Having all essential maths formulas in one place saves time during revision and exam preparation. This cheat sheet covers the most important formulas from Grade 8 to Grade 12, organised by topic for quick reference. Bookmark this page for your next study session.
Algebra Formulas
Algebraic Identities (Grade 8-10)
| Identity | Formula |
|---|---|
| Square of sum | (a + b)² = a² + 2ab + b² |
| Square of difference | (a - b)² = a² - 2ab + b² |
| Difference of squares | a² - b² = (a + b)(a - b) |
| Cube of sum | (a + b)³ = a³ + 3a²b + 3ab² + b³ |
| Cube of difference | (a - b)³ = a³ - 3a²b + 3ab² - b³ |
| Sum of cubes | a³ + b³ = (a + b)(a² - ab + b²) |
| Difference of cubes | a³ - b³ = (a - b)(a² + ab + b²) |
Quadratic Formula (Grade 10-12)
For ax² + bx + c = 0: x = (-b +/- sqrt(b² - 4ac)) / 2a
Discriminant D = b² - 4ac:
- D > 0: Two distinct real roots
- D = 0: Two equal real roots
- D < 0: No real roots (complex roots)
Arithmetic Progression (AP)
Geometric Progression (GP)
Geometry Formulas
2D Shapes
| Shape | Area | Perimeter |
|---|---|---|
| Rectangle | length x width | 2(length + width) |
| Square | side² | 4 x side |
| Triangle | 0.5 x base x height | sum of all sides |
| Circle | pi x r² | 2 x pi x r |
| Parallelogram | base x height | 2(a + b) |
| Trapezium | 0.5 x (a + b) x height | sum of all sides |
3D Shapes
| Shape | Volume | Surface Area |
|---|---|---|
| Cube | side³ | 6 x side² |
| Cuboid | l x w x h | 2(lw + wh + lh) |
| Cylinder | pi x r² x h | 2 x pi x r(r + h) |
| Cone | (1/3) x pi x r² x h | pi x r(r + l) where l is slant height |
| Sphere | (4/3) x pi x r³ | 4 x pi x r² |
Coordinate Geometry (Grade 9-12)
| Formula | Expression |
|---|---|
| Distance between two points | sqrt[(x2-x1)² + (y2-y1)²] |
| Midpoint | ((x1+x2)/2, (y1+y2)/2) |
| Slope of a line | m = (y2-y1)/(x2-x1) |
| Equation of a line | y - y1 = m(x - x1) |
| Slope-intercept form | y = mx + c |
Trigonometry Formulas (Grade 9-12)
Basic Ratios
| Ratio | Definition |
|---|---|
| sin A | opposite / hypotenuse |
| cos A | adjacent / hypotenuse |
| tan A | opposite / adjacent = sin A / cos A |
| cosec A | 1 / sin A |
| sec A | 1 / cos A |
| cot A | 1 / tan A = cos A / sin A |
Standard Values
| Angle | sin | cos | tan |
|---|---|---|---|
| 0 degrees | 0 | 1 | 0 |
| 30 degrees | 1/2 | sqrt(3)/2 | 1/sqrt(3) |
| 45 degrees | 1/sqrt(2) | 1/sqrt(2) | 1 |
| 60 degrees | sqrt(3)/2 | 1/2 | sqrt(3) |
| 90 degrees | 1 | 0 | undefined |
Key Identities
Statistics and Probability (Grade 8-12)
Statistics
| Measure | Formula |
|---|---|
| Mean | Sum of all values / Number of values |
| Median | Middle value when arranged in order |
| Mode | Most frequently occurring value |
| Range | Maximum value - Minimum value |
| Variance | Sum of (xi - mean)² / n |
| Standard deviation | sqrt(Variance) |
Probability
Calculus Essentials (Grade 11-12)
Common Derivatives
| f(x) | f'(x) |
|---|---|
| x^n | nx^(n-1) |
| sin x | cos x |
| cos x | -sin x |
| e^x | e^x |
| ln x | 1/x |
Common Integrals
| f(x) | Integral of f(x) | ||
|---|---|---|---|
| x^n (n not -1) | x^(n+1)/(n+1) + C | ||
| 1/x | ln | x | + C |
| e^x | e^x + C | ||
| sin x | -cos x + C | ||
| cos x | sin x + C |
Key Takeaways
Frequently Asked Questions
How do I memorise so many formulas?
Do not try to memorise them all at once. Learn formulas by topic as you study each chapter. Use them in practice problems — active use is the best way to remember. Keep this cheat sheet handy for quick reference during revision, and test yourself regularly.
Which formulas are most important for board exams?
For Grade 10: algebraic identities, area and volume formulas, coordinate geometry formulas, trigonometric ratios. For Grade 12: calculus formulas (derivatives and integrals), probability rules, AP and GP formulas. These appear in almost every paper.
Should I derive formulas in the exam or just write them directly?
For board exams, you can use formulas directly in your solutions unless the question specifically asks for a derivation. However, understanding the derivation helps you apply the formula correctly and troubleshoot if you forget the exact formula during the exam.
Practise applying these formulas with our free Maths quizzes for Grades 8-12.