Numeracy Tests Numeracy Tests For Dummies®

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Table of Contents

About This Book
Conventions Used in This Book
Foolish Assumptions
How this Book is Organised
Part I: Preparing for Your Numeracy Test
Part II: A Whistle-Stop Tour of the Maths You Need
Part III: Practice Tests
Part IV: The Part of Tens
Icons Used in This Book
Where to Go from Here
Part I: Preparing for Your Numeracy Test
Chapter 1: Getting Started
Covering the Basics
Defining numeracy
What numeracy tests typically cover
Opening Up Your Options with Numeracy Tests
Improving your chances
Examining Common Numeracy Tests
Acing ALAN
Training to be a teacher
Fighting your way into the armed forces
Helping out with the emergency services
UK Clinical Aptitude Test (UKCAT)
And the rest . . .
Reviewing Common Test Types
Mental arithmetic
Real-world maths
Handling data
Taking the Test
Knowing what to expect
Calming yourself down
Chapter 2: Putting a Practice Plan Together
Working Out What to Learn
Finding out what’s in your test
Working out what you already know
Filling in the gaps
Finding Time to Study
Making a habit of it
Finding a space for yourself
Catching Up if You Fall Behind
Being realistic
Meeting yourself where you are
Doing what you can
Revising What You Know
Boosting your confidence with the easy bits
Stretching a little further each time
Working on practice tests
Picking up the Pace
Tackling timing
Flashing cards
Speeding up a little at a time
Keeping on target
Chapter 3: Tackling Test Day
Preparing for Exam Day
Knowing where the exam is
Bringing what you need
Getting in the right frame of mind
Connecting with a Computer Test
What to expect
Magic numbers: Using the on-screen calculator
Previewing a Paper-and-Pencil Test
Answering the exam questions
Making sense of multiple choice
Approaching Tricky Questions
Explaining the problem to the bear
Considering what you’d do with the information
Keeping it tidy
Managing Your Time
Starting off gently
Moving swiftly along
Guessing when you need to
Checking your work
Part II: A Whistle-Stop Tour of the Maths You Need
Chapter 4: Refreshing Your Basic Maths
Handling Whole Numbers
Adding and subtracting
Multiplying and dividing
Roughly Speaking: Finding Approximate Answers
Rounding off with decimal places
Working roughly
Dealing with Fractions
Equivalent fractions and cancelling down
Adding and taking away fractions
Fractions of a number
Multiplying and dividing fractions
Converting between decimals and fractions
Dealing with Decimals
Adding and taking away decimals
Multiplying and dividing decimal numbers
Chapter 5: Blitzing Beyond the Basics
Perfecting Percentages and Parts of the Whole
Doing basic percentages with the Table of Joy
Percentage increase and decrease
Rattling Off Ratios
Normal ratio sums
Total ratio sums
Three-part ratios
Simplifying ratios
The Number Knowledge You Need
Bracing yourself for BIDMAS
Finding the magic formula
Number sequences
Sorting Out Statistics
Mean, median and mode
Chapter 6: Mastering Mental Arithmetic
Breaking Down the Big Four
Adding and subtracting
Multiplying and dividing
Taking stock of tens
Finding factors
Putting Percentages in their Place
Converting percentages into other forms
Finding a percentage
Percentage increase and decrease
Making Sense of Money and Time
Counting your cash
Converting your currency
Time for the 24-hour clock
How long things last
Finding start and end times
Chapter 7: Reaching Into Real-World Maths
