Jacaranda Maths Quest 12 Foundation Mathematics VCE Units 3 & 4 1e

Cover
Half tittle page
Title page
Copyright page
Contents
About this resource
Acknowledgements
Topic 1 Calculations
	1.1 Overview
		1.1.1 Introduction
	1.2 Number operations
		1.2.1 Practical numerical problems
	1.3 Order of operations
		1.3.1 Rules for the order of operations
	1.4 Rounding
		1.4.1 Rounding integers
		1.4.2 Floor and ceiling values
		1.4.3 Rounding decimals
	1.5 Estimation and approximation strategies
	1.6 Decimals and fractions
		1.6.1 Decimal place value
		1.6.2 Comparing decimals
		1.6.3 Adding and subtracting decimals
		1.6.4 Multiplying by powers of 10
		1.6.5 Dividing by powers of 10
		1.6.6 Converting decimals to fractions
		1.6.7 Converting fractions to decimals
	1.7 Rational and irrational numbers
		1.7.1 Rational and irrational numbers
		1.7.2 Roots
		1.7.3 Surds
		1.7.4 Multiplying and dividing surds
		1.7.5 Simplifying surds
		1.7.6 Entire surds
		1.7.7 The irrational number ????
		1.7.8 Rounding rational and irrational numbers to decimal places
		1.7.9 Rounding to significant figures
	1.8 Review
		1.8.1 Summary
	Answers
Topic 2 Ratios, proportion and variation
	2.1 Overview
		2.1.1 Introduction
	2.2 Direct variation (proportion)
	2.3 Direct variation (proportion) and ratios
	2.4 Partial variation (proportion)
	2.5 Inverse variation (proportion)
	2.6 Ratios
	2.7 Ratio and proportion
	2.8 Dividing in a given ratio
	2.9 Review
		2.9.1 Summary
	Answers
Topic
3 Percentages
	3.1 Overview
		3.1.1 Introduction
	3.2 Converting percentages
		3.2.1 Percentages
		3.2.2 Converting between fractions, decimals and percentages
	3.3 Percentage quantities and percentage error
		3.3.1 Calculating the percentage of an amount
		3.3.2 Percentage error
	3.4 Application of percentages
		3.4.1 Discount, sale prices and profit
		3.4.2 Expressing one amount as a percentage of another
	3.5 Profit and loss
		3.5.1 Cost price, selling price and percentages
		3.5.2 Selling price
	3.6 Review
		3.6.1 Summary
	Answers
Topic
4 Linear and simultaneous equations
	4.1 Overview
		4.1.1 Introduction
	4.2 Algebraic substitution and transposition
		4.2.1 Substitution
		4.2.2 Formulas
		4.2.3 Changing the subject of a formula
		4.2.4 Solving problems involving formulas
	4.3 Linear equations
		4.3.1 Solving linear equations
		4.3.2 Equations with variables on both sides
		4.3.3 Developing equations from a word description
	4.4 Linear modelling
		4.4.1 Introduction
	4.5 Solving simultaneous equations graphically
		4.5.1 Introduction
		4.5.2 Special cases of simultaneous equations
	4.6 Solving simultaneous equations by substitution
		4.6.1 Introduction
	4.7 Solving simultaneous equations by elimination
		4.7.1 The elimination method
		4.7.2 Multiplying equations to solve using the elimination method
		4.7.3 Problem-solving with simultaneous equations
	4.8 Review
		4.8.1 Summary
	Answers
Topic 5 Data collection and organisation
	5.1 Overview
		5.1.1 Introduction
	5.2 Types of data
		5.2.1 Types of data
	5.3 Collecting, organising and displaying data
		5.3.1 Data collection
		5.3.2 Organising data
		5.3.3 Displaying data
		5.3.4 Spreadsheets — Displaying numerical data
	5.4 Histograms and frequency polygons
		5.4.1 Displaying data using frequency histograms
	5.5 Contemporary representation of data
		5.5.1 Pictograms
		5.5.2 Bubble charts
		5.5.3 Mekko charts
		5.5.4 Radar charts
		5.5.5 Sunburst charts
		5.5.6 Heat maps
		5.5.7 Area charts
	5.6 Stem-and-leaf plots
