This mini-lesson covers the core Algebra strand of Eduqas GCSE Maths: expanding & factorising, solving linear and quadratic equations, simultaneous equations, rearranging formulae, sequences (the nth term), straight-line graphs (y = mx + c) and inequalities.
Work through each screen, answer the questions as you go (some ask you to expand or factorise, most are calculations) and collect ⭐ stars. Press Start when you're ready.
To expand a bracket, multiply every term inside by the term outside. To factorise, do the reverse: take out the highest common factor.
Expand 4(2x − 3).
4 × 2x = 8x and 4 × (−3) = −12
= 8x − 12
Factorise 6x + 9. The HCF of 6 and 9 is 3.
6x + 9 = 3(2x + 3) (check: 3 × 2x = 6x, 3 × 3 = 9 ✓)
Common slip: when expanding, the sign travels too. 4(2x − 3) is 8x − 12, not 8x − 3 and not 8x + 12.
To factorise x² + bx + c into two brackets, find two numbers that multiply to c and add to b:
Factorise x² − 9.
This is a difference of two squares: x² − 9 = x² − 3².
= (x − 3)(x + 3) (expand to check: x² + 3x − 3x − 9 = x² − 9 ✓)
Watch the signs: for x² − 4x + 4 you need two numbers that multiply to +4 and add to −4 → both are −2, giving (x − 2)(x − 2) = (x − 2)².
Tap a quadratic expression on the left, then its matching factorised form on the right.
To solve an equation, do the same thing to both sides until x is on its own. Undo each operation in reverse.
Solve 5x − 2 = 3x + 8.
Subtract 3x from both sides: 2x − 2 = 8
Add 2: 2x = 10, then divide by 2: x = 5
Golden rule: whatever you do to one side, do to the other. Move terms by doing the opposite operation — a + on one side becomes a − when it crosses.
A quadratic like x² − 7x + 12 = 0 is solved by factorising, then setting each bracket to zero (the null-factor law):
Solve x² + x − 6 = 0.
Two numbers multiply to −6, add to +1: that's +3 and −2.
(x + 3)(x − 2) = 0 → x = −3 or x = 2
Two answers: a quadratic usually has two solutions. If a bracket is (x − 3), the solution is x = +3 (the value that makes the bracket zero), not −3.
Two equations, two unknowns. Add or subtract the equations to eliminate one variable, then solve for the other:
Solve 2x + y = 11 and x + y = 7.
Subtract the second from the first: x = 4.
Put x = 4 into x + y = 7: y = 3. So (x, y) = (4, 3).
Elimination check: if the signs of the matching variable are the same, subtract; if they are opposite, add. Here x + y and x − y have opposite y-signs, so we add.
To make a different letter the subject of a formula, use the same "do the same to both sides" idea as solving an equation — but keep the letters.
Make x the subject of y = 3x + 2.
Subtract 2: y − 2 = 3x
Divide by 3: x = (y − 2) ÷ 3
Using v = u + at, find v when u = 4, a = 3, t = 2.
v = 4 + 3 × 2 = 4 + 6 = 10
Tip: deal with the term furthest from the letter you want first — undo + and − before × and ÷ when isolating the subject.
For a linear (arithmetic) sequence the terms go up by a constant amount — the common difference. That difference is the coefficient of n in the nth-term rule:
Find the nth term of 5, 8, 11, 14.
Common difference = 3, so start with 3n. When n = 1, 3n = 3, but the term is 5 — so add 2.
nth term = 3n + 2. Check n = 4: 3 × 4 + 2 = 14 ✓
Finding a term: to get the 10th term, substitute n = 10 into the rule: 3 × 10 + 2 = 32.
Every straight line has the form y = mx + c, where m is the gradient (steepness) and c is the y-intercept (where it crosses the y-axis).
Reading y = 2x − 3: the gradient is 2 and the y-intercept is −3 — the number multiplying x is m, the number on its own is c.
Solve an inequality almost exactly like an equation — but keep the inequality sign (<, ≤, >, ≥) instead of an equals sign.
Solve 3x − 1 ≥ 8.
Add 1: 3x ≥ 9, then divide by 3: x ≥ 3
The one trap: if you multiply or divide both sides by a negative number, you must flip the inequality sign. Dividing by a positive (like 2) leaves it unchanged.
A linear expression/equation has x to the power 1 (no x²); a quadratic contains an x² term. Tap an item, then tap the box it belongs in.
Expand & factorise: a(b + c) = ab + ac; factorise x² + bx + c into two brackets that multiply to c and add to b; spot the difference of two squares.
Linear equations: do the same to both sides until x is alone.
Quadratic equations: factorise, set each bracket to zero — usually two solutions.
Simultaneous equations: add or subtract to eliminate a variable, then back-substitute.
Rearranging: change the subject the same way you solve; substitute values carefully.
Sequences: common difference gives the n-coefficient; nth term = dn + (adjust).
Straight-line graphs: y = mx + c — m is the gradient, c the y-intercept; gradient = rise ÷ run.
Inequalities: solve like equations, but flip the sign if you × or ÷ by a negative.
You've covered the core Algebra content of Eduqas GCSE Maths. Press Finish to see your score.
You've worked through the Algebra strand for Eduqas GCSE Maths. 🎉
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