CHAPTER 1: Earning Money

• Gross earnings, net earnings, salary
• Wages, overtime, bonus, allowance, annual leave loading
• Spreadsheets, entering a formula, cell references
• Practical application of a spreadsheet
• Wages sheet using a spreadsheet
• Piecework
• Commission
• Chapter 1 Review Exercise

CHAPTER 2: Government Allowances and Pensions

• Age pension, payment rates, income test, work bonus
• Age pension assets test
• Youth allowance, payment rates, income test, income bank
• Austudy, payment rates, income test, income bank
• Abstudy, payment rates, income test, income bank
• Newstart allowance, payment rates, income test
• Chapter 2 Review Exercise

CHAPTER 3: Comparing Prices and Budgets

• Comparing prices, unit cost
• Budgeting, preparing a budget
• Fixed expenses, variable expenses and discretionary expenses
• Using a spreadsheet to prepare a budget
• Chapter 3 Review Exercise

CHAPTER 4: Applying Percentage

• Review of percentage, conversions, calculating a percentage of a quantity
• Finding the original amount of a quantity, percentage change
• Percentage increase and percentage decrease
• Repeated percentage change
• Goods and services tax
• Inflation
• Depreciation
• Profit and loss
• Mark ups, discount
• Chapter 4 Review Exercise

CHAPTER 5: Simple Interest

• Simple interest investments, flat interest
• Calculating principal, rate or time given simple interest
• Simple interest and spreadsheets
• Simple interest or flat rate loans
• Savings bank accounts, minimum monthly balance, daily balance
• Credit cards
• Chapter 5 Review Exercise

CHAPTER 6: Compound Interest

• Compound interest investments compounding annually
• Other compounding periods
• Comparing investments
• Compound interest loans
• Calculating principal, rate, time
• Using the financial program of a calculator
• Chapter 6 Review Exercise

CHAPTER 7: Currency Exchange Rates

• Review of rates, converting and comparing rates
• Exchange rates
• Buying and selling rates
• Currency dealer margin
• Chapter 7 Review Exercise

CHAPTER 8: Shares

• What is a share?, Share listings and prices
• Buying shares, brokerage
• Selling shares
• Dividends, dividend yield
• Price-to-earnings ratio
• Comparing share values
• Chapter 8 Review Exercise

CHAPTER 9: Algebra

• Review of the fundamentals of algebra
• Expanding indicated products
• Substitution into algebraic expressions
• Evaluating algebraic expression using a calculator
• Substitution into a formula
• Using spreadsheets
• Chapter 9 Review Exercise

CHAPTER 10: Matrices

• Terminology, types of matrices
• Matrix operations, adding and subtracting matrices
• Multiplication of matrices
• Powers of matrices
• Applications of matrices
• Application of matrices to networks, one stage routes, two stage routes
• Social networks and matrices
• Chapter 10 Review Exercise

CHAPTER 11: The Theorem of Pythagoras

• Theorem of Pythagoras, use of the theorem
• Pythagorean triples
• Applications of Pythagoras’ Theorem
• Applications of Pythagoras’ Theorem in three dimensions
• Chapter 11 Review Exercise

CHAPTER 12: Perimeter and Area

• Perimeter of polygons
• Circumference of circles
• Perimeter of sectors
• Area, area units, areas of composite shapes
• Applications
• Chapter 12 Review Exercise

CHAPTER 13: Surface Area and Volume

• Prisms, pyramids, cylinders, cones, spheres
• Surface areas of prisms and cylinders
• Surface areas of pyramids, cones and spheres
• Surface areas of composites solids
• Volume and capacity, volume and capacity units
• Volume and capacity of prisms and cylinders
• Volume and capacity of pyramids, cones and spheres
• Volume and capacity of composite solids
• Applications
• Chapter 13 Review Exercise

CHAPTER 14: Similarity

• Scale factors, similar figures
• Similar triangles , conditions for similar triangles
• Applications of similarity
• Similar figures, perimeter and area
• Surface areas and volumes of similar solids
• Scale drawings, explicit scales, ratio scales, graphical scales
• Using scales to find distances, plans and maps
• Chapter 14 Review Exercise

ANSWERS

INDEX

CHAPTER 1: Univariate Data

• Statistical terms, categorical variables
• Displaying categorical data
• Numerical variables
• Organising and displaying numerical data
• Histograms, ungrouped data
• Histograms, grouped data
• Constructing histograms
• Chapter 1 Review Exercise

