This mini-lesson covers the core Number & Algebra content of CCEA GCSE Mathematics: fractions, decimals & percentages, indices, standard form, HCF & LCM, ratio & proportion, plus the algebra of expanding & factorising, linear & quadratic equations, simultaneous equations, sequences, straight-line graphs and inequalities.
Honest heads-up: these quick questions test your recall of facts, formulae and methods — they can't mark full written working. In the real exam you must always show each step.
Work through each screen, answer the questions as you go and collect ⭐ stars. Press Start when you're ready.
You must apply the four rules (+ − × ÷) with the correct hierarchy. Work through operations in this order:
Division and multiplication rank equally, as do addition and subtraction — do those left to right.
Evaluate 12 + 6 × 3.
Multiply first: 6 × 3 = 18 → 12 + 18
Then add: = 30
Common slip: reading left to right gives 12 + 6 = 18, ×3 = 54. That ignores BIDMAS — the × comes before the +.
Every integer is a unique product of prime factors. Write each number in index form, then compare:
Remember which is which: HCF is the small answer (shared factors only); LCM is the big answer (multiply all the factors in the diagram once).
These three are the same idea written three ways. You must move between them freely:
Watch out: when comparing sizes, convert everything to decimals first — it's the fairest common form. ⅗ = 0.6, 55% = 0.55, so ⅗ is the larger.
The quickest way to increase or decrease is a multiplier:
A £40 coat rises by 15%. New price?
Multiplier = 1 + 0.15 = 1.15 → 40 × 1.15 = £46
A sofa costs £360 after a 20% discount. Original price?
£360 is 80% of the original → 360 ÷ 0.80 = £450
The classic trap: a reverse percentage is not "just add the discount back". You must divide by the multiplier to undo the change.
To divide a quantity in a ratio, add the parts to find the total number of parts, then find one part:
Share £360 in the ratio 4 : 5.
Total parts = 4 + 5 = 9, so one part = 360 ÷ 9 = £40
Shares: 4 × 40 = £160 and 5 × 40 = £200 (check: 160 + 200 = 360 ✓)
Always check your shares add back to the original total — a quick way to catch arithmetic slips.
Standard form writes very large or very small numbers compactly:
Watch the rule 1 ≤ a < 10: writing 15 × 10⁷ is not standard form because 15 is bigger than 10. Correct it to 1.5 × 10⁸.
Tap an ordinary number on the left, then its matching standard form on the right.
The index laws let you simplify and evaluate powers:
Simplify 2⁵ × 2².
Add the powers: 2⁵⁺² = 2⁷
2⁷ = 128
Key facts: a⁰ = 1 for any non-zero a, and a negative power means reciprocal: 2⁻³ = 1/8 — it does not make the answer negative.
To expand, multiply every term inside the bracket by the term outside. To factorise, do the reverse — pull out the common factor.
Factorise 6x + 15.
Highest common factor of 6 and 15 is 3.
6x + 15 = 3(2x + 5)
Check by expanding back: 3(2x + 5) = 6x + 15 ✓. Factorising and expanding are opposite processes.
Keep the equation balanced: whatever you do to one side, do to the other. Undo operations in reverse order.
Solve 3x + 4 = 19.
Subtract 4 from both sides: 3x = 15
Divide both sides by 3: x = 5
Check it: substitute back — 3 × 5 + 4 = 15 + 4 = 19 ✓.
To solve x² + bx + c = 0, find two numbers that multiply to c and add to b. Then each bracket equals zero.
(x − 2)(x − 3) = 0 means one bracket is zero.
x − 2 = 0 → x = 2 or x − 3 = 0 → x = 3
Solutions: x = 2 and x = 3
Sign check: for + c and − b, both numbers are negative. For −5x + 6 the pair is −2 and −3, not +2 and +3.
Two equations, two unknowns. Add or subtract the equations to eliminate one letter, then solve.
x + y = 10 and x − y = 4.
Add the two: 2x = 14 → x = 7
Substitute back: 7 + y = 10 → y = 3 (so x = 7, y = 3)
Check both: 7 + 3 = 10 ✓ and 7 − 3 = 4 ✓. Always test your pair in both original equations.
For a sequence going up by a fixed amount, the nth term is (common difference)×n + (adjustment).
Find the 10th term of 5, 9, 13, …
nth term = 4n + 1, so put n = 10: 4 × 10 + 1
= 40 + 1 = 41
Finding the rule: the coefficient of n is always the common difference. Then adjust by comparing to the first term.
A straight line has equation y = mx + c, where m is the gradient (steepness) and c is the y-intercept (where it crosses the y-axis).
Gradient: "up 2 for every 1 across". A steeper line has a larger m; a negative m slopes downhill.
Solve an inequality just like an equation — but there's one special rule: if you multiply or divide by a negative, you must flip the inequality sign.
Solve 2x + 1 < 9.
Subtract 1: 2x < 8
Divide by 2 (positive, so sign stays): x < 4
The flip rule: −x < 3 becomes x > −3 after dividing by −1. Forgetting to flip is the most common inequality error.
An expanded expression has no brackets (terms added); a factorised one is written as a product with brackets. Tap an expression, then the box it belongs in.
Number: BIDMAS order of operations; prime factors → HCF & LCM; convert freely between fractions, decimals & percentages.
Percentages: multipliers for change; reverse percentage = ÷ multiplier.
Ratio & proportion: share by parts; check shares add back to the total.
Standard form: a × 10ⁿ with 1 ≤ a < 10. Index laws: add powers to multiply, subtract to divide.
Algebra: expand by multiplying out; factorise by pulling out common factors.
Equations: keep balanced; quadratics factorise into two brackets; simultaneous equations eliminate one letter.
Sequences: nth term = (difference)n + adjustment.
Graphs & inequalities: y = mx + c (m = gradient, c = intercept); flip the sign when dividing by a negative.
You've covered the core Number & Algebra content of CCEA GCSE Mathematics. Press Finish to see your score.
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