709/03
Paper 3 Pure Mathematics 3 (P3) For Examination from 2017
SPECIMEN PAPER 1 hour 45 minutes
Candidates answer on the Question Paper.
Additional Materials: List of Formulae (MF9)

READ THESE INSTRUCTIONS FIRST

Write your Centre number, candidate number and name in the spaces at the top of this page.
Write in dark blue or black pen.
You may use an HB pencil for any diagrams or graphs.
Do not use staples, paper clips, glue or correction fluid.
DO NOT WRITE IN ANY BARCODES.

Answer all the questions.
Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in
degrees, unless a different level of accuracy is specified in the question.
The use of an electronic calculator is expected, where appropriate.
You are reminded of the need for clear presentation in your answers.

At the end of the examination, fasten all your work securely together.
The number of marks is given in brackets [ ] at the end of each question or part question.
The total number of marks for this paper is 75.

This document consists of 19 printed pages and 1 blank page.

© UCLES 2016 [Turn over

, 2

1 Solve the inequality 2x − 5 > 32x + 1. [4]

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

© UCLES 2016 9709/03/SP/17

, 3

2 Using the substitution u = 3x , solve the equation 3x + 32x = 33x giving your answer correct to 3 significant
figures. [5]

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

© UCLES 2016 9709/03/SP/17 [Turn over

, 4

3 The angles 1 and & lie between 0Å and 180Å, and are such that
tan 1 − & = 3 and tan 1 + tan & = 1.
Find the possible values of 1 and &. [6]

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

© UCLES 2016 9709/03/SP/17

, 5

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

................................................................................................................................................................

© UCLES 2016 9709/03/SP/17 [Turn over

, 6

4 The equation x3 − x2 − 6 = 0 has one real root, denoted by !.

(i) Find by calculation the pair of consecutive integers between which ! lies. [2]

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

(ii) Show that, if a sequence of values given by the iterative formula
_P Q
6
xn+1 = xn +
xn
converges, then it converges to !. [2]

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

© UCLES 2016 9709/03/SP/17

, 7

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

(iii) Use this iterative formula to determine ! correct to 3 decimal places. Give the result of each
iteration to 5 decimal places. [3]

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

© UCLES 2016 9709/03/SP/17 [Turn over

, 8

5 The equation of a curve is y = e−2x tan x, for 0 ≤ x < 12 0.

dy
(i) Obtain an expression for and show that it can be written in the form e−2x a + b tan x2 , where
dx
a and b are constants. [5]

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

© UCLES 2016 9709/03/SP/17

, 9

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

(ii) Explain why the gradient of the curve is never negative. [1]

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

(iii) Find the value of x for which the gradient is least. [1]

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

© UCLES 2016 9709/03/SP/17 [Turn over

, 10

6 The polynomial 8x3 + ax2 + bx − 1, where a and b are constants, is denoted by p x. It is given that
x + 1 is a factor of p x and that when p x is divided by 2x + 1 the remainder is 1.

(i) Find the values of a and b. [5]

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

© UCLES 2016 9709/03/SP/17

The benefits of buying summaries with Stuvia:

Guaranteed quality through customer reviews

Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.

Quick and easy check-out

You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.

Focus on what matters

Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!

Frequently asked questions

What do I get when I buy this document?

You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.

Satisfaction guarantee: how does it work?

Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.

Who am I buying these notes from?

Stuvia is a marketplace, so you are not buying this document from us, but from seller SKH392. Stuvia facilitates payment to the seller.

Will I be stuck with a subscription?

No, you only buy these notes for $5.37. You're not tied to anything after your purchase.

Can Stuvia be trusted?

4.6 stars on Google & Trustpilot (+1000 reviews)

52510 documents were sold in the last 30 days

Founded in 2010, the go-to place to buy study notes for 14 years now

Start selling

Popular Universities in the United States

Popular books

Find notes and summaries for these qualifications

Seller

Exam (elaborations)

Compilation Booklet of Past Papers for Paper 3 - Pure Mathematics 2 & 3

Document information

Subjects

Connected book

More summaries for

Written for