Exam (elaborations)
Preparing for A level (A guaranteed)
- Course
- Institution
- Book
Preparing for A level Mathematics 9709 Workbook. Questions and Answers included.
[Show more]
Connected book
Book Title:
Author(s):
- Edition:
- ISBN:
- Edition:
More summaries for
-
Cambridge International AS & A Level Mathematics
-
Pure Mathematics
-
Pure Math Notes
Seller
Follow
SKH392
Reviews received
Content preview
You will sit two papers, one in Pure Mathematics (P1) and one in Statistics (S1) at the end of year12. These are followed by another Pure paper (P3) and a Mechanics paper (M1) in year 13.
The Mathematics Department is committed to ensuring that you make good progress throughout
your A level or AS course. In order that you make the best possible start to the course, we have
prepared this booklet.
It is vitally important that you spend some time working through the questions in this booklet over
the summer - you will need to have a good knowledge of these topics before you commence your
course in September. You should have met all the topics before at iGCSE. Work through the
introduction to each chapter, making sure that you understand the examples. Then tackle the
exercise – not necessarily every question, but enough to ensure you understand the topic
thoroughly. The answers are given at the back of the booklet.
A mock test is provided at the back of this booklet.
We hope that you will use this introduction to give you a good start to your AS work and that it will
help you enjoy and benefit from the course more.
Sources for further help are indicated throughout the booklet. You may also find the following
book useful
AS-Level Maths Head Start
Published by CGP Workbooks
ISBN: 978 1 84146 993 5
Cost: £4.95
CONTENTS
Chapter 1 Removing brackets page 3
Chapter 2 Linear equations 5
Chapter 3 Simultaneous equations 9
Chapter 4 Factors 11
Chapter 5 Change the subject of the formula 14
Chapter 6 Solving quadratic equations 17
Chapter 7 Indices 19
Dr A Duncombe 1
,Chapter 1: REMOVING BRACKETS
To remove a single bracket, we multiply every term in the bracket by the number or the expression
on the outside:
Examples
1) 3 (x + 2y) = 3x + 6y
2) -2(2x - 3) = (-2)(2x) + (-2)(-3)
= -4x + 6
To expand two brackets, we must multiply everything in the first bracket by everything in the
second bracket. We can do this in a variety of ways, including
* the smiley face method
* FOIL (Fronts Outers Inners Lasts)
* using a grid.
Examples:
1) (x + 1)(x + 2) = x(x + 2) + 1(x + 2)
or
(x +1)(x + 2) = x2 + 2 + 2x + x
= x2 + 3x +2
or
x 1 (x +1)(x + 2) = x2 + 2x + x + 2
x x2 x = x2 + 3x +2
2 2x 2
2) (x - 2)(2x + 3) = x(2x + 3) - 2(2x +3)
= 2x2 + 3x – 4x - 6
= 2x2 – x – 6
or
(x - 2)(2x + 3) = 2x2 – 6 + 3x – 4x = 2x2 – x – 6
or
x -2 (2x +3)(x - 2) = 2x2 + 3x - 4x - 6
2x 2x2 -4x = 2x2 - x - 6
3 3x -6
Dr A Duncombe 2
, EXERCISE A Multiply out the following brackets and simplify.
1. 7(4x + 5)
2. -3(5x - 7)
3. 5a – 4(3a - 1)
4. 4y + y(2 + 3y)
5. -3x – (x + 4)
6. 5(2x - 1) – (3x - 4)
7. (x + 2)(x + 3)
8. (t - 5)(t - 2)
9. (2x + 3y)(3x – 4y)
10. 4(x - 2)(x + 3)
11. (2y - 1)(2y + 1)
12. (3 + 5x)(4 – x)
Two Special Cases
Perfect Square: Difference of two squares:
(x + a)2 = (x + a)(x + a) = x2 + 2ax + a2 (x - a)(x + a) = x2 – a2
(2x - 3)2 = (2x – 3)(2x – 3) = 4x2 – 12x + 9 (x - 3)(x + 3) = x2 – 32
= x2 – 9
EXERCISE B Multiply out
1. (x - 1)2
2. (3x + 5)2
3. (7x - 2)2
4. (x + 2)(x - 2)
5. (3x + 1)(3x - 1)
6. (5y - 3)(5y + 3)
More help on expanding brackets is available by downloading this video tutorial:
http://stream.port.ac.uk/streams/play/play.asp?id=465&stream=MediumBand
Dr A Duncombe 3
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 $5.74. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
73314 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now