Perimeter and area of flat shapes
| Shape | Perimeter | Area |
|---|---|---|
| Rectangle (length l, breadth b) | 2(l + b) | l × b |
| Square (side a) | 4a | a2 |
| Triangle (base b, height h) | Sum of the three sides | ½ × b × h |
| Parallelogram (base b, height h) | 2(a + b) for sides a and b | b × h |
| Rhombus (diagonals d1, d2) | 4 × side | ½ × d1 × d2 |
| Trapezium (parallel sides a and b, height h) | Sum of the four sides | ½ × (a + b) × h |
| Circle (radius r) | 2πr (circumference) | πr2 |
Use π = 22/7 or 3.14 as the question says. The diameter d = 2r.
Solid shapes
| Solid | Volume | Curved or lateral surface area | Total surface area |
|---|---|---|---|
| Cube (side a) | a3 | 4a2 | 6a2 |
| Cuboid (l, b, h) | l × b × h | 2h(l + b) | 2(lb + bh + hl) |
| Cylinder (radius r, height h) | πr2h | 2πrh | 2πr(r + h) |
Percentage, profit and interest
| Idea | Formula |
|---|---|
| Percentage | (part ÷ whole) × 100 |
| Profit | Selling price - Cost price (when SP is more) |
| Loss | Cost price - Selling price (when CP is more) |
| Profit percent | (Profit ÷ Cost price) × 100 |
| Loss percent | (Loss ÷ Cost price) × 100 |
| Discount | Marked price - Selling price |
| Simple interest | SI = (P × R × T) ÷ 100 |
| Amount | A = P + SI |
| Compound interest amount (yearly) | A = P(1 + R/100)n |
P is the principal, R the rate percent per year, T and n the time in years.
Average, speed and ratio
| Idea | Formula |
|---|---|
| Average (mean) | Sum of observations ÷ number of observations |
| Range | Highest value - lowest value |
| Speed | Distance ÷ time |
| Distance | Speed × time |
| Time | Distance ÷ speed |
| Probability of an event | Number of favourable outcomes ÷ total number of outcomes |
Probability is always between 0 (impossible) and 1 (certain).
Algebra identities and exponents
| Name | Rule |
|---|---|
| Square of a sum | (a + b)2 = a2 + 2ab + b2 |
| Square of a difference | (a - b)2 = a2 - 2ab + b2 |
| Difference of squares | a2 - b2 = (a + b)(a - b) |
| Product of two binomials | (x + a)(x + b) = x2 + (a + b)x + ab |
| Multiplying powers | am × an = am+n |
| Dividing powers | am ÷ an = am-n |
| Power of a power | (am)n = amn |
| Power of a product | (ab)m = ambm |
| Zero power | a0 = 1 (a is not 0) |
| Negative power | a-n = 1 ÷ an |
Angles, triangles and polygons
| Idea | Rule |
|---|---|
| Complementary angles | Add up to 90° |
| Supplementary angles | Add up to 180° |
| Angles on a straight line | Add up to 180° |
| Angles at a point | Add up to 360° |
| Angle sum of a triangle | 180° |
| Exterior angle of a triangle | Equals the sum of the two opposite interior angles |
| Angle sum of a polygon with n sides | (n - 2) × 180° |
| Each angle of a regular polygon | (n - 2) × 180° ÷ n |
| Sum of exterior angles of any polygon | 360° |
| Number of diagonals of an n-sided polygon | n(n - 3) ÷ 2 |
| Pythagoras theorem (right-angled triangle) | Hypotenuse2 = base2 + height2 |
Divisibility rules
| Divisible by | Test |
|---|---|
| 2 | Last digit is 0, 2, 4, 6 or 8 |
| 3 | Sum of the digits is divisible by 3 |
| 4 | Last two digits form a number divisible by 4 |
| 5 | Last digit is 0 or 5 |
| 6 | Divisible by both 2 and 3 |
| 8 | Last three digits form a number divisible by 8 |
| 9 | Sum of the digits is divisible by 9 |
| 10 | Last digit is 0 |
| 11 | Difference between the sum of digits in odd places and in even places is 0 or a multiple of 11 |