Jacaranda Maths Quest 11 Foundation Mathematics VCE Units 1 & 2 2e

Cover
Half tittle page
Title page
Copyright page
Contents
About this resource
Acknowledgements
Topic 1 Integers
	1.1 Overview
		1.1.1 Introduction
	1.2 Adding and subtracting integers
		1.2.1 Addition and subtraction of integers using a number line
		1.2.2 Addition and subtraction of integers using symbols
		1.2.3 Addition and subtraction of integers by applying rules
	1.3 Multiplying integers
		1.3.1 Multiplication of integers
		1.3.2 Powers, squares and square roots of integers
	1.4 Dividing integers
		1.4.1 Division of integers
	1.5 Combining operations on integers
		1.5.1 Order of operations
		1.5.2 Reasonableness
	1.6 Review
		1.6.1 Summary
	Answers
Topic 2 Fractions
	2.1 Overview
		2.1.1 Introduction
	2.2 Introducing fractions
		2.2.1 Understanding fractions
		2.2.2 Equivalent fractions
		2.2.3 Fractions on a number line
		2.2.4 Comparing fractions by using a fraction wall and number line
		2.2.5 Comparing fractions by using comparison symbols
	2.3 Simplifying fractions
		2.3.1 Simplifying fractions
		2.3.2 Simplifying mixed numbers
	2.4 Mixed numbers and improper fractions
		2.4.1 Converting improper fractions to mixed numbers
		2.4.2 Converting mixed numbers to improper fractions
	2.5 Adding and subtracting fractions
		2.5.1 Adding and subtracting proper fractions with equal denominators
		2.5.2 Adding and subtracting fractions with different denominators
	2.6 Multiplying fractions
		2.6.1 Multiplying fractions
		2.6.2 Using the word of
	2.7 Dividing fractions
		2.7.1 Dividing fractions
	2.8 Working with mixed numbers
		2.8.1 Adding and subtracting mixed numbers
		2.8.2 Checking answers by estimation
		2.8.3 Multiplying and dividing mixed numbers
	2.9 Review
		2.9.1 Summary
	Answers
Topic 3 Decimals
	3.1 Overview
		3.1.1 Introduction
	3.2 Place value and comparing decimals
		3.2.1 Whole numbers and decimal parts
		3.2.2 Comparing decimals
	3.3 Converting decimals to fractions and fractions to decimals
		3.3.1 Converting decimals to fractions
		3.3.2 Converting fractions to decimals
	3.4 Rounding and repeating decimals
		3.4.1 Rounding
		3.4.2 Rounding to the nearest 5 cents
		3.4.3 Repeating decimals
	3.5 Adding and subtracting decimals
		3.5.1 Adding decimals
		3.5.2 Subtracting decimals
	3.6 Multiplying decimals (including powers of 10)
		3.6.1 Multiplying decimals
		3.6.2 Squaring decimals
		3.6.3 Multiplying by multiples of 10
	3.7 Dividing decimals (including powers of 10)
		3.7.1 Dividing a decimal by a whole number
		3.7.2 Dividing a decimal number by a multiple of 10
		3.7.3 Dividing a decimal number by another decimal number
	3.8 Review
		3.8.1 Summary
	Answers
Topic 4 Powers and roots
	4.1 Overview
		4.1.1 Introduction
	4.2 Index (power) notation
		4.2.1 Introduction to indices (powers)
		4.2.2 Indices (powers) and place values
	4.3 Squares and square roots
		4.3.1 Square numbers
		4.3.2 Square roots
		4.3.3 Order of operations
	4.4 Using powers and roots to solve practical problems
		4.4.1 Roots
		4.4.2 Non-integer roots
		4.4.3 Pythagoras’ theorem
		4.4.4 Application of powers to problems involving growth and decay
	4.5 Review
		4.5.1 Summary
	Answers
Topic 5 Estimation and approximation
