Maths in Focus 11 & 12 have been rewritten and updated to cover the new senior mathematics courses: Advanced and Mathematics Extension 1 & 2. The student book includes graded exercises with multiple-choice questions and realistic applications, while the included Investigations allow students to explore the syllabus in more detail, providing ideas for research projects and modelling activities.
Author(s): Margaret Grove
Edition: 3
Publisher: Cengage Learning Australia
Year: 2018
Language: English
Pages: 830
City: South Melbourne, Victoria
Tags: HSC
Title
Contents
1. ALGEBRAIC TECHNIQUES
1.01 Index laws
1.02 Zero and negative indices
1.03 Fractional indices
1.04 Simplifying algebraic expressions
1.05 Expansion
1.06 Binomial products
1.07 Special products
1.08 Factorisation
1.09 Factorisation by grouping in pairs
1.10 Factorising trinomials
1.11 Further trinomials
1.12 Perfect squares
1.13 Difference of two squares
1.14 Mixed factorisation
1.15 Simplifying algebraic fractions
1.16 Operations with algebraic fractions
1.17 Substitution
1.18 Simplifying surds
1.19 Operations with surds
1.20 Rationalising the denominator
Test yourself 1
Challenge exercise 1
2. EQUATIONS AND INEQUALITIES
2.01 Equations
2.02 Inequalities
2.03 Absolute value
2.04 Equations involving absolute values
2.05 Exponential equations
2.06 Solving quadratic equations by factorisation
2.07 Solving quadratic equations by completing the square
2.08 Solving quadratic equations by quadratic formula
2.09 Formulas and equations
2.10 Linear simultaneous equations
2.11 Non-linear simultaneous equations
2.12 Simultaneous equations with three unknown variables
2.13 EXT1 Quadratic inequalities
2.14 EXT1 Inequalities involving the unknown in the denominator
2.15 EXT1 Inequalities involving absolute values
Test yourself 2
Challenge exercise 2
3. PERMUTATIONS AND COMBINATIONS
3.01 EXT1 Counting techniques
3.02 EXT1 The pigeonhole principle
3.03 EXT1 Factorial notation
3.04 EXT1 Permutations
3.05 EXT1 Combinations
3.06 EXT1 Pascal’s triangle and binomial coefficients
Test yourself 3
Challenge exercise 3
PRACTICE SET 1
4. FUNCTIONS
4.01 Functions
4.02 Function notation
4.03 Properties of functions
4.04 Linear functions
4.05 The gradient of a straight line
4.06 Finding a linear equation
4.07 Parallel and perpendicular lines
4.08 Quadratic functions
4.09 Axis of symmetry
4.10 EXT1 Quadratic inequalities
4.11 The discriminant
4.12 Finding a quadratic equation
4.13 Cubic functions
4.14 Polynomial functions
4.15 Intersection of graphs
Test yourself 4
Challenge exercise 4
5. TRIGONOMETRY
5.01 Trigonometric ratios
5.02 Finding a side of a right-angled triangle
5.03 Finding an angle in a right-angled triangle
5.04 Applications of trigonometry
5.05 The sine rule
5.06 The cosine rule
5.07 Area of a triangle
5.08 Mixed problems
5.09 Radians
5.10 Length of an arc
5.11 Area of a sector
Test yourself 5
Challenge exercise 5
6. POLYNOMIALS AND INVERSE FUNCTIONS
6.01 EXT1 Division of polynomials
6.02 EXT1 Remainder and factor theorems
6.03 EXT1 Polynomial equations
6.04 EXT1 Roots and coefficients of polynomial equations
6.05 EXT1 Graphing polynomial functions
6.06 EXT1 Multiple roots
6.07 EXT1 The inverse of a function
6.08 EXT1 Graphing the inverse of a function
6.09 EXT1 Inverse functions
Test yourself 6
Challenge exercise 6
PRACTICE SET 2
7. FURTHER FUNCTIONS
7.01 The hyperbola
7.02 Absolute value functions
7.03 Circles and semicircles
7.04 Reflections of functions
7.05 Combined and composite functions
7.06 EXT1 Sums and products of functions
7.07 EXT1 Reciprocal functions
7.08 EXT1 Square root relations
7.09 EXT1 Further absolute value functions
7.10 EXT1 Parametric equations of a function
Test yourself 7
Challenge exercise 7
8. INTRODUCTION TO CALCULUS
8.01 Gradient of a curve
8.02 Differentiability
8.03 Differentiation from first principles
8.04 Short methods of differentiation
8.05 Derivatives and indices
8.06 Tangents and normals
8.07 Chain rule
8.08 Product rule
8.09 Quotient rule
8.10 Rates of change
8.11 EXT1 Related rates of change
8.12 EXT1 Motion in a straight line
8.13 EXT1 Multiple roots of polynomial equations
Test yourself 8
Challenge exercise 8
9. PROBABILITY
9.01 Set notation and Venn diagrams
9.02 Relative frequency
9.03 Theoretical probability
9.04 Addition rule of probability
9.05 Product rule of probability
9.06 Probability trees
9.07 Conditional probability
Test yourself 9
Challenge exercise 9
PRACTICE SET 3
10. EXPONENTIAL AND LOGARITHMIC FUNCTIONS
10.01 Exponential functions
10.02 Euler's number, e
10.03 Differentiation of exponential functions
10.04 Logarithms
10.05 Logarithm laws
10.06 Logarithmic functions
10.07 Exponential equations
10.08 EXT1 Exponential growth and decay
10.09 EXT1 Further exponential growth and decay
Test yourself 10
Challenge exercise 10
11. TRIGONOMETRIC FUNCTIONS
11.01 Angles of any magnitude
11.02 Trigonometric identities
11.03 EXT1 Further trigonometric identities
11.04 Radians
11.05 Trigonometric functions
11.06 Trigonometric equations
11.07 Applications of trigonometric functions
11.08 EXT1 Inverse trigonometric functions
11.09 EXT1 Properties of inverse trigonometric functions
Test yourself 11
Challenge exercise 11
12. DISCRETE PROBABILITY DISTRIBUTIONS
12.01 Random variables
12.02 Discrete probability distributions
12.03 Mean or expected value
12.04 Variance and standard deviation
Test yourself 12
Challenge exercise 12
PRACTICE SET 4
ANSWERS
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
INDEX
