Form 5 puts the Form 4 algebra to work and adds calculus. This page lists the topics in a study order and shows how they connect to Form 4.
It belongs to SPM Additional Mathematics and follows the Form 4 route.
What are the Form 5 topics?
Start with the calculus pair: Differentiation and Integration. They undo each other, so learning one helps the other.
Next come Circular Measure and Trigonometric Functions. Counting and chance follow with Permutations and Combinations and Probability Distributions.
Linear Programming uses lines and inequalities from earlier topics. Your school may teach these in a different order, so follow your teacher’s sequence in class.
Which Form 4 skills does Form 5 use?
| Form 5 topic | Form 4 skill it leans on |
|---|---|
| Differentiation | Indices, expanding brackets, quadratic equations |
| Integration | Indices, differentiation in reverse |
| Trigonometric Functions | Functions and graphs |
| Linear Programming | Straight-line graphs from Coordinate Geometry |
How do differentiation and integration fit together?
Take this example. The derivative of y = x² is 2x.
Now go the other way. The area under the line y = 2x from x = 0 to x = 3 is the integral of 2x, which is [x²] from 0 to 3 = 9. The triangle with base 3 and height 6 has area 1/2 × 3 × 6 = 9, so the two methods agree.
Where should you start?
- Fresh to Form 5: begin with the differentiation guide, then integration.
- Form 4 gaps showing: run the prerequisite gap finder first and repair the named gap.
- Near the exam: read the exam guide and practise mixed questions under time.
When is tuition worth considering?
Free lessons show the method. A one-to-one teacher watches you meet a question you have not seen, and shows how to begin it.
Read online one-to-one Additional Mathematics tuition to see how a lesson runs.