Western Australian Mathematics Methods

CHAPTER 1: Fundamentals of Algebra

• Summary of algebraic terms
• Rearrangement of algebraic expressions, collecting like terms, expanding brackets
• Factorisation, common factor, difference of squares, trinomials, grouping of terms
• Completing the square
• Sum and difference of cubes
• Review of algebraic fractions
• Chapter 1 Review Exercise

CHAPTER 2: Linear Equations

• Solving linear equations
• Rearranging linear equations
• Solution of linear equations in two variables, substitution, elimination, graphing
• Problem solving involving two variable linear equations
• Chapter 2 Review Exercise

CHAPTER 3: Relations and Functions

• Mapping, domain, codomain, range
• Types of relations, one-to-many, one-to-one, many-to-one
• Function, line test for mapping diagrams
• Graphical representation relations and functions
• Vertical line test for functions
• Function notation
• Representation of functions
• Chapter 3 Review Exercise

CHAPTER 4: Lines and Linear Relationships

• Linear functions
• Gradient, methods of finding the gradient of a line
• Finding the equation of a line given a table of values
• Finding the equation of a line given a point and the gradient, two points
• Parallel and perpendicular lines
• Finding the distance between two points
• Finding the midpoint of a line segment
• Chapter 4 Review Exercise

CHAPTER 5: Quadratic Equations

• Solving quadratic equations, pure quadratic equations
• Solving quadratic equations in factored form
• Solving quadratic equations in non-factored form
• Solving quadratic equations involving fractions
• Solving quadratic equations graphically
• Solving quadratic equations by completing the square
• Solving quadratic equations using the quadratic formula
• Chapter 5 Review Exercise

CHAPTER 6: Quadratic Functions

• Finding the equation of a quadratic function given a table of values
• General form of a quadratic function
• Line of symmetry and turning point
• Graphing quadratic functions of the form y =ax² + bx + c
• Turning point form of a quadratic function
• Graphing quadratic functions of the form y =a(x-b)² + c
• Factor form of a quadratic function
• Graphing quadratic functions of the form y = a(x – b)(x – c)
• Application of parabolas to practical situations
• Chapter 6 Review Exercise

CHAPTER 7: Polynomials and Other Functions

• Polynomial expressions, functions, equations
• Graphs of function, Graphical terms
• Graphs of polynomial functions, linear, quadratic. cubic, quartic
• Factorising polynomials, synthetic division
• Remainder theorem, factor theorem
• Cubic equations, solving in factored and non-factored form
• Graphing cubic functions
• Graphs of reciprocal functions, square root function, cube root function
• Power function
• Chapter 7 Review Exercise

CHAPTER 8: Linear Transformations

• Translations, vertical, horizontal
• Dilations, vertical, horizontal
• Reflections, in the x-axis, in the y-axis
• Compound transformations, invariance
• Chapter 8 Review Exercise

CHAPTER 9: Graphs of Relations

• Graphs of y² = x
• Linear transformations of y² = x
• Graphing linear transformations of y² = x
• Graph of a circle centre (0,0) and radius r
• Graph of a circle centre (a,b) and radius r
• Chapter 9 Review Exercise

CHAPTER 10: Proportion

• Direct proportion or variation
• Indirect proportion or variation
• Chapter 10 Review Exercise

CHAPTER 11: Unit Circle Trigonometry

• Rotational motion, angle in standard position
• Definition of cosine and sine
• Definition of tangent, unit circle
• Definition of tangent in terms of sine and cosine
• Signs of cosine, sine and tangent
• Cosine, sine, tangent and right triangles
• Reference angles
• Exact trigonometric values
• Angle of inclination of a line
• Chapter 11 Review Exercise

CHAPTER 12: Solution of Triangles

• Solution of right triangles
• Angles of elevation and depression
• Bearings, applications of bearings
• Solution of non-right-angled triangles, sine rule, ambiguous case
• Cosine rule
• Area of a triangle
• Applications of trigonometry
• Chapter 12 Review Exercise

CHAPTER 13: Circular Measure

• Review of arcs, sectors and segments
• Circular measure, radian measure
• Exact trigonometric values
• Length of arcs and chords
• Area of sectors and segments
• Chapter 13 Review Exercise

CHAPTER 14: Trigonometric Functions

• Graphing the function y = sin_x, important properties of the sine function
• Graphing the function y = cos_x, important properties of the cosine function
• Graphing the function y = tan_x, important properties of the tangent function
• Amplitude changes
• Period changes
• Phase changes
• Graphing trigonometric functions
• Angle sum and difference identities
• Solving trigonometric equations graphically
• Solving trigonometric equations algebraically
• Quadratic trigonometric equations
• Solving trigonometric equations that do not involve exact values
• Solving practical problems involving trigonometric functions
• Chapter 14 Review Exercise

