Basiskurs
Algebra
- Algebraic simplification
- factorisation
- expansion up to binomial expansion
- Pascal’s triangle
- combinations
- solving linear equations
- solving quadratics
- solving simultaneous equations
- formula rearrangement and operations with surds
Functions
- definition of a function
- linear and quadratic functions
- domain and range
- mapping
- exponential functions (graphs and applications)
- intersection points and angles
- polynomial functions
Exponents and Logs
- review exponent laws
- exponential laws including fractions and simple surds
- calculating surds
- logarithms
Probability
- basic concepts
- definition of Laplace experiment
- Law of Big Numbers
- data types
- data analysis
- interpretation of charts and graphs
- variance
- standard deviation
- box and whisker plots
Differential Calculus
- rate of change of a function
- tangents and normals to a curve
- definition of a derivative as the slope of a tangent line
- stationary point
- points of inflection
Profilkurs
Algebra
- Inequalities,
- absolute value,
- interval notation,
- series and sequences and
- various methods of proof.
Functions
- Composite functions,
- inverse functions,
- finding parameters of exponential functions,
- trigonometric and rational functions,
- complex numbers
Exponents and Logs
- Generalisation of exponential laws,
- calculating logarithms,
- logarithm laws,
- introduction of the number e
Statistics and Probability
- Probability using tree diagrams,
- Vierfeldertafeln and Venn diagrams.
- Conditional and total probability
Differential Calculus
- chain rule,
- product rule and quotient rule.
- Basic curve analysis of polynomial and rational functions.
- Using the definition of the derivative to deduce basic rules of differentiation for exponential, logarithmic and trigonometric functions,
- analysis of exponential and logarithmic functions