	5.1 Overview
		5.1.1 Introduction
	5.2 Rounding and estimation
		5.2.1 Rounding
		5.2.2 Estimation
	5.3 Reasonableness and calculator skills
		5.3.1 Reasonableness
		5.3.2 Calculator skills
		5.3.3 Scientific notation
	5.4 Order of magnitude
		5.4.1 What is an order of magnitude?
		5.4.2 Using orders of magnitude
		5.4.3 Scientific notation and orders of magnitude
		5.4.4 Units of measure
		5.4.5 Logarithmic scales
		5.4.6 Why use a logarithmic scale instead of a linear scale?
	5.5 Approximation
		5.5.1 Approximating calculations
		5.5.2 Approximation from graphs
	5.6 Review
		5.6.1 Summary
	Answers
Topic 6 Ratios and proportions
	6.1 Overview
		6.1.1 Introduction
	6.2 Introduction to ratios
		6.2.1 What is a ratio?
		6.2.2 Ratios as fractions
		6.2.3 Equivalent ratios
		6.2.4 Simplifying ratios
		6.2.5 Ratios and decimal numbers
	6.3 Ratios of two quantities
		6.3.1 Weight ratios
		6.3.2 Length ratios
		6.3.3 Area ratios
		6.3.4 Volume and capacity ratios
		6.3.5 Time ratios
		6.3.6 Money ratios
	6.4 Divide into ratios
		6.4.1 Divide a number of items into a ratio
		6.4.2 Dividing weights into ratios
		6.4.3 Dividing lengths into ratios
		6.4.4 Dividing areas into ratios
		6.4.5 Dividing volumes and capacities into ratios
		6.4.6 Dividing time into ratios
	6.5 Scales, diagrams and maps
		6.5.1 Introduction to scales
		6.5.2 Calculating dimensions
		6.5.3 Scale drawing
		6.5.4 Maps and scales
		6.5.5 Maps and distances
	6.6 Proportion
		6.6.1 Proportion
	6.7 Review
		6.7.1 Summary
	Answers
Topic 7 Rates
	7.1 Overview
		7.1.1 Introduction
	7.2 Identifying rates
		7.2.1 Rates
		7.2.2 Common rates
	7.3 Conversion of rates
		7.3.1 Expressing a rate in simplest form
		7.3.2 Equivalent rates
		7.3.3 Using rates
	7.4 Comparison of rates
		7.4.1 Comparing rates
	7.5 Rates and costs
		7.5.1 Costs for trades
		7.5.2 Living costs: food
		7.5.3 Living costs: transport
		7.5.4 Living costs: clothing
		7.5.5 Living costs on spreadsheets
	7.6 Review
		7.6.1 Summary
	Answers
Topic
8 Percentages
	8.1 Overview
		8.1.1 Introduction
	8.2 Calculating percentages
		8.2.1 Converting percentages to fractions
		8.2.2 Converting percentages to decimals
		8.2.3 Converting a fraction or a decimal to a percentage
		8.2.4 Determining the percentage of a given amount
		8.2.5 A shortcut for determining 10% of a quantity
	8.3 Express as a percentage
		8.3.1 Expressing one amount as a percentage of another
		8.3.2 Expressing one amount as a percentage of another for different units
		8.3.3 Percentage discounts
	8.4 Percentage decrease and increase
		8.4.1 Percentage decrease
		8.4.2 Percentage increase
		8.4.3 Repeated percentage change
	8.5 Simple interest
		8.5.1 Principal, interest and value
		8.5.2 Calculating the interest rate
	8.6 Review
		8.6.1 Summary
	Answers
Topic 9 Equations
	9.1 Overview
		9.1.1 Introduction
	9.2 Number patterns and pronumerals
		9.2.1 Number patterns
		9.2.2 Pronumerals (Variables)
		9.2.3 Terms and expressions
	9.3 Building expressions
		9.3.1 Flow charts
		9.3.2 Substituting numerical values
	9.4 Backtracking to solve equations
		9.4.1 Backtracking
	9.5 Balancing equations
		9.5.1 Keeping equations balanced
		9.5.2 Equivalent equations
	9.6 Solving equations
		9.6.1 Solving equations using inverse operations
