STEP, MAT, TMUA: Skills for success in University Admissions Tests for Mathematics

667 Pages·2021·13.203 MB·English

by  Richard Lissaman, Tim Honeywill, David Bedford, Phil Chaffe

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ISBN: 978 1 3983 2331 5
eISBN: 978 1 3983 2219 6
© David Bedford, Phil Chaffé, Tim Honeywill and Richard Lissaman 2021.
Selected STEP questions reproduced with the permission of Cambridge
Assessment Admissions Testing.
(Permission to use the material does not imply that Cambridge Assessment
Admissions Testing endorses the content of the book/resource.)
First published in 2021 by
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Contents
How to use this book
Section 1: Getting started with problem solving
  1 An introduction to the Mathematics Admissions Tests
  2 Mathematical problem solving in admissions tests
Section 2: Problem solving in multiple choice questions
  3 Introductory number and algebra techniques
  4 Geometry and coordinate geometry
  5 Functions
  6 Calculus
  7 Graph sketching, identification and transformation
  8 Sequences and series
  9 Trigonometry
10 Logic and proof
Section 3: Problem solving in extended questions
11 Getting started with longer questions
12 Number theory and combinatorics
13 Further trigonometry
14 Calculus – integration and differential equations
15 Complex numbers
16 Matrices
Answers

How to use this book
Hello and welcome to this book about the mathematics used in admissions
tests. It is designed to grow with you from the start of your post-16
mathematics studies. The content of the early chapters will be accessible to
you even if you have not covered much in your school studies to date. As
you progress through your school course, you will be able to engage with
more and more of the book. The later chapters require knowledge from most
of a two-year course, including some further mathematics. You should
attempt each chapter as soon as you feel confident that you have covered
enough in your school mathematics lessons.
The book is in three sections
Section one describes the main mathematics admissions tests, giving
information about the papers, how they are graded, their syllabus and some
of the universities that require students to sit an admissions test or will lower
their admission requirements for good results in an admissions test.
Admissions tests are meant to be difficult and place a high value on problem
solving skills. Section one concludes with some key techniques for
developing those skills.
Section two focuses on the MAT and TMUA examinations. Students who
will be sitting the STEP examination will also find this part useful,
particularly early on in their studies. The chapters in this section cover some
key topics that frequently occur in admissions tests. There are also worked
examples accompanied by explanations of the thought processes required to
solve them. You should read these examples carefully as there are many
useful techniques within them. There are questions to try as you go along as
well as exercises to reinforce your skills. Each chapter closes with some
questions that are written in the same style as the MAT and TMUA
questions.
Section three covers the longer questions that you find on the MAT papers
and the STEP papers. Chapters 11 to 13 are aimed at students preparing for
either the MAT or STEP examinations. Chapters 14 to 16 are aimed at
students preparing for the STEP papers. Chapter 11 is an introduction to the
algebraic skills required for admissions tests and forms the bridge between
the earlier MAT and TMUA chapters and the more advanced chapters at the
end of the book. Each chapter includes annotated examples and exercises
before concluding with a MAT or STEP style question.
If at any stage you find that you are struggling with any of the problems, put
them to one side and come back to them later. It is often a good idea to let
your ideas settle before coming back to an initially intractable problem.