Years 9 - 10 Maths For Students E-Book

• Herausgeber: John Wiley & Sons
• Kategorie: Bildung
• Sprache: Englisch

Seitenzahl: 537

Veröffentlichungsjahr: 2015

Beschreibung

Your tutor in a book! Master the essential mathematical skills for success! 'I don't know how to do this' is a refrain heard whilst many a student is doing homework. Parents are increasingly called on for assistance, but are themselves struggling to help their children. Years 9-10 Maths For Students is a reference guide for both students and parents, aiming to fill the gaps in a student's knowledge base, build confidence and reduce stress. Written with the same friendly, how-to approach of the successful For Dummies books, this new educational reference will empower students and develop their mathematical skills for exams, NAPLAN testing and, most importantly, life beyond secondary school. With worries that students are being taught to pass tests at the expense of understanding -- this guide will help students cement their mathematical foundations. * Grasp the nuts and bolts of numbers, algebra, geometry and measurement. * Master simple to complex maths questions, including worded problems * Complete homework and prepare for tests with confidence Save money on expensive tutors. Years 9-10 Maths For Students empowers students to improve their educational outcomes.

Leseprobe

Years 9–10 Maths for Students

Published byWiley Publishing Australia Pty Ltd42 McDougall StreetMilton, Qld 4064www.dummies.com

Copyright © 2016 Wiley Publishing Australia Pty Ltd

The moral rights of the authors have been asserted.

National Library of AustraliaCataloguing-in-Publication data:

Author:Mary Jane SterlingContributors:Ingrid Kemp, Christopher Danielson, Mark Ryan, Mark ZegarelliTitle:Years 9–10 Maths for StudentsISBN:9780730326779 (pbk.)9780730326793 (ebook)Series:For DummiesNotes:Includes index.Subjects:Mathematics — TextbooksMathematics — Study and teaching (Secondary)Mathematics — Problems, exercises, etc.Dewey Number:510.76

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Contents at a Glance

Introduction

Part I: Reviewing the Basics

Chapter 1: Assembling Your Tools

Chapter 2: Working with Whole Numbers

Chapter 3: Ups and Downs: Positive and Negative Numbers

Chapter 4: Parts of the Whole: Fractions, Decimals and Percentages

Chapter 5: Understanding Order of Operations

Part II: Algebra is Part of Everything

Chapter 6: Understanding the Basics of Algebra

Chapter 7: Working with the Variability of Variables

Chapter 8: Smaller is Better: Factoring Down

Chapter 9: Going for the Second Degree with Quadratics

Part III: Solving Algebraic Equations

Chapter 10: Establishing the Ground Rules and Solving Linear Equations

Chapter 11: Taking a Crack at Quadratic Equations

Part IV: Applying Algebra and Understanding Geometry

Chapter 12: Graphing Basics

Chapter 13: Graphing Lines, Gradients and Circles

Chapter 14: Getting Familiar with Functions

Chapter 15: Pythagoras, Trigonometry and Measurement

Chapter 16: Geometry Basics

Part V: The Part of Tens

Chapter 17: Ten Ways to Avoid Algebra Pitfalls

Index

Years 9-10 Maths for Students

Table of Contents

Introduction

About This Book

Foolish Assumptions

Icons Used in This Book

Where to Go From Here

Part I: Reviewing the Basics

Chapter 1: Assembling Your Tools

Starting with the Basics

Whole numbers: Adding, subtracting, multiplying and dividing

Parts of the whole: Fractions, decimals and percentages

Moving On to Algebra

Speaking in Algebra

Taking aim at algebra operations

What About Geometry?

Playing with Maths

Experimenting with symbols

Building models

Arguing is heaps of fun

Connecting ideas

What Parents Can Do to Help

Focusing on asking questions

Helping your child with homework (without doing the work yourself)