	9.7 Rearranging formulas
		9.7.1 Rearranging formulas using backtracking
		9.7.2 Rearranging formulas using inverse operations
	9.8 Applications of equations and formulas
		9.8.1 Solving worded problems
	9.9 Review
		9.9.1 Summary
	Answers
Topic 10 Collecting and classifying data
	10.1 Overview
		10.1.1 Introduction
	10.2 Collecting data
		10.2.1 Collecting data by census
		10.2.2 Collecting data by surveys and sampling
	10.3 Simple survey procedures
		10.3.1 Surveys
	10.4 Classifying data
		10.4.1 Types of data
		10.4.2 Categorical data with numerical values
	10.5 Categorical data
		10.5.1 One-way or frequency tables
		10.5.2 Two-way frequency tables
		10.5.3 Two-way relative frequency tables
		10.5.4 Grouped column graphs
		10.5.5 Misuses of grouped column graphs
	10.6 Numerical data
		10.6.1 Displaying numerical data
		10.6.2 Dot plots
		10.6.3 Histograms
		10.6.4 Stem-and-leaf plots
	10.7 Comparing and interpreting data
		10.7.1 Back-to-back stem-and-leaf plots
		10.7.2 Choosing appropriate data representations
	10.8 Review
		10.8.1 Summary
	Answers
Topic 11 Financial systems and income payments
	11.1 Overview
		11.1.1 Introduction
	11.2 Purchasing methods
		11.2.1 Cash purchases
		11.2.2 Credit and debit cards
		11.2.3 Debit cards
		11.2.4 Personal loans
		11.2.5 The effective rate of interest
	11.3 Financial systems — permanent employment
		11.3.1 Salaries, wages and penalty rates
		11.3.2 Superannuation
		11.3.3 Annual leave loading
	11.4 Financial systems — taxation and deductions
		11.4.1 The purpose of taxation
		11.4.2 The Medicare levy
		11.4.3 Pay As You Go (PAYG) tax
	11.5 Income payments — commission, piecework and royalties
		11.5.1 Commission
		11.5.2 Salary and commissions
		11.5.3 Piecework
		11.5.4 Royalties
	11.6 Income payments and calculations
		11.6.1 Calculating percentage change
		11.6.2 Calculating tax payable
		11.6.3 Preparing a wage sheet
	11.7 Review
		11.7.1 Summary
	Answers
Topic 12 Length and area
	12.1 Overview
		12.1.1 Introduction
	12.2 SI units, length and estimation
		12.2.1 International System of Units (SI)
		12.2.2 Measuring tools
	12.3 Perimeters of familiar and composite shapes
		12.3.1 Perimeter
		12.3.2 Pythagoras’ theorem
		12.3.3 Circumference
		12.3.4 Perimeter of a sector
		12.3.5 Perimeter of composite shapes
	12.4 Units of area and estimation
		12.4.1 Conversion of area units
		12.4.2 Area of a rectangle
		12.4.3 Estimation of area
	12.5 Areas of regular shapes
		12.5.1 Areas of two-dimensional shapes
		12.5.2 Area of a circle
		12.5.3 Area of a sector
	12.6 Surface areas of familiar prisms
		12.6.1 Total surface area of a prism
		12.6.2 Total surface area of a cylinder
		12.6.3 Total surface area of a sphere
	12.7 Review
		12.7.1 Summary
	Answers
Topic 13 Volume, capacity and mass
	13.1 Overview
		13.1.1 Introduction
	13.2 Volume of prisms and capacity
		13.2.1 Volume of a right prism
		13.2.2 Volume of a cylinder
		13.2.3 Capacity
	13.3 Volume of spheres and composite shapes
		13.3.1 Volume of a sphere
		13.3.2 Volume of composite shapes
	13.4 Mass
		13.4.1 Units of mass
	13.5 Review
		13.5.1 Summary
	Answers
Topic 14 Presenting and interpreting data
	14.1 Overview
		14.1.1 Introduction
