Syllabus
Below is a summary of the topics to be covered in the S7, five periods mathematics class.
| Module / Topic | Key Content |
|---|---|
| Complex Numbers | Algebraic form, modulus and argument, polar form, operations, roots of complex numbers. |
| Sequences: Arithmetic and Geometric | Arithmetic and geometric sequences and their limits, sum of consecutive terms, applications. |
| Study of Real Functions | Indeterminate forms of limits. Oblique Asymptotes. |
| Integration | Indefinite and definite integrals, integral properties, fundamental theorem of calculus, improper integral, area under a curve, volume of revolution. |
| Vectors in 3D | Orthogonal system. Lines in 3D, parallelism/orthogonality in 3D, vector product, volume of parallelepiped, test for coplanar points. Planes in 3D. Intersections, angles, and distances in 3D. Orthogonal projection in 3D. |
| Continuous Random Variables | Continuous distribution, probability density function, cumulative distribution function. Expectation, variance, and standard deviation. |
| Normal Distribution | Modelling with normal distribution. Calculate probabilities of a random variable with normal distribution given the mean and standard deviation. Normal quantiles. Standardisation. |
| Bivariate Statistics | Visualisation, correlation, regression, data interpretation, applications. |
How To Navigate the Programme
With the exception of Bivariate Statistics (which appears immediately after vectors), 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.
In particular, here you will find a small breakdown of what each of these sections and units contain, in the order they appear.
Some topics, such as sequences and continuous random variables 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.
Complex Numbers: Introduction, Complex Locus, and De Moivre’s Theorem.
Sequences: Arithmetic and Geometric
Integration: Introduction, Techniques of Integration (Substitution and Integration by Parts), Area and Volume calculations with Integrals, and Improper Integrals.
Vectors in 3D: Introduction, Relative Position of lines in 3D, Vector Product and Planes in 3D, Distances in 3D, Angles in 3D, Intersections in 3D, and Final Vector Applications.
Continuous Random Variables: Introduction and Examples.
Normal Distribution: Introduction and Basic Concepts, Standard Normal Distribution, and Binomial Approximation.
Bivariate Statistics: Line of Best Fit and Pearson Correlation Coefficient and Regression Models.
How to Approach Difficult Questions
While everything you need to know is technically here, some skills you can only develop once you look at harder or longer questions combining some of these topics.
For example, the topic of sequences can be combined with complex numbers or even vectors (to create a sequence of complex numbers, or a sequence of lines/planes). This combination is not dealt with neither in the Complex Numbers pages nor the Sequence pages.
In particular, the geometry unit (i.e.: vectors in 3D) is generally easier if you can visualise the problem described in the question.
In future, dedicates pages for high-level, more demanding questions will be offered.