Becoming unstuck: What to do

Chapter 2: Getting Bigger and Smaller: Sequences, Addition and Subtraction

Adding Things Up

In line: Adding larger numbers in columns

Carry on: Dealing with two-digit answers

Take It Away: Subtracting

Columns and stacks: Subtracting larger numbers

Can you spare a ten? Borrowing to subtract

Multiplying

Signs of the times

Memorising the multiplication table

Double digits: Multiplying larger numbers

Doing Division Lickety-Split

Making short work of long division

Working through an example

Chapter 3: Ups and Downs: Positive and Negative Numbers

Showing Some Signs

Picking out positive numbers

Making the most of negative numbers

Comparing positives and negatives

Zeroing in on zero

Operating with Signed Numbers

Adding like to like: Same-signed numbers

Adding different signs

Subtracting signed numbers

Multiplying and dividing signed numbers

Working with Nothing: Zero and Signed Numbers

Chapter 4: Parts of the Whole: Fractions, Decimals and Percentages

Multiplying and Dividing Fractions

Multiplying numerators and denominators straight across

Multiplying mixed numbers

Doing a flip to divide fractions

Dividing mixed numbers

All Together Now: Adding Fractions

Finding the sum of fractions with the same denominator

Adding fractions with different denominators

Taking It Away: Subtracting Fractions

Subtracting fractions with the same denominator

Subtracting fractions with different denominators

Performing the Main Four Operations with Decimals

Adding decimals

Subtracting decimals

Multiplying decimals

Dividing decimals

Checking your answers

Converting to and from Percentages, Decimals and Fractions

Going from percentages to decimals

Changing decimals into percentages

Switching from percentages to fractions

Turning fractions into percentages

Chapter 5: Understanding Order of Operations

Ordering Operations

Applying order of operations to the main four expressions

Using order of operations in expressions with exponents and roots

Gathering Terms with Grouping Symbols

Understanding order of precedence in expressions with parentheses

Putting it all together

Checking Your Answers

Making sense or cents or scents

Plugging in to get a charge of your answer

Part II: Parts of the Whole

Chapter 6: Understanding the Basics of Algebra

Looking at the Basics: Numbers

Really real numbers

Counting on natural numbers

Wholly whole numbers

Integrating integers

Being reasonable: Rational numbers

Restraining irrational numbers

Picking out primes and composites

Deciphering the Symbols in Algebra Operations

Grouping

Defining relationships

Taking on algebraic tasks

Associating and Commuting with Expressions

Reordering operations: The commutative property

Associating expressions: The associative property

I Got the Power! Using Exponents

Understanding what exponents are

The first index law

The second index law

Getting Complicated with Exponents

The third index law: The power of zero

The fourth, fifth and sixth index laws: Powers of powers

The seventh index law: Working with negative exponents

The eighth index law

Comparing with Exponents

Taking notes on scientific notation

Exploring exponential expressions

Chapter 7: Working with the Variability of Variables

Representing Numbers with Letters

Attaching factors and coefficients

Interpreting the operations

Doing the Maths

Adding and subtracting variables

Adding and subtracting with powers

Multiplying and Dividing Variables

Multiplying variables

Dividing variables

Doing it all

Expanding Expressions

Getting your equal share

Distributing first

Adding first

Distributing Signs

Distributing positives

Distributing negatives

Reversing the roles in distributing

Mixing It Up with Numbers and Variables

Negative exponents yielding fractional answers

Working with fractional powers

Binomials and Trinomials: Distributing More Than One Term

Distributing binomials

Distributing trinomials

Multiplying a polynomial by another polynomial

Making Special Distributions

Recognising the perfectly squared binomial

Spotting the sum and difference of the same two terms

Chapter 8: Smaller is Better: Factoring Down

Beginning with the Basics

Composing Composite Numbers

Writing Prime Factorisations

Dividing while standing on your head

Getting to the root of primes with a tree

Wrapping your head around the rules of divisibility

Getting Down to the Prime Factor

Taking primes into account

Pulling out factors and leaving the rest

Getting to First Base with Factoring

Factoring out numbers

Factoring out variables

Unlocking combinations of numbers and variables

Changing factoring into a division problem

Grouping Terms

Chapter 9: Going for the Second Degree with Quadratics

The Standard Quadratic Expression

Reining in Big and Tiny Numbers

FOILing

FOILing basics

FOILed again, and again

Applying FOIL to a special product

UnFOILing

Unwrapping the FOILing package

Coming to the end of the FOIL roll

Making Factoring Choices

Combining unFOIL and the greatest common factor

Grouping and unFOILing in the same package

Factoring the Difference of Two Perfect Squares

Ending with binomials

Knowing when to quit

Part III: Solving Algebraic Equations

Chapter 10: Establishing the Ground Rules and Solving Linear Equations

Creating the Correct Setup for Solving Equations

Keeping Equations Balanced

Balancing with binary operations

Squaring both sides and suffering the consequences

Taking a root of both sides

Undoing an operation with its opposite