Syllabus
Below is a summary of the topics to be covered in the S6, three periods mathematics class.
| Module / Topic | Key Content |
|---|---|
| Concept of a Function and Models | Determining the domain and range of a function. Understanding basic concept of a function. Review models seen in S4 and S5. |
| Rate of Change and Differentiation | Investigate the difference between the average and instantaneous rate of change of a function. Define the tangent line and understand its concept. Understand the derivative as the gradient function. Know that the derivative of a constant is 0 and know how to differentiate polynomials. Find the gradient at a particular point. |
| Applications of Derivatives | Understand the behaviour of a function (increasing/decreasing) from the derivative. Find extreme points and classify them. Velocity problems. |
| Periodic Modelling | Investigate the impact of parameters  and  in  on the graph using a technological tool. Define the period. Determine amplitude, period, phase, and vertical shift given a sine function. Model real-life situations with sine functions. |
| Combinatorics | Recognise and model situations leading to counting the number of arrangements of length  of  distinct objects with and without repetition. Permutations of objects from a set of distinct objects. Combinations without repetition. Calculate number of arrangements using permutations, factorials, powers. |
| Probability (basic) | Elementary probability rules, conditional probability, independence. Total probability law and Bayes’ theorem. |
| Discrete Random Variables | Definition, probability density function, cumulative distribution function. Expected value, variance, and standard deviation. Bernoulli trials and Binomial distribution, including calculating probabilities, expectation, variance, and standard deviation. Modelling with binomial distribution. |
How to Navigate the Programme
The first topic, introduction to real functions, is meant to have a revision of the basic ideas seen in S4 and S5 of the most important types of functions: linear, quadratic, how to solve the equations, understand and recognise graphs.
The remaining topics are all new and not revisited in S7. They all appear often enough in your final baccalaureate.
Below is a small breakdown of the topics included in the table above.
Real Functions: Introduction.
Rate of Change and Differentiation: Rate of Change and the Derivative, Tangent Lines.
Applications of Derivatives: Extreme Points, General Exercises, Velocity Problems.
Periodic Models: Graphs of Periodic Functions, Modelling with Periodic Functions.
Combinatorics: Introduction, Permutations, Combinations without repetition.
Probability: Introduction and Basic Forms of Representations, Basic Probabilistic Formulas, Independence, Total Probability and Bayes’ Law.
Discrete Random Variables: Introduction, Expectation, Variance, and Standard Deviation, Bernoulli Processes and Binomial Distribution.