The student...

Functions, equations and inequalities (30%)

• . . . solves equations and inequalities of standard functions (or family of functions) and interprets the solutions.
• . . . solves systems of two linear equations and interprets the solutions.
• . . . determines the asymptotic behaviour of functions and demonstrates this behaviour with the calculation of limits.
• . . . draws up and conceptually uses the inverse of a function.
• . . . names and uses the characteristic features of standard functions (e.g. domain, range, zeros).

Trigonometry (15%)

• . . . draws up and edits formulas for periodic phenomena, solves equations and uses the periodicity with insight, using the formula list where necessary.
• . . . analyses behaviour of Lissajous figures and solves for position or speed.

Differentiation (20%)

• . . . interprets the first and second derivative of a function (or family of functions) conceptually, uses these to examine the function and its critical points, and uses these in applications.
• . . . solves optimization problems using the derivative.
• . . . uses differentiation rules (sum, product, quotient and chain rule) to determine the first and second derivatives of functions.

Geometry (20%)

• . . . examines the properties and mutual location of points, lines, circles and other suitable figures by means of algebraic representations, and forms algebraic representations of figures in a coordinate system and uses algebraic representations to solve geometrical problems (e.g. crossing lines and circles, perpendicular lines, parametric representations).
• . . . investigates and demonstrates geometrical properties of objects, using geometric and algebraic techniques when necessary.
• . . . derives properties from figures in the plane with the help of vectors and dot products and performs calculations.

Integration (15%)

• . . . finds the antiderivatives of the standard functions and simple combinations thereof (direct integration).
• . . . draws up a definite integral and calculates this exactly in suitable applications (e.g. enclosed area and volume of a solid of revolution).

Standard functions include: power functions (with rational exponents), rational functions, exponential functions, logarithmic functions, trigonometric functions, the absolute value function, including functions with parameters (family of functions).