Measuring Up with the Metric System
Weighing things up
The long and short of it
Converting between units
Showing Shapes Who’s Boss
Finding your angle
The shapes you need to know
All about area
A walk around the perimeter
How much things hold
Working with speed, distance and time
Chapter 8: Interpreting Data
Getting on Top of Graphs
Which graph to use
Battling with bar charts
Making pie charts a piece of cake
Living with line graphs
Scatter graphs
Beating box plots
Conquering cumulative frequency
Drilling into Data Tables
Tackling two-way tables
Tallying up
Dealing with data tables
Taming table sums
Moving Swiftly Along: Working with Time-Based Questions
Reading timetables
Part III: Practice Tests
Chapter 9: Mental Arithmetic Tests
Test A: Armed Forces and Emergency Services
Test A Questions
Worked Answers for Test A
Test B: ALAN
Test B Questions
Worked Answers for Test B
Test C: Qualified Teacher Status
Test C Questions
Worked Answers for Test C
Test D: General Mental Arithmetic
Test D Questions
Worked Answers for Test D
Answers at a Glance
Test A
Test B
Test C
Test D
Chapter 10: Testing Real-World Maths
Test A: British Army Technical Skills Test
Test A Questions
Worked Answers for Test A
Test B: Qualified Teacher Status Numeracy Test
Test B Questions
Worked Answers for Test B
Test C: ALAN Numeracy Exam
Test C Questions
Worked Answers for Test C
Test D: General
Test D Questions
Worked Answers for Test D
Answers at a Glance
Test A
Test B
Test C
Test D
Chapter 11: Data Handling Tests
Test A: Armed Forces Entrance Exam
Test A Questions
Worked Answers for Test A
Test B: Emergency Services Data Handling
Test B Questions
Worked Answers for Test B
Test C: ALAN Level 2 Data Handling
Questions for Test C
Worked Answers for Test C
Test D: General Data Handling
Test D Questions
Worked Answers for Test D
Answers at a Glance
Test A
Test B
Test C
Test D
Chapter 12: Advanced Data Handling Tests
Test A: Qualified Teacher Status Exam
Test A Questions
Worked Answers for Test A
Test B Questions
Worked Answers for Test B
Answers at a Glance
Test A
Test B
Chapter 13: Mixed Tests
Test A: ALAN Level 2 Qualification
Test A Questions
Worked Answers for Test A
Test B: The Army Technical Test
Test B Questions
Worked Answers for Test B
Test C: General Numeracy
Test C Questions
Worked answers for Test C
Answers at a Glance
Test A
Test B
Test C
Part IV: The Part of Tens
Chapter 14: Ten Ways to Find a Sense of Calm While Studying
Talk Yourself Up
Sit Up Straight
Breathe Like a Singer
Put Out the Welcome Mat
Make Mistakes Merrily
Work Within Limits
Make Studying a Habit
Stay Well-Fuelled
Jump Around
Warm Up Gently
Chapter 15: Ten Ways To Motivate Yourself To Study
Remember Why You’re Studying
Make Your Workspace Wonderful
Cross Off the Days
Treat Yourself
Find a Study Buddy
Get Your Friends and Family Onside
Set a Timer
Remember it’s not Forever
Give Yourself a Good Name
Think of the Outcome
Chapter 16: Ten Tips For Tackling Tough Test Questions
Read the Question
Eliminate Wrong Answers
Think of Similar Problems
Try the Answers
Explain the Question to Yourself
Use a Smart Estimate
Come Back to it Later
Break it Down into Smaller Parts
Guess Wildly
Chapter 17: Ten Ways To Make Your Exam Easier
Knowing Your Enemy
Practising the Hard Parts
Practising the Easy Parts
Keeping Your Energy Up
Accentuating the Positive
Using the Last Few Minutes
Having a Ritual
Read the Paper First
Managing Your Time
Checking Your Work and Putting it Right
Cheat Sheet