	14.2 Measures of central tendency and the outlier effect
		14.2.1 Measures of central tendency — the mean
		14.2.2 Measures of central tendency — the median
		14.2.3 Measures of central tendency — the mode
		14.2.4 Determining the mean, median and mode from a frequency distribution table
		14.2.5 Outliers and their effect on data
	14.3 Measures of spread
		14.3.1 The quantiles
		14.3.2 The range
		14.3.3 The interquartile range (IQR)
		14.3.4 The standard deviation
		14.3.5 Calculating outliers
	14.4 Describing graphical distributions
		14.4.1 Modality
		14.4.2 Shape
		14.4.3 Central tendency, spread and outliers
	14.5 Characteristics of data sets
		14.5.1 Reading and interpreting two-way tables
		14.5.2 Graphical representations of data
		14.5.3 Conversion graphs
		14.5.4 Step graphs
		14.5.5 Comparing line graphs
	14.6 Drawing and using column and pie graphs
		14.6.1 Drawing column graphs
		14.6.2 Drawing pie graphs
	14.7 Misleading graphs
		14.7.1 Methods of misrepresenting data
	14.8 Graphing and technology
		14.8.1 Drawing lines in Excel worksheets
		14.8.2 Drawing a column graph in an Excel worksheet
		14.8.3 Drawing a pie graph in an Excel worksheet
	14.9 Review
		14.9.1 Summary
	Answers
Topic 15 Managing finances
	15.1 Overview
		15.1.1 Introduction
	15.2 Products and services
		15.2.1 Internet services
		15.2.2 Health insurance
		15.2.3 Car insurance
	15.3 Rent and utilities costs
		15.3.1 Rent
		15.3.2 Electricity and gas bills
		15.3.3 Water bills
		15.3.4 Council rates
	15.4 Credit cards
		15.4.1 Credit card fees and surcharges
		15.4.2 Interest-free period
		15.4.3 Annual fees and cash advances
		15.4.4 Surcharges
		15.4.5 Comparing credit cards and personal loans
	15.5 Personal income–related expenses
		15.5.1 Youth Allowance
		15.5.2 Child Care Subsidy
		15.5.3 Age Pension
		15.5.4 Student loans
	15.6 Car expenses
		15.6.1 Planning for the purchase of a vehicle
		15.6.2 On-road costs for new and used vehicles
		15.6.3 Sustainability, fuel consumption rates, servicing and tyres
		15.6.4 Calculate and compare the cost of purchasing different vehicles using a spreadsheet
	15.7 Managing money
		15.7.1 Monthly income
		15.7.2 Fixed and variable expenses
		15.7.3 Financial planning
	15.8 Financial and economic data trends
		15.8.1 Data trends
		15.8.2 Inflation
	15.9 Review
		15.9.1 Summary
	Answers
Topic 16 Space, time and measurement
	16.1 Overview
		16.1.1 Introduction
	16.2 Conventions and geometric shapes
		16.2.1 Geometric terms
		16.2.2 Polyhedron solids
		16.2.3 Angles and triangles
		16.2.4 Quadrilaterals
	16.3 Angles and polygons
		16.3.1 Polygons
	16.4 Angles, parallel lines and transversals
		16.4.1 Parallel lines and transversals
	16.5 Constructing triangles
		16.5.1 Construct a
triangle
	16.6 Using scales
		16.6.1 Scales
	16.7 Time and temperature
		16.7.1 Time
		16.7.2 Time intervals
		16.7.3 Temperature
		16.7.4 Converting between °C and °F
	16.8 Map distances
		16.8.1 Interpreting
maps
	16.9 Directions
		16.9.1 Directions on
maps
	16.10 Speed
		16.10.1 Calculating speed
		16.10.2 Calculating distance
		16.10.3 Calculating time
	16.11 Travel
times
		16.11.1 Time of journeys
		16.11.2 Speed, distance and time of travel
	16.12 Review
		16.12.1 Summary
	Answers
GLOSSARY
INDEX