This mini-lesson covers the Algebra strand of AQA GCSE Maths (8300): expanding & factorising, solving linear and quadratic equations, simultaneous equations, rearranging formulae, sequences (nth term), straight-line graphs y = mx + c, and inequalities.
These games test recall of facts, formulae and methods — not full multi-step working. Answer the questions as you go and collect ⭐ stars. Press Start when you're ready.
To expand, multiply everything inside the bracket by the term outside. For two brackets, multiply every term in the first by every term in the second (FOIL).
3(2x + 5) = 3×2x + 3×5 = 6x + 15
(x + 3)(x + 4) = x² + 4x + 3x + 12 = x² + 7x + 12
Common slip: forgetting the middle terms. (x + 3)(x + 4) is not x² + 12 — you must add the two cross-terms 4x + 3x = 7x.
Factorising is the reverse of expanding. For x² + bx + c, find two numbers that multiply to c and add to b.
Factorise x² + 7x + 12.
Need two numbers: product 12, sum 7 → 3 and 4.
= (x + 3)(x + 4)
Difference of two squares: x² − 9 = (x + 3)(x − 3). It has no middle term because +3x and −3x cancel.
Do the same operation to both sides to keep the equation balanced, undoing operations in reverse (inverse) order until x is alone.
Solve 3x + 7 = 22.
Subtract 7: 3x = 15
Divide by 3: x = 5
Check: substitute back — 3×5 + 7 = 22 ✓. Always a fast way to catch a slip.
To solve x² + bx + c = 0, factorise, then set each bracket to zero. On Higher, use the quadratic formula:
Solve x² + 7x + 12 = 0.
Factorise: (x + 3)(x + 4) = 0
So x + 3 = 0 or x + 4 = 0 → x = −3 or x = −4
Sign trap: if (x + 3) = 0 then x = −3, not +3. The solutions are the values that make each bracket zero.
Two equations, two unknowns. Eliminate one variable by adding or subtracting the equations (after matching coefficients), then back-substitute.
Solve x + y = 10 and x − y = 4.
Add the equations: 2x = 14 → x = 7
Substitute: 7 + y = 10 → y = 3 (so x = 7, y = 3)
Check both: 7 + 3 = 10 ✓ and 7 − 3 = 4 ✓. Your pair must satisfy both equations.
Rearranging a formula uses the same balancing rules as solving an equation — do inverse operations to both sides until the required letter is the subject.
Make r the subject of C = 2πr.
Divide both sides by 2π:
r = C ÷ (2π)
Tip: whatever is "attached" to the letter you want, undo it. Here r is multiplied by 2π, so you divide by 2π.
For an arithmetic sequence, the nth term is: (common difference)×n + (adjust to term 0).
Sequence: 5, 8, 11, 14, …
Common difference d = 3, so start with 3n.
3×1 = 3, but first term is 5, so add 2 → nth term = 3n + 2
Check: put n = 4 into 3n + 2 → 14 ✓, the 4th term.
Every straight line has equation y = mx + c. The gradient m = rise ÷ run; c is where the line crosses the y-axis.
Parallel lines have the same gradient m. On Higher, perpendicular gradients multiply to −1.
Tap a factorised expression on the left, then its correct expanded form on the right.
Solve an inequality just like an equation — but there's one special rule: multiplying or dividing by a negative flips the sign.
Solve 2x + 1 < 9.
Subtract 1: 2x < 8
Divide by 2 (positive, no flip): x < 4
The flip rule: if you divide by −2, e.g. −2x < 6 becomes x > −3. The inequality sign reverses.
A linear expression has x to the power 1 (a straight line); a quadratic contains an x² term (a curve). Tap an expression, then the box it belongs in.
Expand: multiply out brackets (FOIL for doubles); factorise is the reverse.
Linear equations: do the same to both sides until x is alone.
Quadratics: factorise then set each bracket = 0; or use the quadratic formula.
Simultaneous: eliminate a variable, then back-substitute.
Rearrange: change the subject with inverse operations.
Sequences: nth term = dn + (a − d) for a linear sequence.
Graphs: y = mx + c — gradient m, intercept c; parallel lines share m.
Inequalities: solve like equations, but flip the sign when ÷ or × by a negative.
You've covered every Algebra sub-topic in AQA 8300. Press Finish to see your score.
You've worked through Algebra for AQA GCSE Maths (8300). 🎉
Your stars: 0 / 0
Next: test yourself in the Evaluate stage Confidence Quiz, then lock it in with Verify.