Numeracy Tests Numeracy Tests For Dummies®




About the Author

Colin Beveridge is a maths confidence coach for Flying Colours Maths, author of Basic Maths For Dummies and co-author of the Little Algebra Book.

He holds a PhD in Mathematics from the University of St Andrews and worked for several years on NASA’s Living With A Star project at Montana State University, where he came up with an equation which is named after him. It’s used to help save the world from being destroyed by solar flares. So far so good.

He became tired of the glamour of academia and returned to the UK to concentrate on helping students come to terms with maths and show that not all mathematicians are boring nerds; some are exciting, relatively well-adjusted nerds.

Colin lives in Poole, Dorset with an espresso pot, several guitars and nothing to prove. Feel free to visit his website at or follow him on Twitter at


For my students and teachers, past and present.

Author’s Acknowledgements

I’m very grateful to the team at Dummies Towers for their help and guidance, especially my editors Rachael Chilvers and Mike Baker.

The Little Red Roaster coffee shop in Parkstone provided the enormous quantities of excellent coffee needed to turn half-baked ideas into a fully-formed book; without Martin Stellar’s hospitality and flakey internet connection, it would have taken twice as long to write. I’m thankful to the students who helped me to shape this book, especially Julie Carter, Phil Jewell and Rebecca Murray.

And as always, I thank my parents – Linda Hendren and Ken Beveridge – for their endless support and encouragement. 

Publisher’s Acknowledgements

We’re proud of this book; please send us your comments through our Dummies online registration form located at

Some of the people who helped bring this book to market include the following:

Commissioning, Editorial, and Media Development

Project Editor: Rachael Chilvers

Commissioning Editor: Mike Baker

Assistant Editor: Ben Kemble

Technical Editors: Sam Harrison and Giles Webberley

Proofreader: James Harrison

Production Manager: Daniel Mersey

Publisher: David Palmer

Cover Photo: © iStock / CTR design LLC

Cartoons: Ed McLachlan

Composition Services

Project Coordinator: Kristie Rees

Layout and Graphics: Sennett Vaughan Johnson, Lavonne Roberts, Erin Zeltner

Proofreader: Lindsay Amones

Indexer: BIM Indexing & Proofreading Services

Publishing and Editorial for Consumer Dummies

Kathleen Nebenhaus, Vice President and Executive Publisher

Kristin Ferguson-Wagstaffe, Product Development Director

Ensley Eikenburg, Associate Publisher, Travel

Kelly Regan, Editorial Director, Travel

Publishing for Technology Dummies

Andy Cummings, Vice President and Publisher

Composition Services

Debbie Stailey, Director of Composition Services


Hi, I’m Colin, and I want maths to be easy for you.

I don’t want to turn you into a geek like me – I couldn’t if I tried. I don’t want to cram maths down your throat, either – that would be pretty rude.

All I want to do is help you learn enough maths to do well in your numeracy test and to feel confident tackling the kinds of maths problems that will come up in your future career and/or studies.

As you work through this book, answering the questions will get quicker and easier with time and practice, and you’ll be in great shape for your numeracy test. Once you have that, you may never have to do another maths test again! Here’s hoping!

I’d love to hear how you get on. The best way to catch me is on Twitter (I’m – I’ll read your news and get back to you if I can!

About This Book

This book is for you if you have to take a numeracy test in order to follow your chosen career path or to qualify for further study.

I take you through the maths you need to know to do well in these tests and try to help you understand how it all fits together.

Maths might sometimes look like a chaotic system of funny symbols and bizarre rules, but it’s actually a very neat and concise way to communicate information.

I break down maths into smaller, simpler parts that I hope you’ll understand.

Among other things, I cover the following in this book:

check.png Preparing for your test – both for studying and for keeping yourself calm while you sit it.

check.png Working with whole numbers the ‘big four’ of adding, subtracting, multiplying and dividing are pretty much the key to doing well in numeracy tests.

check.png Handling maths on paper – the dreaded ‘mental arithmetic’ questions don’t have to be dreadful!

check.png Dealing with decimals and fractions – these are easier than they seem, honestly! You already use decimals every time you do anything with money, and you only need to know a few fraction rules.

check.png Making sense of measurements – you may have a head start here! If you’ve ever used a scale, a clock or a ruler, you have some idea of how measurements work.

check.png Getting on top of graphs and tables – reading data in a neat table or graph is normally easier than from a raw, disorganised list. Once you figure out the rules, you’re off to the races!

That sounds like fun, doesn’t it?

Conventions Used in This Book

I keep the conventions to a minimum in this book. Here are the ones I use:

check.png I use italics for emphasis or to highlight new words or phrases.

check.png Boldfaced text indicates key words in bulleted lists or the key steps of action lists.

check.png Monotype font is used for Internet and email addresses.

