Jacaranda Maths Quest 10 + 10A Victorian Curriculum Revised Edition

Half title page
Title page
Copyright page
Contents
About this resource
CAS support in Maths Quest
Acknowledgements
TOPIC 1 Indices
1.1 Overview
1.2 Review of index laws
1.3 Negative indices
1.4 Fractional indices
1.5 Combining index laws
1.6 Review
Answers
TOPIC 2 Algebra and equations
2.1 Overview
2.2 Substitution
2.3 Adding and subtracting algebraic fractions
2.4 Multiplying and dividing algebraic fractions
2.5 Solving simple equations
2.6 Solving multi-step equations
2.7 Literal equations
2.8 Review
Answers
TOPIC 3 Coordinate geometry
3.1 Overview
3.2 Sketching linear graphs
3.3 Determining linear equations
3.4 The distance between two points
3.5 The midpoint of a line segment
3.6 Parallel and perpendicular lines
3.7 Review
Answers
TOPIC 4 Simultaneous linear equations and inequalities
4.1 Overview
4.2 Graphical solution of simultaneous linear equations
4.3 Solving simultaneous linear equations using substitution
4.4 Solving simultaneous linear equations using elimination
4.5 Applications of simultaneous linear equations
4.6 Solving simultaneous linear and non-linear equations
4.7 Solving linear inequalities
4.8 Inequalities on the Cartesian plane
4.9 Solving simultaneous linear inequalities
4.10 Review
Answers
TOPIC 5 Trigonometry I
5.1 Overview
5.2 Pythagoras’ theorem
5.3 Pythagoras’ theorem in three dimensions
5.4 Trigonometric ratios
5.5 Using trigonometry to calculate side lengths
5.6 Using trigonometry to calculate angle size
5.7 Angles of elevation and depression
5.8 Bearings
5.9 Applications
5.10 Review
Answers
TOPIC 6 Surface area and volume
6.1 Overview
6.2 Area
6.3 Total surface area
6.4 Volume
6.5 Review
Answers
TOPIC 7 Quadratic expressions
7.1 Overview
7.2 Expanding algebraic expressions
7.3 Factorising expressions with three terms
7.4 Factorising expressions with two or four terms
7.5 Factorising by completing the square
7.6 Mixed factorisation
7.7 Review
Answers
TOPIC 8 Quadratic equations
8.1 Overview
8.2 Solving quadratic equations algebraically
8.3 The quadratic formula
8.4 Solving quadratic equations graphically
8.5 The discriminant
8.6 Review
Answers
TOPIC 9 Non-linear relationships
9.1 Overview
9.2 Plotting parabolas
9.3 Sketching parabolas
9.4 Sketching parabolas in turning point form
9.5 Sketching parabolas of the form y = ax2 + bx + c
9.6 Exponential functions and graphs
9.7 The hyperbola
9.8 The circle
9.9 Review
Answers
TOPIC 10 Deductive geometry
10.1 Overview
10.2 Angles, triangles and congruence
10.3 Similar triangles
10.4 Quadrilaterals
10.5 Polygons
10.6 Review
Answers
TOPIC 11 Probability
11.1 Overview
11.2 Review of probability
11.3 Tree diagrams
11.4 Independent and dependent events
11.5 Conditional probability
11.6 Subjective probability
11.7 Review
Answers
TOPIC 12 Univariate data
12.1 Overview
12.2 Measures of central tendency
12.3 Measures of spread
12.4 Box-and-whisker plots
12.5 The standard deviation
12.6 Comparing data sets
12.7 Review
Answers
TOPIC 13 Bivariate data
13.1 Overview
13.2 Bivariate data
13.3 Lines of best fit
13.4 Time series
13.5 Review
Answers
TOPIC 14 Statistics in the media
14.1 Overview
14.2 Populations and samples
14.3 Primary and secondary data
14.4 Evaluating inquiry methods and statistical reports
14.5 Statistical investigations
14.6 Review
Answers
TOPIC 15 Financial mathematics
15.1 Overview
15.2 Purchasing goods
15.3 Buying on terms
15.4 Successive discounts
15.5 Compound interest
15.6 Depreciation
15.7 Loan repayments
15.8 Review
Answers
TOPIC 16 Real numbers
16.1 Overview
16.2 Number classification review
16.3 Surds
16.4 Operations with surds
16.5 Fractional indices
16.6 Negative indices
16.7 Logarithms
16.8 Logarithm laws
16.9 Solving equations
16.10 Review
Answers
TOPIC 17 Polynomials
17.1 Overview
17.2 Polynomials
17.3 Adding, subtracting and multiplying polynomials
17.4 Long division of polynomials
17.5 Polynomial values
17.6 The remainder and factor theorems
17.7 Factorising polynomials
17.8 Solving polynomial equations
17.9 Review
Answers
TOPIC 18 Functions and relations
18.1 Overview
18.2 Functions and relations
18.3 Exponential functions
18.4 Cubic functions
18.5 Quartic functions
18.6 Transformations
18.7 Review
Answers
TOPIC 19 Circle geometry
19.1 Overview
19.2 Angles in a circle
19.3 Intersecting chords, secants and tangents
19.4 Cyclic quadrilaterals
19.5 Tangents, secants and chords
19.6 Review
Answers
TOPIC 20 Trigonometry II
20.1 Overview
20.2 The sine rule
20.3 The cosine rule
20.4 Area of triangles
20.5 The unit circle
20.6 Trigonometric functions
20.7 Solving trigonometric equations
20.8 Review
Answers
TOPIC 21 Programming
21.1 Overview
21.1.1 Why learn this?
21.1.2 What do you know?
21.2 Programs
21.2.1 Values
21.2.2 Variables
21.2.3 Numerical expressions
21.2.4 Assigning
21.2.5 Reassigning
21.2.6 If structure
21.2.7 If else structure
Exercise 21.2 Programs
21.3 Data structures
21.3.1 Data structures and numbers
21.3.2 Strings
21.3.3 Booleans
21.3.4 Arrays
21.3.5 Objects
21.3.6 Accessing properties
21.3.7 Pointers
21.3.8 Linked lists
Exercise 21.3 Data structures
21.4 Algorithms
21.4.1 Output
21.4.2 Comments
21.4.3 Defining a function
21.4.4 Return at any point
21.4.5 Designing an algorithm
21.4.6 Implement an algorithm
21.4.7 Linked list algorithms and empty lists
21.4.8 Remove data
21.4.9 Accessing data
Exercise 21.4 Algorithms
21.5 Matrices
21.5.1 Two-dimensional arrays
21.5.2 Array indexes
21.5.3 Matrices and arrays
21.5.4 Matrix size
21.5.5 Matrix representation
21.5.6 Matrix indexes
Exercise 21.5 Matrices
21.6 Graphics
21.6.1 Web pages
21.6.2 Canvas coordinates
21.6.3 Polygons
21.6.4 Circles
21.6.5 Colour
Exercise 21.6 Graphics
21.7 Simulations
21.7.1 Random numbers
21.7.2 For loops
21.7.3 Nested loops
21.7.4 Initialising arrays
21.7.5 The Game of Life
21.7.6 Adjacent cells
21.7.7 Matrix transforms
21.7.8 Simulation animations
Exercise 21.7 Simulations
21.8 Review
21.8.1 Review questions
Answers
Appendix CAS Calculator companion
Glossary
Index