A level Maths leans on GCSE algebra from the very first lesson. Most students who find the start of Year 12 hard are not missing anything new: they are rusty on a handful of GCSE skills. These ten are the ones that come up again and again.
Start with the check to see which ones you need, then work through those skills below. Everything on this page is free.
The ten skills
1 Indices
What GCSE expects
Index laws with whole-number powers, and negative and fractional powers such as 82/3.
What A level expects
Every term rewritten as a power of x (1/√x = x−1/2) before you differentiate or integrate, and the same laws again with exponentials and logs.
Videos and worksheets: Indices
Comes up in A level: Binomial expansion · Differentiation · Integration · Logs and exponentials
2 Surds
What GCSE expects
Simplifying surds like √48 and rationalising 1/√3.
What A level expects
Exact answers everywhere: the discriminant, exact trig values, vector lengths, and rationalising harder denominators.
Videos and worksheets: Surds
Comes up in A level: Quadratics · Trigonometry · Vectors
3 Algebraic fractions
What GCSE expects
Simplifying, adding and solving with algebraic fractions.
What A level expects
Algebraic division, partial fractions, and tidying fractions before you differentiate.
Videos and worksheets: Algebraic Fractions
Comes up in A level: Polynomials · Algebraic fractions (A2)
4 Quadratics
What GCSE expects
Factorising, the quadratic formula and completing the square.
What A level expects
The discriminant, turning points from the completed square, and quadratics in disguise such as x4 − 5x2 + 4 = 0.
Videos and worksheets: Factorising · Solving Quadratics · Completing the Square
Comes up in A level: Quadratics · Polynomials
5 Rearranging and simultaneous equations
What GCSE expects
Changing the subject, and linear and quadratic simultaneous equations.
What A level expects
Where a line meets a curve, tangents, parametric equations and modelling: rearranging is in nearly every question.
Videos and worksheets: Changing the Subject · Simultaneous Equations
Comes up in A level: Co-ordinate geometry · Parametric equations
6 Inequalities
What GCSE expects
Linear and quadratic inequalities, with the solution set.
What A level expects
Quadratic inequalities from the discriminant (“has real roots”), set notation and regions.
Videos and worksheets: Quadratic Inequalities · Linear Inequalities
Comes up in A level: Quadratics
7 Straight lines and circles
What GCSE expects
y = mx + c, gradients, parallel and perpendicular lines, and x2 + y2 = r2.
What A level expects
y − y1 = m(x − x1), circles with any centre (by completing the square), tangents and chords.
Videos and worksheets: Linear Graphs & Gradients · Drawing & Using Graphs
Comes up in A level: Co-ordinate geometry
8 Functions and graphs
What GCSE expects
Composite and inverse functions, and graph transformations like y = f(x + a).
What A level expects
Domain and range, modulus, sketching from key features, and combined transformations.
Videos and worksheets: Functions · Graphical Transformations
Comes up in A level: Sketching graphs · Functions (A2)
9 Trigonometry
What GCSE expects
SOHCAHTOA, the sine and cosine rules, exact values and trig graphs.
What A level expects
Solving trig equations in a range, identities, radians, and resolving forces in mechanics.
Videos and worksheets: Basic Trigonometry · Advanced Trigonometry · Exact Trig & Graphs
Comes up in A level: Trigonometry · Vectors · Radians
10 Proof
What GCSE expects
“Show that” questions and simple algebraic proof (odd and even, consecutive numbers).
What A level expects
Proof by deduction, by exhaustion, by counter-example and by contradiction.
Videos and worksheets: Show That & Proof
Comes up in A level: Proof
The bridging course
For the summer before Year 12, or the first weeks of A level. Tick Bridging course: GCSE to A level on My progress › My topics, and Today’s 5 works through all ten skills with Higher GCSE questions, a few a day, coming back to each one before you forget it. Five questions a day for four to six weeks covers the lot.
Already on A level? You do not need to do anything: when an A level topic is going badly, Today’s 5 slips in one GCSE question on the skill it needs (“GCSE you need first”), and the A level course support pages say which skills each topic uses.
For teachers
- Set the check. Give your Year 12 group this link: westiesworkshop.com/question-bank/my-progress/?v=bridge. Each student does 20 Higher GCSE questions, two on each skill, and marks them as they go. No logins.
- See the results. Students share their progress with you from My progress (“Share with a teacher”). In My class each student’s row shows their check score and their weakest skills, and Topics to reteach builds up across the class.
- Print it. The printable booklet is a fixed set of 30 questions (three per skill) with the mark scheme, through the exam builder. Each student’s own check also has a Print as a booklet button.
Other bridging resources
Bridging resources from other websites (Pearson, AMSP, CIMT, Stoke Maths, Piximaths, Underground Mathematics and Isaac Maths) are all listed together on Pre-A Level Maths, alongside everything on this page.