CHAPTER 15: Sets

• Definitions and notation for sets
• Set operations, complement, intersection, union, disjoint sets
• Problem solving using Venn Diagrams
• Chapter 15 Review Exercise

CHAPTER 16: Counting Techniques

• Methods of counting the number of ways of performing a task
• Multiplication principle
• Factorial notation
• Permutations(Optional)
• Combinations
• Addition principle
• Pascal’s triangle
• General form of the binomial expansion
• Total number of subsets
• Chapter 16 Review Exercise

CHAPTER 17: Probability

• Estimating probability
• Assigning probability, subjective probability, terminology
• Range of probability
• Methods of finding the sample space:
  • systematic listing
  • product tables
  • tree diagrams
  • Venn diagrams, probability Venn diagrams
  • counting techniques
• Complementary events law, addition law, mutually exclusive events
• Conditional probability
• Independent events
• Multiplication law
• Probability tree diagrams
• Chapter 17 Review Exercise

ANSWERS

INDEX

CHAPTER 1: Indices and Index Laws

• Exponent or index form of a number
• Index laws
• The zero exponent, negative exponents
• Fractional or rational exponents
• Radical or surd form
• Addition and subtraction of exponential terms
• Rounding off numbers to a given degree of accuracy
• Rounding off numbers to a given number of significant figures
• Addition, subtraction, multiplication and division with significant figures
• Standard form or scientific notation
• Solving exponential equations
• Power equations, finding the base
• Finding the base or exponent of equations that are not easily factored
• Chapter 1 Review Exercise

CHAPTER 2: Exponential Functions

• Graphs and properties of exponential functions with b > 1 and 0 < b < 1
• Tabled values and their equations:
• Linear, quadratic, cubic, reciprocal, and exponential functions
• Transformation of exponential graphs,
• Applications of exponential functions, growth and decay
• Chapter 2 Review Exercise

CHAPTER 3: Sequences

• Sequence
• Recursive formula
• Finding sequences given a term other than the first term
• Chapter 3 Review Exercise

CHAPTER 4: Arithmetic and Geometric Sequences

• Arithmetic sequences general term
• Explicit Formula
• Recurrence relations for arithmetic sequences
• Arithmetic sequences and linear functions, graphical displays
• Geometric sequences general term, explicit formula
• Recurrence relations for geometric sequences
• Geometric sequences and exponential functions, graphical displays
• Chapter 4 Review Exercise

CHAPTER 5: Practical Problems Involving Sequences

• Simple interest investments
• Compound interest investments
• Miscellaneous linear and geometric growth
• Growth applications of recurrence relations which are not linear nor geometric
• Linear and geometric decay, flat rate loans
• Reducing rate loans
• Chapter 5 Review Exercise

CHAPTER 6: Arithmetic and Geometric Series

• Arithmetic series
• Applications of arithmetic series
• Geometric series
• Applications of geometric series - growth and decay
• Infinite geometric series, divergent series, oscillating series, convergent series
• Applications of infinite geometric series
• Chapter 6 Review Exercise

CHAPTER 7: Differentiation

• Rates of change
• Average rates of change of a function
• General statement of the average rate of change of a function, difference quotient
• Leibniz notation
• Introduction to limits
• Determining the gradient of a curve at a point
• Definition of the derivative
• Leibniz notation for the derivative
• Differentiating power functions
• Differentiating axⁿ where a is a constant
• Derivative of a constant function
• Differentiating sums and differences
• Chapter 7 Review Exercise

CHAPTER 8: Applications of Differentiation

• Rates of change
• Numerical derivatives using a calculator
• Equation of a tangent to a curve
• Tangent lines using a calculator
• Graphical applications, increasing and decreasing functions, stationary points
• Nature of stationary points
• Testing stationary points Points of inflection, horizontal, oblique
• Curve sketching
• Optimisation
• Chapter 8 Review Exercise

CHAPTER 9: Integration

• Differential calculus, integral calculus
• The indefinite integral of powers of x
• The indefinite integral of axⁿ
• Integration notation, properties of indefinite integrals
• Algebraic functions from the gradient function
• Determining the function from the rate of change
• Chapter 9 Review Exercise

CHAPTER 10: Rectilinear Motion

• Displacement and velocity
• Graphical treatment of linear position-time relationships
• Displacement, distance travelled, average velocity, average speed,
• instantaneous velocity, instantaneous speed
• Graphical treatment of non-linear position-time relationships
• Displacement from velocity
• Chapter 10 Review Exercise

ANSWERS

INDEX