This mini-lesson works through the core Algebra strand of Edexcel GCSE Maths (1MA1): expanding & factorising (including quadratics), solving linear equations, solving quadratics, simultaneous equations, rearranging formulae, sequences (nth term), straight-line graphs (y = mx + c) and inequalities.
Work through each screen, answer the questions as you go (most are calculations) and collect ⭐ stars. Press Start when you're ready.
To expand, multiply every term inside the bracket by the term outside. For a double bracket, multiply each term in the first by each term in the second (FOIL), then collect like terms.
Expand 3(2x − 5).
3 × 2x = 6x and 3 × (−5) = −15
= 6x − 15
Expand (x + 4)(x + 2).
x·x = x², x·2 = 2x, 4·x = 4x, 4·2 = 8
= x² + 2x + 4x + 8 = x² + 6x + 8
Common slip: when expanding (x + 5)², don't write x² + 25. It means (x + 5)(x + 5), giving the middle term: x² + 10x + 25.
Factorising is expanding in reverse. For x² + bx + c, find two numbers that multiply to c and add to b:
Factorise x² + 7x + 12.
Need two numbers with product 12 and sum 7 → 3 and 4 (3 × 4 = 12, 3 + 4 = 7).
= (x + 3)(x + 4) (check by expanding: x² + 4x + 3x + 12 = x² + 7x + 12 ✓)
Signs matter: for x² − 5x + 6 the two numbers multiply to +6 but add to −5, so both are negative: (x − 2)(x − 3).
An equation is a balance. Do the same operation to both sides to isolate the letter. Aim to gather the letters on one side and the numbers on the other.
Solve 5x − 3 = 2x + 18.
Subtract 2x from both sides: 3x − 3 = 18
Add 3 to both sides: 3x = 21
Divide by 3: x = 7 (check: 5×7 − 3 = 32 and 2×7 + 18 = 32 ✓)
Golden rule: whatever you do to one side, you must do to the other — otherwise the balance breaks and the answer is wrong.
To solve a quadratic = 0, factorise it, then use the fact that if two things multiply to zero, at least one of them must be zero.
Solve x² + 5x + 6 = 0.
Two numbers multiplying to 6, adding to 5 → 2 and 3.
(x + 2)(x + 3) = 0
x + 2 = 0 → x = −2 or x + 3 = 0 → x = −3
So x = −2 or x = −3.
Sign flip: the bracket (x + 2) gives the root x = −2, not +2. Always change the sign of the number in the bracket.
Tap an equation on the left, then its solution on the right.
Two equations, two unknowns. Eliminate one letter by adding or subtracting the equations (after matching coefficients), solve for the other, then substitute back.
Solve 2x + y = 11 and x + y = 7.
Subtract the second from the first: (2x − x) + (y − y) = 11 − 7 → x = 4.
Substitute x = 4 into x + y = 7: 4 + y = 7 → y = 3.
x = 4, y = 3 (check: 2×4 + 3 = 11 ✓)
Tip: if the letters have the same sign, subtract to eliminate; if they have opposite signs, add.
To make a different letter the subject, use the same balancing moves as solving an equation — get the wanted letter on its own.
Make x the subject of y = 4x − 3.
Add 3 to both sides: y + 3 = 4x
Divide by 4: x = (y + 3) ÷ 4
Order matters: undo operations in reverse. In 4x − 3 you multiplied then subtracted, so to reverse it you add first, then divide.
A linear (arithmetic) sequence goes up by the same amount each time — the common difference. The nth term is:
Find the nth term of 5, 8, 11, 14, …
Common difference d = 3, so it starts "3n". First term is 5, and 3×1 = 3, so add 2.
nth term = 3n + 2. Check n = 2: 3×2 + 2 = 8 ✓
10th term: 3 × 10 + 2 = 32.
Careful: "3n + 2" is a rule, not a term. To get an actual term you must substitute a value of n.
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).
Read it straight off: in y = 4x − 3 the gradient is 4 and the line crosses the y-axis at −3. The number in front of x is always the gradient.
Solve an inequality just like an equation — but there's one special rule: if you multiply or divide by a negative number, you must flip the inequality sign.
Solve −2x > 6.
Divide both sides by −2 → x < −3 (the > flips to <).
The one trap: forgetting to flip. Dividing by a negative reverses the direction of the inequality every time.
A linear equation has no x² term; a quadratic contains an x² term. Tap an equation, then tap the box it belongs in.
Expanding: multiply out brackets; (x + a)(x + b) = x² + (a+b)x + ab; watch the middle term in (x + 5)².
Factorising: reverse of expanding — two numbers that multiply to c and add to b.
Linear equations: balance both sides; gather letters one side, numbers the other.
Quadratics: factorise = 0, then each bracket = 0 (flip the sign for the root).
Simultaneous: eliminate one letter, solve, substitute back.
Rearranging: undo operations in reverse to change the subject.
Sequences: nth term = dn + (a − d); substitute n for a term.
Graphs: y = mx + c — m is the gradient, c the y-intercept.
Inequalities: solve like equations, but flip the sign when × or ÷ by a negative.
You've covered the core Algebra topics in Edexcel 1MA1. Press Finish to see your score.
You've worked through the Algebra strand for Edexcel GCSE Maths (1MA1). 🎉
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