CHAPTER 2: Measures of Central Tendency

• Mean, ungrouped and grouped data, advantages/disadvantages, uses, properties
• Median, ungrouped and grouped data, advantages/disadvantages, uses
• Mode, advantages/disadvantages, uses
• Measure of spread, range
• Chapter 2 Review Exercise

CHAPTER 3: Measures of Dispersion or Spread

• Range, interquartile range
• Mean deviation, variance, standard deviation
• Outliers, measures of central tendency and spread
• Identifying outliers
• Grouped data
• Chapter 3 Review Exercise

CHAPTER 4: Describing Distributions

• Modality of distributions
• Shape of distributions, location, spread, unusual features
• Displayed by dot frequency graphs
• Displayed by stem plots
• Displayed by histograms
• Chapter 4 Review Exercise

CHAPTER 5: Box Plots

• Constructing box plots
• Using a calculator to draw and investigate box plots
• Box plots and outliers
• Shape of box plots
• Box plots and histograms, advantages/disadvantages
• Parallel box plots
• Chapter 5 Review Exercise

CHAPTER 6: Comparing Data Sets

• Categorical data
• Numerical data using summary statistics
• Graphical displays
• Comparing dot plots
• Back-to-back stem and leaf plots
• Comparing histograms
• Standardised scores
• Chapter 6 Review Exercise

CHAPTER 7: Normal Distribution

• Normal distribution
• Properties of the normal curve
• The 68-95-99.7 rule
• Standard normal distribution
• Non standard normal distribution
• Quantiles
• Applications of the normal distribution
• Chapter 7 Review Exercise

CHAPTER 8: Right Triangle Trigonometry

• Sine, cosine and tangent
• Finding the length of an unknown side
• Finding the size of and unknown angle
• Angles of elevation and depression
• Bearings, applications
• Chapter 8 Review Exercise

CHAPTER 9: Non Right Angled Triangle Trigonometry

• The sine rule, finding the length of a side
• Finding the size of an angle using the sine rule
• The cosine rule
• Area of a triangle
• Area of a triangle using Heron’s formula
• Non right angled triangle applications
• Chapter 9 Review Exercise

CHAPTER 10: Solving Equations

• Equations, linear equations
• Solving linear equations:
  • inverse operations
  • multiple operations
  • variable occurring more than once
  • with parentheses
  • with fractions
• Solving linear equations using a calculator
• Algebraic expressions
• Solving number problems,
• Solving worded problems
• Chapter 10 Review Exercise

CHAPTER 11: Straight Line Graphs

• Cartesian coordinate plane, ordered pairs, straight line graphs
• Gradient and intercepts from the equation of a line in gradient-intercept form
• Gradient and intercepts from the equation of a line in general form
• Gradient and intercepts from a graph
• Gradient of a line given two points
• Gradient of a line from a table of values
• Constructing straight line graphs given:
  • a table of values
  • the equation of the line
• Equation of a straight line from a graph
• Equations of horizontal and vertical lines
• Equation of a straight line from a table of values
• Equation of a line given one point and the gradient
• Equation of a line given two points
• Using a calculator to graph lines
• Linear modelling
• Chapter 11 Review Exercise

CHAPTER 12: Simultaneous Linear Equations

• Solution of simultaneous linear equations by substitution
• Solving simultaneous equations by elimination
• Solving simultaneous equations by graphing
• Solving simultaneous equations using a calculator
• Problem solving using two variable linear equations
• Solving practical problems graphically
• Chapter 12 Review Exercise

CHAPTER 13: Piece-wise and Step Graphs

• Interval notation, graphing intervals
• Piece-wise linear graphs
• Applications of piece-wise graphs
• Step graphs
• Chapter 13 Review Exercise

ANSWERS

INDEX

CHAPTER 1: Bivariate Categorical Variables

• Variables of bivariate data distributions, categorical variables
• Explanatory variable and response variable
• Two-way frequency tables
• Percentage two-way frequency tables, whole table, row and column
• Association between categorical variables
• Segmented column graphs
• Chapter 1 Review Exercise

CHAPTER 2: Bivariate Numerical Variables

• Numerical variables
• Scattergraphs
• Linear relationships, correlation
• Measuring linear relationship, covariance, Pearson’s correlation coefficient
• Interpreting Pearson’s correlation coefficient
• Outliers and the correlation coefficient
• Association and causation, lurking variable
• Chapter 2 Review Exercise

CHAPTER 3: Linear Models for Numerical Data

• Line of best fit or regression line
• Intercepts and slope of regression lines, properties of
• The coefficient of determination, properties of
• Population and sample regression lines
• Making predictions, interpolation and extrapolation
• Outliers and regression lines
• Testing the linear regression model – residuals
• Chapter 3 Review Exercise