Foolish Assumptions

Making assumptions is always a risky business, but knowing where I’m coming from may put you at ease. So, in writing this book, I assume that:

check.png You know how to count and are familiar with the basic maths symbols.

check.png You understand the idea of money and changing a banknote for an equivalent value of coins or smaller notes.

check.png You know what the basic shapes look like.

check.png You’re prepared to think fairly hard about maths and want either to pass a numeracy qualification or to simply brush up on your maths skills.

How this Book is Organised

Like all For Dummies books, Numeracy Tests For Dummies is a reference book, and each topic is allotted its own part in the book. Within each part are individual chapters relating specifically to the topic in question.

Part I: Preparing for Your Numeracy Test

Part I is all about setting yourself up so that when you sit your exam you’ll find it relatively easy to stay calm and show what you can do.

You’ll learn about the various types of numeracy tests, what’s in them and why you need to sit one, as well as how to prepare properly and what you need to do on test day.

Part II: A Whistle-Stop Tour of the Maths You Need

This part is a quick but thorough guide to all the maths you need to know for your numeracy test. I cover:

check.png Working with whole numbers – the building blocks of maths and really, the key to doing well in any numeracy test.

check.png Dealing with decimals, fractions and percentages – a traditional stumbling block, but I show you how to deal with them quickly and confidently.

check.png Making sense of measures – nothing is particularly difficult about working with measurements (such as kilograms, miles and litres) compared to working with real numbers: all you need to remember is how to convert between units and you’re most of the way there.

check.png Getting to grips with graphs and statistics – once you nail the vocabulary and remember how to work out the different types of average, you’ll know pretty much all you need to.

check.png Handling sums in your head – many numeracy tests have a non-calculator component, in which you have to work out the sums on paper or a whiteboard. I take you through some of the tricks of the trade for doing well in this type of test.

Part III: Practice Tests

Part III is all about checking what you know! In this part, I give you a whole range of tests on the various levels and topics so you can figure out what you can do already, and what you need to spend a bit more time studying.

The tests are followed by worked answers, where I explain how I reached the solution I came up with.

Part IV: The Part of Tens

All For Dummies books finish with ‘The Part of Tens’, a bunch of lists full of practical tips to help you manage the material in the rest of the book.

I run you through ways of calming down and some ideas for remembering your number facts. I show you how to deal with some of the tougher questions examiners may set, and I offer some exam-technique tips so you can get in there and ace it.

Icons Used in This Book

Here are the icons I use to draw your attention to particularly noteworthy paragraphs:

Tip.eps Theories are fine, but anything marked with a Tip icon in this book tells you something practical to help you get to the right answer. These are the tricks of the mathematical trade.

remember.eps Paragraphs marked with the Remember icon contain the key takeaways from the book and the essence of each subject.

warning_bomb.eps The Warning icon highlights errors and mistakes that can cost you marks or your sanity, or both.

technicalstuff.eps You can skip anything marked with the Technical Stuff icon without missing out on the main message, but you may find the information useful for a deeper understanding of the subject.

Where to Go from Here

Now, no two numeracy exams are the same, and the different tests range over quite different types of content. Before you start studying a section, it’s a good idea to make sure it’s part of the test you’re working towards! Head to Chapter 1 for an explanation of what you’re likely to find in each test. If you’re in a hurry to see where you are, you may want to jump straight into the tests in Chapters 9–13. On the other hand, if you have plenty of time before you start the exam, you may prefer to start with Chapter 2 and set yourself up with a detailed study plan.

You can also use the index and Table of Contents to find the areas you want to study. This book is a reference – keep it with your maths kit and turn to it whenever you have something you want to look up!

I wish you the very best in your numeracy exam, and hope this book helps you to get the best mark you can. Good luck!

Part I

Preparing for Your Numeracy Test


In this part . . .

Whatever kind of numeracy test you’re taking, you need a solid plan of action for studying and for doing well in the exam. These chapters give you an idea of what each type of numeracy test involves, ways you can organise yourself to give yourself the best chance, and suggestions for how to handle exam day so you can make the most of your time in the test.