Grade 9 maths formulas in one place: exponent laws, factorising patterns, gradient, Pythagoras, area and volume, interest, and data handling, with notes.
Grade 9 exams don't come with a formula sheet, so you need to know these by heart. This page collects every formula and rule from the CAPS Grade 9 syllabus in one place, grouped by topic, with a note on when to use each one.
Use it to revise before tests, and to check yourself: cover the expression column and see whether you can write each formula from memory.
| Formula | Expression | Note |
|---|---|---|
| Multiplying powers | aᵐ × aⁿ = aᵐ⁺ⁿ | Same base: add the exponents. |
| Dividing powers | aᵐ ÷ aⁿ = aᵐ⁻ⁿ | Same base: subtract the exponents. |
| Power of a power | (aᵐ)ⁿ = aᵐⁿ | Multiply the exponents. |
| Zero exponent | a⁰ = 1 | For any a ≠ 0. |
| Negative exponent | a⁻ⁿ = 1/aⁿ | A negative exponent means 'one over'. |
| Scientific notation | a × 10ⁿ, 1 ≤ a < 10 | n is negative for numbers smaller than 1. |
| Formula | Expression | Note |
|---|---|---|
| Distributive law | a(b + c) = ab + ac | Multiply every term in the bracket. |
| Square of a sum | (a + b)² = a² + 2ab + b² | Don't forget the middle term. |
| Square of a difference | (a − b)² = a² − 2ab + b² | The last term is always positive. |
| Difference of two squares | a² − b² = (a − b)(a + b) | Two perfect squares with a minus between them. |
| Trinomial | x² + (p + q)x + pq = (x + p)(x + q) | Find two numbers that multiply to pq and add to p + q. |
| Formula | Expression | Note |
|---|---|---|
| Linear pattern | Tₙ = bn + c | b is the constant difference. |
| Gradient | m = (y₂ − y₁)/(x₂ − x₁) | Change in y divided by change in x. |
| Straight line | y = mx + c | m is the gradient; c is the y-intercept. |
| Formula | Expression | Note |
|---|---|---|
| Theorem of Pythagoras | c² = a² + b² | Right-angled triangles only; c is the hypotenuse. |
| Area of a triangle | A = ½ × b × h | h is the perpendicular height. |
| Area of a trapezium | A = ½(a + b) × h | a and b are the parallel sides. |
| Circle | C = 2πr, A = πr² | Use the radius, not the diameter. |
| Volume of a prism or cylinder | V = area of base × height | Cylinder: V = πr²h. |
| Angles of a triangle | Â + B̂ + Ĉ = 180° | Exterior angle = sum of the interior opposite angles. |
| Formula | Expression | Note |
|---|---|---|
| Simple interest | SI = P × i × n | i as a decimal; n in years. |
| Compound growth (year by year) | Amount × (1 + i) each year | Interest is added to the amount every year. |
| Mean | mean = sum of values ÷ number of values | Sensitive to outliers. |
| Range | range = largest − smallest | A simple measure of spread. |
| Probability | P(E) = favourable outcomes ÷ total outcomes | Always between 0 and 1. |
Usually not. Grade 9 exams are set by schools, and most expect you to know these formulas. Check with your teacher.
The exponent laws, the factorising patterns, y = mx + c, the gradient formula and Pythagoras are used constantly in Grade 10.
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