CHAPTER 4: Sequences

• Sequence, finite, infinite, general term
• Recurrence relations
• Calculator and sequences, spreadsheets
• Finding sequences given a term other than the first term
• First order linear recurrence relation
• Chapter 4 Review Exercise

CHAPTER 5: Arithmetic and Geometric Sequences

• Arithmetic sequences, common difference, general term
• Explicit formula, applications of
• Recurrence relations for arithmetic sequences
• Arithmetic sequences and linear functions
• Geometric sequences, common ratio, general term, explicit formula
• Recurrence relations for geometric sequences
• Geometric sequences and exponential functions
• First-order linear recurrence relations
• Displaying first-order linear recurrence relations, arithmetic and geometric
• Graphical displays of first-order recurrence relations which are neither arithmetic
• nor geometric
• Long-term steady-state solutions of first order recurrence relations
• Finding the steady-state solution of a sequence
• Chapter 5 Review Exercise

CHAPTER 6: Practical Problems involving Sequences

• Using arithmetic and geometric sequences to model practical situations
• Linear and geometric growth, simple interest investments
• Compound interest investments
• Growth applications of recurrence relations which are neither linear nor geometric
• Linear and geometric decay, loans, flat rate
• Reducing rate loans, reducible interest loan
• Bouncing balls and other applications of decay
• Chapter 6 Review Exercise

CHAPTER 7: Graph Theory

• Terms and definitions
• Representation of graphs, vertex edge sets, adjacency lists, matrices
• Drawing graphs
• Types of graphs
• Bipartite graphs
• Testing if a graph is bipartite
• Adjacency matrices, undirected graphs, directed graphs, properties
• Powers of the adjacency matrix – undirected graphs
• Powers of the adjacency matrix – directed graphs
• Planar graphs and Euler’s formula
• Platonic Solids
• Chapter 7 Review Exercise

CHAPTER 8: Paths and Cycles

• Networks, terms and definitions
• Eulerian and semi-Eulerian graphs, trials, circuits
• Hamiltonian and semi-Hamiltonian, paths, graphs, cycles
• Eulerian and Hamiltonian graphs
• Shortest path using a systematic approach
• Chapter 8 Review Exercise

ANSWERS

INDEX

CHAPTER 1: Time Series Analysis

• Time intervals, time series plots
• Components of time series
• Smoothing time series, moving averages
• Smoothing time series, centred moving averages
• Using spreadsheets
• Predictions and the moving averages, seasonal indices
• Seasonally adjusted data
• Predicting or forecasting
• Chapter 1 Review Exercise

CHAPTER 2: Compound Interest and Depreciation

• Review of simple interest and flat rate loans
• Review of compound interest formulae
• Compound interest investments and loans using recurrence relations
• Using the financial application of a calculator
• Comparing investments and loans
• Effective annual interest rate
• Inflation
• Depreciation
• Unit cost method of depreciation
• Reducing balance depreciation
• Chapter 2 Review Exercise

CHAPTER 3: Reducing Balance Loans

• Loans, flat rate loans, reducing rate loans
• Using the financial application of a calculator
• Using the amortization application of a calculator
• Comparing loans
• Changing the terms of a loan
• Chapter 3 Review Exercise

CHAPTER 4: Annuities and Perpetuities

• Annuities
• Using the financial application of a calculator
• Perpetuities
• Increasing annuity investments
• Number of payments per year ≠ number of times interest is compounded per year
• Chapter 4 Review Exercise

CHAPTER 5: Spanning Trees

• Trees
• Spanning trees
• Weighted graphs, minimum spanning trees
• Prim’s Algorithm from a graph or network
• Prim’s Algorithm from a distance table
• Chapter 5 Review Exercise

CHAPTER 6: Maximum Flow

• Directed graph, flow network
• Algorithm for determining maximum flow
• Maximum flow and minimum cut
• Chapter 6 Review Exercise

CHAPTER 7: Project Networks

• Minimum completion time, critical path
• Forward scanning, earliest starting time
• Backward scanning, latest starting time
• Finding the critical path
• Float or slack
• Construction of project networks
• Dummy activities
• Chapter 7 Review Exercise

CHAPTER 8: Assignment Problems

• Allocation of tasks
• Assignment problem
• Assignment problem involving two workers and two jobs
• Assignment problem involving three workers and three jobs
• Assignment problem involving four workers and four jobs
• The Hungarian algorithm
• Maximisation using the Hungarian algorithm
• Unbalanced assignment problems
• Chapter 8 Review Exercise

ANSWERS

INDEX