Syllabus
Below is a summary of the topics to be covered in the S7, three periods mathematics class.
| Module / Topic | Key Content |
|---|---|
| Exponential and Logarithmic Functions | Properties (domain, derivative, limits, asymptotes, and growing phenomena). Understand their inverses. Study exponential/logarithmic models. Solve exponential/logarithmic equations using a technological tool. Applications. |
| Integration | Area through approximation. Antiderivatives, definite integrals, area under/between curves, basic applications of integration. Calculating arc lengths and volumes of solids of revolutions. Velocity problems. |
| Bivariate Statistics | Visualisation, correlation, regression, data interpretation, applications. Modelling with a linear function. |
| Continuous Random Variables | Understand continuous random variables and its probabilities using integrals. |
| Normal Distribution | Recognise data sets modelled with normal distribution. Know the probabilities of being within 1, 2, or 3 standard deviations of the mean. Calculate probabilities and normal quantiles given the expected value and standard deviation of a variable. |
| Null Hypothesis Significance Testing | Understand and use NHST procedure. Accepting/Rejecting the null hypothesis. Determining critical value and region. Creating null and alternative hypotheses. Calculating Type 1 and Type 2 errors. |
How To Navigate the Programme
This list follows the order of the syllabus. Each section here will take you to an introductory lesson, at the end of which you will find a button to navigate to the next page in that unit. Once there are no more “Next Page” buttons, you are done with that part of the programme at a basic/intermediate level.
Below you will find a small breakdown of what each of these sections and units contain, in the order they appear.
Some topics are relatively short and are typically meant as an introduction or are combined with other topics. A future section with high-level questions is planned for the future where these examples will be included.
Exponential and Logarithmic Functions: Introduction to Exponential and Logarithmic Functions, Logarithmic Functions and Models, Final Remarks on Exponential and Logarithmic Models.
Integration: Introduction, Area Calculations with Integrals, Volume and Arc Length Calculation with Integrals, Velocity Problems.
Bivariate Statistics: Line of Best Fit and Pearson Correlation Coefficient and Regression Models.
Continuous Random Variables: Introduction and Examples.
Normal Distribution: Introduction and Basic Concepts, Standard Normal Distribution, and Binomial Approximation.
Null Hypothesis Significance Testing: Basic Concepts, examples, type I and type II errors.