Start with the rules in isolation: differentiate xⁿ, then practise sums and differences, then products and quotients. Integration follows the same logical progression. Spend 15 minutes daily on calculus; short, focused practice beats long, irregular sessions. Cambridge examiners note that students who master the chain rule early find the rest of calculus significantly easier.

Calculus (differentiation and integration) appears in every exam and carries the highest mark allocation. Functions, quadratic functions, trigonometry, and logarithmic and exponential functions are also heavily tested. Coordinate geometry of the circle, vectors, and series appear regularly. Your Diagnostic Report will reveal which high-weight topics need attention.

Paper 1 tests topics without calculators and includes functions, quadratics, polynomials, simultaneous equations, and straight-line graphs. Paper 2 allows calculators and covers calculus, trigonometry, logarithms, vectors, circular measure, and series. Both papers require full working; Cambridge examiners cannot award method marks if your working is not shown.

Method marks are awarded even when the final answer is incorrect, provided the working is shown clearly. A student who differentiates correctly but substitutes the wrong x value still earns 3 out of 4 marks. A student who writes only the final answer and gets it wrong scores zero. Show every algebraic step; it is your safety net.

The report breaks down your performance by topic and by skill type: algebraic manipulation, graphical interpretation, calculus application, trigonometric reasoning. If your calculus score is strong but your trigonometry score is weak, you know exactly where to focus. Use topic questions to target the specific techniques that are dragging your overall grade down.

Create a rules summary sheet: power rule, chain rule, product rule, quotient rule for differentiation; reverse power rule, definite integrals, area under a curve for integration. Practise each rule with five questions, then attempt mixed exercises that combine multiple techniques. Cambridge examiners report that students who practise integration by recognition score consistently higher marks.

Students forget that trigonometric equations often have multiple solutions within the given range. They also confuse log rules, particularly log(a + b) with log a + log b. Another frequent error is misapplying the identity sin²θ + cos²θ = 1 when rearranging. Practise identifying the correct rule before starting the calculation.

The most common reason is insufficient working. Even with a correct final answer, if key steps are missing, such as stating the derivative before integrating, or showing the substitution in the chain rule — Cambridge examiners cannot award full marks. Another reason is not simplifying answers fully, such as leaving surds in the denominator.

Revision notes teach you the rules and methods. Mock exams test whether you can apply them under timed conditions without a textbook beside you. Your Diagnostic Report shows which rules you are applying incorrectly. Past papers then train you to manage the two-paper structure and the time pressure of the real examination.

Know exactly what your calculator can do — solving quadratic equations, evaluating definite integrals, finding logarithms, and checking trigonometric values. Practise entering complex expressions in one go rather than breaking them into steps. But never rely on the calculator alone: Cambridge examiners require written working for all method marks.