Different forms of the equation of a straight line. Gradient; intercepts. Lines with gradients m1 and m2 Parallel lines m1 = m2. Perpendicular lines m1 × m2 = − 1.

Concept of a function, domain, range and graph. Function notation, for example f (x), v(t), C(n). The concept of a function as a mathematical model. Informal concept that an inverse function reverses or undoes the effect of a function. Inverse function as a reflection in the line y = x, and the notation f −1(x).

The graph of a function; its equation y = f (x). Creating a sketch from information given or a context, including transferring a graph from screen to paper. Using technology to graph functions including their sums and differences.

Determine key features of graphs. Finding the point of intersection of two curves or lines using technology.

Composite functions. Identity function. Finding the inverse function −1 f (x).

The quadratic function f (x) = ax2 + bx + c: its graph, y -intercept (0, c). Axis of symmetry. The form f (x) = a(x − p)(x − q), x-intercepts (p, 0) and (q, 0). The form f (x) = a (x − h)2 + k, vertex (h, k).

Solution of quadratic equations and inequalities. The quadratic formula. The discriminant Δ = b2 − 4ac and the nature of the roots, that is, two distinct real roots, two equal real roots, no real roots.

The reciprocal function f (x) = , x ≠ 0: its graph and self-inverse nature. Rational functions of the form f (x) = their graphs. Equations of vertical and horizontal asymptotes.

Exponential functions and their graphs: f (x) = ax, a > 0, f (x) = ex Logarithmic functions and their graphs: f (x) = loga x, x > 0, f (x) = lnx, x > 0.

Solving equations, both graphically and analytically. Use of technology to solve a variety of equations, including those where there is no appropriate analytic approach. Applications of graphing skills and solving equations that relate to real-life situations.

Transformations of graphs. Translations: y = f (x) + b; y = f (x − a). Reflections (in both axes): y = − f (x); y = f ( − x). Vertical stretch with scale factor p: y = p f (x). Horizontal stretch with scale factor : y = f (qx). Composite transformations.

Polynomial functions, their graphs and equations; zeros, roots and factors. The factor and remainder theorems. Sum and product of the roots of polynomial equations.

Rational functions of the form ax + b f (x) = cx2 + dx + e

Odd and even functions. Finding the inverse function, f −1(x), including domain restriction. Self-inverse functions.

Solutions of g(x) ≥ f (x), both graphically and analytically.

The graphs of the functions, y = | f (x)| and y = f (|x|), y = f (x) Solution of modulus equations and inequalities.