IGCSE Math RevisionAlgebra: Edexcel IGCSE Maths (4MA1) knowledge organiser
Everything to know about algebra on one page: key definitions, the formulas, a worked example, the mistakes to avoid and a checklist of what you should be able to do.
Key definitions
- Linear Equations and Inequalities
- An inequality replaces ‘=’ with ‘<, >, ≤, ≥’. Solve like an equation — but flip the inequality if you multiply/divide by a negative.
- Factorising Quadratics
- Factorising x² + bx + c means finding two brackets that multiply back to the quadratic.
- Linear Simultaneous Equations
- Simultaneous equations are two equations in two unknowns. Solve by elimination, substitution, or graphically.
- Completing the Square
- Completing the square rewrites x² + bx as (x + b/2)² − (b/2)² — useful for finding the vertex of a parabola.
Key formulas
Formulas marked with a label are given in the exam (we only say so where our formula sheet confirms it). Learn the rest.
| Expanding | \((a+b)^2=a^2+2ab+b^2,\) \((a-b)^2=a^2-2ab+b^2,\) \(a^2-b^2=(a+b)(a-b)\) |
| Quadratic formula, \(ax^2+bx+c=0\)On the 4MA1 formulae page | \(x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\) |
| Completing the square | \(x^2+bx+c=\left(x+\tfrac b2\right)^2-\tfrac{b^2}4+c\) |
| Turning point of \(y=(x+p)^2+q\) | \((-p,\,q)\) |
| Arithmetic series, sum of \(n\) termsOn the 4MA1 formulae page | \(S_n=\tfrac n2\big[2a+(n-1)d\big]\) |
| Arithmetic \(n\)th term | \(u_n=a+(n-1)d\) |
| Proportion | \(y\propto x^n\Rightarrow y=kx^n;\) \(y\propto\tfrac1{x^n}\Rightarrow y=\tfrac k{x^n}\) |
| Functions | \(fg(x)=f\big(g(x)\big);\) \(f^{-1}\text{: swap }x,y\text{ and rearrange}\) |
| Transformations: \(f(x)+a\) up \(a\); \(f(x+a)\) left \(a\); \(-f(x)\) reflect in \(x\)-axis; \(f(-x)\) reflect in \(y\)-axis | |
| Inequalities: multiplying or dividing by a negative number reverses the sign |
Worked example
Solve y = x + 1 and x² + y² = 25.
- x² + (x + 1)² = 25 → x² + x − 12 = 0 → x = 3 or −4 → (3, 4) and (−4, −3).
Common mistakes
- Completing the square with a negative x² coefficient
- Simultaneous equations with a quadratic: expanding (5 − x)²
- Writing 3a × 2a = 6a
- Collecting unlike terms such as x and x²
More on what examiners see students get wrong: Examiner Insights.
You should be able to…
- Evaluate and use zero, negative and fractional indices, such as 5⁰, 2⁻³ and 27^(2/3), and simplify algebraic expressions with these powers.
- Factorise quadratic expressions of the form ax² + bx + c, such as 3x² + 10x − 8, using grouping or another systematic method.
- Solve pairs of linear simultaneous equations by elimination, including those where both equations must be multiplied first.
- Show that algebraic statements are identities by expanding and simplifying, and set out 'show that' answers so every step is clear.
- Solve equations with algebraic fractions by multiplying through by a common denominator, including equations that lead to quadratics.
- Solve quadratic inequalities such as x² − x − 6 < 0 using the graph or a sign diagram, and give the solution set.
The printable sheet
Revise it next
Other Edexcel IGCSE Maths (4MA1) topics: Number · Graphs, sequences and calculus · Geometry and trigonometry · Statistics and probability · All Edexcel IGCSE Maths (4MA1) organisers