Pure Maths
A-Level Algebra
Algebra underpins every other area of A-Level Maths. Fluency with indices, surds, quadratics and simultaneous equations makes later topics far quicker.
What you need to know
- Laws of indices and manipulation of surds
- Completing the square and the discriminant
- Solving simultaneous equations, including one linear and one quadratic
- Inequalities and their solution sets
Key concepts
- The discriminant b² − 4ac tells you how many real roots a quadratic has.
- Completing the square gives the vertex of a parabola directly.
- A rationalised denominator makes surd answers comparable and markable.
Common mistakes
- Losing a sign when expanding brackets with a negative multiplier
- Forgetting the second solution when square rooting
- Reversing an inequality when multiplying by a negative number
Example question
Simplify .
Show explanation
50 = 25 × 2, and √25 = 5, so √50 = 5√2.
Practise Algebra
5 original questions with worked explanations, mixed across easy, medium and challenging difficulty.
Algebra questions students ask
- How much algebra appears in the A-Level papers?
- Algebraic manipulation appears in almost every question, even in statistics and mechanics, so it is the highest-value topic to secure early.
- Is a calculator allowed?
- All A-Level Maths papers allow a calculator, but exact surd and fraction answers are still expected where the question asks for them.