Module 6
Equations & 2D shapes
Quick-reference revision notes for parents.
6.1 Equations reminder
An equation has an equals sign and an unknown. To solve, do the same operation to both sides until the unknown is alone.
Worked example — 3x + 5 = 20
3x + 5 = 20
3x = 15 (subtract 5)
x = 5 (divide by 3)
Always check
Substitute back: 3(5) + 5 = 20 ✓.
6.2 Solving equations with unknown on both sides
Get all the x's on one side, all the numbers on the other.
Worked example — 5x − 3 = 2x + 9
5x − 3 = 2x + 9
3x − 3 = 9 (subtract 2x)
3x = 12 (add 3)
x = 4 (divide by 3)
Strategy
Move the smaller x term to keep the coefficient positive — fewer sign mistakes.
6.3 Solving equations with brackets
Expand the brackets first, then solve as usual.
Worked example — 4(x − 2) = 12
4(x − 2) = 12
4x − 8 = 12 (expand)
4x = 20 (add 8)
x = 5 (divide by 4)
Worked example — 3(2x + 1) = 5(x − 2)
6x + 3 = 5x − 10
x + 3 = −10
x = −13
6.4 Types of quadrilateral
| Shape | Key properties |
|---|---|
| Square | 4 equal sides, 4 right angles |
| Rectangle | Opposite sides equal, 4 right angles |
| Parallelogram | Opposite sides parallel and equal; opposite angles equal |
| Rhombus | Parallelogram with 4 equal sides |
| Trapezium | One pair of parallel sides |
| Kite | Two pairs of adjacent equal sides; one line of symmetry |
6.5 Area of parallelogram, triangle and trapezium
Parallelogram
A = base × height (perpendicular height, not slant)
Triangle
A = ½ × base × height
Trapezium
A = ½ × (a + b) × h — a and b are the parallel sides, h is the perpendicular distance between them
Watch out
"Height" always means perpendicular height. Don't use the slanted edge.
Worked example — trapezium with parallel sides 8cm, 12cm and height 5cm
A = ½ × (8 + 12) × 5 = ½ × 20 × 5 = 50 cm²
Quick reference
- Equations: same operation on both sides; unknowns on one side, numbers on the other
- Brackets: expand first
- Parallelogram area = base × perpendicular height
- Triangle area = ½ × base × height
- Trapezium area = ½(a + b) × h