Week 1- Algebraic techniques
- Index rules
- Factorising methods
- Algebraic fractions
- Perfect squares (sums and difference)
- Sum and difference of two cubes
Week 2 - Equations
- Solving linear equations
- Quadratic equations by factorising, complete the square, the formula
- Equations reducing to quadratics
Week 3 - Review Test – algebra and equations
Week 4 - Functions
- Notation – definition, function-relation
- Define domain and range
- Dependent/independent variables
- Odd/even
- Define composite functions f(g(x)), g(f(x)). Given f(x) and g(x).
Week 5 - Linear Functions
- Recognise direct variation
- Significance of m and c in f(x) = mx + c
- Use y – y1 = m(x – x1) to find the equation of a line
- Use two points to find the equation of a line
- Parallel and perpendicular lines
- Model and solve problems involving linear functions
Week 6 - Quadratic functions
- Recognise features of a quadratic function including turning points, axis of symmetry and intercepts
- Find the x-intercepts by solving the equation using an appropriate method
- Understand the rule of the discriminant in relation to the graph
- Solve practical problems involving a pair of simultaneous equations, linear and/or quadratic
Week 7 - The cubic function f(x) = x3
- Graph y = x3, f(x) = (x – b)3 and f(x) = (x – a)(x – b)(x – c)
- The polynomial function: identify coefficients and degree
- Graph a polynomial given a factorised form
- Hyperbolic functions: f(x) = k/x
Week 8 - Review Test on functions: linear, quadratic and cubic
Week 9 - Absolute value function, f(x) = |x|
- Definition, graph
- Shape and features of the graph of y =|ax + b|
- Solve |ax + b| = k both graphically and algebraically
Week 10 - All reflections and shifts of graphs
- Use g = f(x) to graph y = -f(x) and y = f(-x)
- Circle: (x – a)2 + (y – b)2 = r2 and graphs
- Semi circles