		5.6.1 Stem-and-leaf plots
		5.6.2 Class size of a stem-and-leaf plot
		5.6.3 Stem-and-leaf plot: medians and quartiles
	5.7 Five-number summary and boxplots
		5.7.1 Boxplots (box-and-whisker plots)
	5.8 Graphical methods of misrepresenting data
		5.8.1 Methods of misrepresenting data
		5.8.2 Spreadsheets creating misleading graphs
	5.9 Review
		5.9.1 Summary
	Answers
Topic 6 Measures of central tendency and spread
	6.1 Overview
		6.1.1 Introduction
	6.2 Measures of central tendency
		6.2.1 Mean and median
		6.2.2 The mode
		6.2.3 Measures of central tendency in dot plots and stem plots
		6.2.4 Measures of central tendency in frequency distribution tables
		6.2.5 Measures of central tendency in real-world contexts
		6.2.6 Grouped data
	6.3 Measures of spread
		6.3.1 Spread
		6.3.2 Quartiles, deciles and percentiles
		6.3.3 The range and interquartile range
		6.3.4 The standard deviation
	6.4 Outliers
		6.4.1 Introduction
		6.4.2 The effect of outliers on the mean and median
	6.5 Applications of measures of central tendency
	6.6 Review
		6.6.1 Summary
	Answers
Topic
7 Comparing data sets and long-term prediction
	7.1 Overview
		7.1.1 Introduction
	7.2 Constructing boxplots
		7.2.1 Five-number summary
		7.2.2 Boxplots
		7.2.3 Interpreting a boxplot
		7.2.4 Identification of outliers
	7.3 Comparing parallel boxplots
	7.4 Comparing back-to-back stem plots
	7.5 Comparing histograms
		7.5.1 Frequency histograms
		7.5.2 Describing the shape of a histogram
	7.6 The line of best fit
		7.6.1 Fitting a line of best fit by eye
		7.6.2 Determining the equation of a line of best fit
	7.7 Making predictions using a line of best fit
		7.7.1 Methods of creating a line of best fit
		7.7.2 Algebraic predictions
		7.7.3 Graphical predictions
		7.7.4 Reliability of predictions
	7.8 Review
		7.8.1 Summary
	Answers
Topic
8 Simulations and simple probability
	8.1 Overview
		8.1.1 Introduction
	8.2 Theoretical probability and sample spaces
		8.2.1 The probability scale
		8.2.2 Sample spaces
		8.2.3 Calculating theoretical probability
		8.2.4 The complement of an event
	8.3 Multi-stage experiments
		8.3.1 Arrays
		8.3.2 Tree diagrams
	8.4 Relative frequency, simulations and long-term data
		8.4.1 Relative frequency
		8.4.2 Simulations
		8.4.3 Using technology to perform simulations
		8.4.4 Factors that could complicate simulations
		8.4.5 Using relative frequencies: polls
		8.4.6 Calculating the number of successful trials
		8.4.7 Long-term data
	8.5 Review
		8.5.1 Summary
	Answers
Topic
9 Interest and loans
	9.1 Overview
		9.1.1 Introduction
	9.2 Simple interest
		9.2.1 Introducing simple interest
		9.2.2 Rearranging the simple interest formula
	9.3 Compound interest
		9.3.1 Compound interest investment or loan
		9.3.2 Non-annual compounding
		9.3.3 Using a spreadsheet to calculate compound interest
	9.4 Comparing simple and compound interest
		9.4.1 Simple interest or compound interest?
		9.4.2 Graphing simple interest functions
		9.4.3 Graphing compound interest functions
	9.5 Comparing interest, rental and loan costs
		9.5.1 Interest paid on loans
		9.5.2 Rent
		9.5.3 Comparing rental and loan costs
	9.6 Review
		9.6.1 Summary
	Answers
Topic
10 Financial and consumer mathematics
	10.1 Overview
		10.1.1 Introduction
	10.2 Taxation and superannuation
		10.2.1 Council rates
		10.2.2 Superannuation
		10.2.3 Income tax
		10.2.4 Tax deductions
		10.2.5 Medicare levy
		10.2.6 Calculating tax
	10.3 Business income and expenditure
