Exercise Solutions Available
Step-by-step answers for all textbook questions in this chapter
Chapter 1 — Rational Numbers
| Concept | Statement / Formula |
|---|---|
| Rational number | p/q where p, q ∈ ℤ and q ≠ 0 |
| Standard form | q > 0 and HCF(p, q) = 1 |
| Additive inverse | −p/q |
| Multiplicative inverse | q/p |
| Density property | Infinitely many rationals between any two rationals |
| Addition (unlike fractions) | Convert to LCM denominator, then add numerators |
| Division | Multiply by reciprocal of divisor |
Chapter 2 — Measurements
| Shape | Formula |
|---|---|
| Area of trapezium | ½ × (a + b) × h |
| Area of rhombus | ½ × d₁ × d₂ |
| Perimeter of rhombus | 4s |
| LSA of cube | 4a² |
| TSA of cube | 6a² |
| Volume of cube | a³ |
| LSA of cuboid | 2h(l + b) |
| TSA of cuboid | 2(lb + bh + lh) |
| Volume of cuboid | lbh |
| Unit conversion | 1 m³ = 1000 litres |
Chapter 3 — Algebra (Identities)
| Identity | Expansion |
|---|---|
| (a + b)² | a² + 2ab + b² |
| (a − b)² | a² − 2ab + b² |
| (a + b)(a − b) | a² − b² |
| (x + a)(x + b) | x² + (a + b)x + ab |
Factorisation reverse:
- a² + 2ab + b² = (a + b)²
- a² − 2ab + b² = (a − b)²
- a² − b² = (a + b)(a − b)
Chapter 4 — Geometry
| Property / Rule | Statement |
|---|---|
| Angle sum of triangle | = 180° |
| Exterior angle theorem | Exterior angle = sum of two remote interior angles |
| SSS | All three sides equal |
| SAS | Two sides and included angle equal |
| ASA | Two angles and included side equal |
| RHS | Right angle, hypotenuse, one side equal |
| Parallelogram — sides | Opposite sides equal and parallel |
| Parallelogram — angles | Opposite angles equal; consecutive supplementary |
| Parallelogram — diagonals | Bisect each other |
| Rhombus — diagonals | Bisect at right angles; bisect vertex angles |
| Rectangle — diagonals | Equal in length |
Chapter 5 — Coordinate Geometry
| Concept | Formula / Fact |
|---|---|
| Origin | (0, 0) |
| Quadrant signs | I:(+,+) II:(−,+) III:(−,−) IV:(+,−) |
| Distance formula | √[(x₂−x₁)² + (y₂−y₁)²] |
| Distance from origin | √(x² + y²) |
Chapter 6 — Statistics
| Measure | Formula |
|---|---|
| Mean | Sum of all observations ÷ number of observations |
| Median | Middle value when data is arranged in order |
| Mode | Most frequently occurring value |
Chapter 7 — Graphs
| Concept | Statement |
|---|---|
| Linear graph | Straight line; represents constant rate of change |
| Slope (informally) | Steeper line = faster rate of change |
| Intersection | Point where two graphs meet; both equations satisfied |
Quick Recall Test
Cover the right column and write each formula from memory. Check your answers and circle anything you missed. Revise circled formulae daily until the exam.
Frequently Asked Questions
Cover the formula column and try to recall each formula from the chapter and topic names alone. Any formula you cannot recall goes on your revision card.