Morris S., Barnes M. Jacaranda Maths Quest General Mathematics 11 VCE Units 1&2

Milton: John Wiley & Sons Australia, Ltd, 2019. — 796 p.Half titleCopyrightAbout this resource
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AcknowledgementsKick off with CAS
Identifying linear relations
Rules for linear relations
Transposing linear equations
Solving linear equations with one variable
Substituting into linear equations
Literal linear equations
Word problems with more than one unknown
Tables of values
Linear relations defined recursively
Solving simultaneous equations graphically
Solving simultaneous equations using substitution
Solving simultaneous equations using elimination
Setting up simultaneous equations
Break-even points
Review: exam practice
Linear relations and equationsKick off with CAS
Order of operations
Directed numbers
Scientific notation
Significant figures and rounding
Exact and approximate answers
Scientific notation and orders of magnitude
Units of measure
Logarithmic scales
Why use a logarithmic scale instead of a linear scale?
Percentages
Ratios
Rates
The unitary method
Review: exam practice
Computation and practical arithmeticKick off with CAS
Calculating percentage change
Percentage dividends
Mark-ups and discounts
Goods and services tax (GST)
The simple interest formula
Calculating the principal, rate or time
Simple interest loans
Cash flow
Minimum balance calculations
Step-by-step compounding
The compound interest formula
Calculating the interest rate or principal
Non-annual compounding
Spending power
Debit cards
Personal loans
The effective rate of interest
Review: exam practice
Financial arithmeticKick off with CAS
Describing matrices
Networks
Elements of matrices
The zero matrix
Matrix addition and subtraction
Subtracting matrices
Scalar multiplication
Multiplying matrices
Multiplying by the identity matrix
Powers of square matrices
Inverse matrices
Finding inverse matrices
Using inverse matrices to solve problems
Using inverse matrices to solve a system of simultaneous equations
Using matrix equations to solve worded problems
Adjacency matrices
Determining the number of connections between objects
Review: exam practice
MatricesKick off with CAS
Graphs
The degree of a vertex
Isomorphic graphs
Characteristics of adjacency matrices
Planar graphs
Euler’s formula
Traversing connected graphs
Hamiltonian pathsand cycles
Weighted graphs
Prim’s algorithm
Review: exam practice
Graphs and networksKick off with CAS
Sequences expressed as functions
The common difference
Equations representing arithmetic sequences
Determining other values of an arithmetic sequence
Graphical displays of sequences
Drawing graphs of sequences
Simple interest
Depreciating assets
Common ratios
Equations representing geometric sequences
Determining future terms of a geometric sequence
Determining other values of a geometric sequence
Graphs of geometric sequences
Compound interest
Reducing balance depreciation
Using first-order linear recurrence relations to generate number sequences
Using a recurrence relation to generate arithmetic sequences
Spotting geometric sequences
The Fibonacci sequence
Graphing the Fibonacci sequence
Review: exam practice
SequencesKick off with CAS
Review of Pythagoras’ theorem
Pythagorean triads
Pythagoras’ theorem in three dimensions
Units of length and area
Perimeter and area of standard shapes
Heron’s formula
Composite shapes
Annulus
Sectors
Applications
Prisms
Common prisms
Cones
Pyramids
Spheres
Volumes of composite solids
Nets
Surface area formulas
Surface areas of composite solids
Review: exam practice
Shape and measurementKick off with CAS
Conditions for similarity
Similar triangles
Linear scale factors
Area scale factor
Volume scale factor
Review: exam practice
SimilarityKick off with CAS
The sine ratio
The cosine ratio
The tangent ratio
The unit circle
Extending sine and cosine to °
SOH–CAH–TOA
Angles of elevation and depression
Bearings
Bearings from A to B
Using trigonometry in bearings problems
Formulating the sine rule
The ambiguous case of the sine rule
Determining when we can use the ambiguous case
Formulating the cosine rule
Sets of sufficient information to determine a triangle
Area of triangles
Heron’s formula
Review: exam practice
Applications of trigonometryKick off with CAS
Gradient–intercept form
Determining the gradient from a graph
Finding the gradient given two points
Plotting linear graphs
Sketching graphs using the gradient and y-intercept method
Sketching graphs using the x- and y-intercepts
Solving practical problems
The domain of a linear model
Finding the equation of straight lines given two points
Creating a line of best fit when given only two points
Reliability of predictions
Piecewise linear and step graphs
Modelling with piecewise linear and step graphs
Review: exam practice
Linear graphs and modelsKick off with CAS
Graphing linear inequalities
Linear inequalities in one variable
Transposing linear inequalities
Linear inequalities in two variables
Simultaneous linear inequalities
Linear programming
Identifying the constraints in a linear programming problem
The objective function
The corner point principle
The sliding-line method
Solving linear programming problems
Review: exam practice
Inequalities and linear programmingKick off with CAS
Direct variation
Joint variation
Linearising data
Transforming data with x
Transforming data with /x
Transforming data with technology
Modelling non-linear data
Modelling with y =k/x+ c
Functions of the type y = a log(x) + c
Review: exam practice
VariationKick off with CAS
Numerical data
Frequency tables
Bar charts
The mode
Displaying numerical distributions
Histograms
Back-to-back stem plots
Dot plots
Shape
Outliers
The mean (or arithmetic mean)
Calculating the mean for grouped data
The median
Limitations of the median as a measure of centre
Choosing between measures of centre
The interquartile range
Standard deviation
Preferred measures of spread
The shape of boxplots
Identifying possible outliers
Lower and upper fences
Parallel boxplots
Review: exam practice
Investigating and comparing data distributionsKick off with CAS
Scatterplots
Correlation
Pearson’s product-moment correlation coefficient
Causation and coefficient of determination
Line of best fit by eye
Least squares regression
Manually calculating the equation for the least squares regression line
Interpreting the regression line equation
Using the regression line equation to make predictions
Limitations of regression line predictions
Review: exam practice
Relationships between two numerical variables
Overview
Revisiting recurrence relations
Modelling reducing balance loans with a recurrence relation
Amortisation of a reducing balance loan using a table
Reducing balance loan problems using the Finance Solver
Finding the payments
Finding the present value
Finding time
Finding the interest rate
Modelling an annuity using a recurrence relation
Annuity problems and the Finance Solver
The perpetuity formula
Perpetuity problems and the Finance Solver
Review: exam practice
Financial Extension