		10.3.1 Goods and services tax (GST)
		10.3.2 Invoices
		10.3.3 Leave entitlements
		10.3.4 Preparing a wage sheet
	10.4 Financial products
		10.4.1 Mobile phones
		10.4.2 Insurance
		10.4.3 Hire purchase
	10.5 Financial and economic data
		10.5.1 The exchange rate
		10.5.2 Inflation
		10.5.3 Data trends
	10.6 Review
		10.6.1 Summary
	Answers
Topic
11 Scales, plans and models
	11.1 Overview
		11.1.1 Introduction
	11.2 Reading and interpreting scale drawings
		11.2.1 Scale and scale factor
		11.2.2 Maps and scales
		11.2.3 Scale factor
	11.3 Calculating measurements from scale drawings
		11.3.1 Perimeters
		11.3.2 Areas
		11.3.3 Problem-solving with scale drawings
	11.4 Creating scale drawings
		11.4.1 Calculating the dimensions of the drawing
		11.4.2 Constructing scale drawings
		11.4.3 Labelling scale drawings
	11.5 Review
		11.5.1 Summary
	Answers
Topic 12 Right-angled triangles
	12.1 Overview
		12.1.1 Introduction
	12.2 Pythagoras’ theorem
		12.2.1 Introduction
		12.2.2 Shorter sides of right-angled triangles
		12.2.3 Using Pythagoras’ theorem to solve real-world problems
	12.3 Trigonometric ratios — sine, cosine and tangent
		12.3.1 The sine ratio
		12.3.2 The cosine ratio
		12.3.3 The tangent ratio
		12.3.4 Inverse trigonometric functions
	12.4 Calculating unknown side lengths of right-angled
triangles
		12.4.1 Remembering trigonometric ratios
		12.4.2 Determining trigonometric ratios
		12.4.3 Solving practical problems
	12.5 Calculating unknown angles in right-angled
triangles
		12.5.1 Introduction
		12.5.2 Solving practical problems
	12.6 Angles of elevation and depression
		12.6.1 Solving problems involving angles of elevation and depression
		12.6.2 Calculating angles of elevation and depression
	12.7 Review
		12.7.1 Summary
	Answers
Topic
13 Measurement
	13.1 Overview
		13.1.1 Introduction
	13.2 Units of measurement
		13.2.1 Units of measurement
		13.2.2 Taking measurements
		13.2.3 Converting between units of measurements
	13.3 Areas of composite figures
		13.3.1 Sum of areas
		13.3.2 Difference between areas
	13.4 Surface areas of pyramids and irregular solids
		13.4.1 Review of total surface area
		13.4.2 Total surface area of a cone
		13.4.3 Total surface area of a pyramid
		13.4.4 Surface area of a composite shape
	13.5 Limits of accuracy
		13.5.1 Accuracy
		13.5.2 Limits of accuracy
		13.5.3 Types of error
		13.5.4 Accuracy of measurement
		13.5.5 The absolute error
		13.5.6 Percentage error
	13.6 Scientific notation and significant figures
		13.6.1 Scientific notation
		13.6.2 Measuring very large and very small units using
scientific notation
		13.6.3 Significant figures
	13.7 Review
		13.7.1 Summary
	Answers
Topic 14 Volume
	14.1 Overview
		14.1.1 Introduction
	14.2 Review of volume of prisms, units of volume and capacity
		14.2.1 Units of volume
		14.2.2 Capacity
		14.2.3 Volume of prisms
	14.3 Volume of cylinders and spheres
		14.3.1 Volume of a cylinder
		14.3.2 Volume of spheres
	14.4 Volume of composite shapes
		14.4.1 Volume of composite shapes
	14.5 Review
		14.5.1 Summary
	Answers
Topic
15 Shapes
	15.1 Overview
		15.1.1 Introduction
	15.2 Polygons
		15.2.1 Introduction
		15.2.2 Constructing polygons
	15.3 Transformations
		15.3.1 Transformations
		15.3.2 Translations
		15.3.3 Reflections
		15.3.4 Rotations
	15.4 Similarity
		15.4.1 Similar figures
	15.5 Symmetry
		15.5.1 Axes of symmetry
		15.5.2 Rotational symmetry
	15.6 Review
		15.6.1 Summary
	Answers
GLOSSARY
INDEX