Module 5

Algebra & circles

Quick-reference revision notes for parents.

5.1 Algebra reminder

Multiply everything inside the bracket by what's outside.

Worked examples

3(x + 4) = 3x + 12
5(2y − 3) = 10y − 15
−2(a + 5) = −2a − 10
x(x + 7) = x² + 7x

Watch out — minus signs

−4(x − 3) = −4x + 12 (the minus times the minus becomes plus).

The reverse of expanding. Find the highest common factor (HCF) of the terms and pull it outside the bracket.

Worked examples

6x + 9 = 3(2x + 3)
10y − 15 = 5(2y − 3)
x² + 4x = x(x + 4)
6a² + 8a = 2a(3a + 4)

Check your answer

Always expand it back. If you don't get the original expression, you missed a factor.

Change which letter is the subject. Same rules as solving equations — do the same to both sides, working backwards through the operations.

Worked example — make x the subject of y = 3x + 5

y = 3x + 5
y − 5 = 3x (subtract 5)
(y − 5) ÷ 3 = x (divide by 3)
x = (y − 5) / 3

Worked example — make r the subject of A = πr²

A = πr²
A / π = r² (divide by π)
r = √(A / π)

C = π × d or C = 2 × π × r

where d = diameter, r = radius. Diameter = 2 × radius.

Worked example — radius 5cm

C = 2 × π × 5 = 10π ≈ 31.4 cm

A = π × r²

Worked example — radius 6cm

A = π × 6² = 36π ≈ 113.1 cm²

Watch out

If you're given the diameter, halve it first to get the radius. The formula uses radius, not diameter.