Is A Level Maths Hard? The Jump From IGCSE and O Level

Most students who found IGCSE or O Level maths comfortable are surprised by the first few weeks of A Level. That does not mean A Level is out of reach. It means the kind of maths changes. Here is what actually changes, based on the Cambridge syllabuses, and how to get ready.

What does Cambridge assume you already know?

The 9709 syllabus assumes the content of IGCSE Mathematics 0580 (Extended) or O Level Mathematics 4024. On top of that, you should be able to:

• manipulate simple surds, such as writing √12 as 2√3;
• know the shapes of graphs of y = kxⁿ for integer n and n = ±½.

Cambridge plans about 180 guided learning hours for AS Level and 360 for the full A Level. That is a lot of new material in two years, and the pace is the first thing students notice.

What is actually new?

Area	At IGCSE / O Level	At A Level (9709)
Quadratics	Factorise and use the formula	Completing the square, the discriminant, quadratics in disguise (x⁴ − 5x² + 4 = 0)
Functions	Simple notation and composite functions	Domain, range, inverses, transformations of graphs
Trigonometry	Right-angled and non-right-angled triangles	Radians, identities, solving equations in intervals, R cos(θ − α) form
Sequences	Simple nth terms	Arithmetic and geometric series, sums to infinity, binomial expansion
Calculus	None in 4024; basic differentiation in 0580 Extended	Differentiation and integration from Paper 1, then much more in Paper 3
Logarithms	Exponential growth and decay	Laws of logarithms, ln and eˣ, linear law
Vectors	2D vectors and vector geometry	3D vectors, lines, the scalar product
New areas	None	Complex numbers, differential equations, mechanics, probability distributions

Two things stand out:

1. O Level students start calculus from zero. 4024 has no differentiation, while 0580 Extended includes derivatives of axⁿ and stationary points. Students who took Additional Maths have already done both differentiation and integration.
2. Algebra is everywhere. Nearly every A Level question is a chain of algebraic steps. A slip in rearranging or factorising costs more than any single topic.

Why does it feel harder?

• Questions are less signposted. IGCSE questions often walk you through each step. A Level questions give you the goal and expect you to choose the method.
• Answers are more often exact. Surds, fractions and terms in π are expected, so you cannot lean on the calculator.
• Working is assessed. Cambridge gives no marks for unsupported calculator answers in 9709, so you need to write clear algebraic steps.
• The content builds. Paper 1 is the foundation for every other paper. A weak spot in Year 12 shows up again in Paper 3.

How to prepare in the summer before Year 12

Spend most of your time on algebra. In this order:

1. Expanding brackets and factorising, including quadratics with a ≠ 1.
2. Indices (including negative and fractional) and surds, including rationalising the denominator.
3. Rearranging formulas and solving linear and quadratic equations.
4. Simultaneous equations, including one linear and one quadratic.
5. Straight-line graphs: gradient, y = mx + c, parallel and perpendicular lines.
6. Basic trigonometry: SOH CAH TOA, the sine and cosine rules.

If you finish those, look ahead to completing the square and the basics of differentiation. Then read the 9709 guide and the Paper 1 guide so you know how the course is structured.

In the first term

• Do a little every day rather than a lot on the weekend.
• When a method clicks in class, do five more questions on it that evening.
• Keep a list of algebra slips you make and check for them before moving on.
• Ask early. Gaps in Paper 1 topics compound by Paper 3.

Back to the O Level and IGCSE Maths guide.