GCSE Maths

everything

LCM of 12 and 18

36

Calculate: 5 + 2 × (8 - 3)

15

Convert 0.75 to a fraction in its simplest form

3/4

New price after 15% increase on £80

£92

Simplify √50 + √8

5√2 + 2√2 = 7√2

Write 0.00032 in standard form

3.2 × 10⁻⁴

Round 347.856 to 2 significant figures

350

Expand (x + 3)(x - 5)

x² - 5x + 3x - 15 = x² - 2x - 15

Solve x² - 5x + 6 = 0 by factorising

(x - 2)(x - 3) = 0, so x = 2 or x = 3

Find the nth term of the sequence 3, 7, 11, 15, ...

4n - 1

Share £60 in the ratio 2:3

£24:£36

Value of a car after 2 years with 10% depreciation

£9,720

Sum of interior angles of a hexagon

(6 - 2) × 180 = 720°

Find x in a right-angled triangle where opposite = 4 cm, hypotenuse = 8 cm

sin x = 4/8 = 0.5, so x = 30°

Probability of picking a red ball from a bag with 4 red and 6 blue balls

4/10 = 0.4

Mean of 3, 7, 7, 10, 12

(3 + 7 + 7 + 10 + 12)/5 = 7.8

Find f(4) if f(x) = 2x + 3

f(4) = 2(4) + 3 = 11

Find a + b if a = (2, 3) and b = (-1, 4)

(1, 7)

Area of a circle with radius 5 cm

25π cm²

Solve 2x - 3 = 7

x = 5

Mode of the numbers 2, 3, 3, 4, 4, 4, 5

4

Median of 1, 3, 7, 8, 9, 10, 12

8

Convert 5/8 into a decimal

0.625

Calculate 3⁴

81

Factorise x² - 9

(x - 3)(x + 3)

Work out 2/3 + 3/5

19/15

Express 56 as a product of its prime factors

2³ × 7

Value of 7!

5040

Exterior angle of a regular octagon

360/8 = 45°

Convert 250 cm to metres

2.5 m

Probability of rolling a 6 on a fair dice

1/6

Solve x² = 49

x = ±7

Surface area of a cube with side length 3 cm

6(3²) = 54 cm²

Solve 3x + 4 = 19

x = 5

Reciprocal of 2/5

5/2

Gradient of the line y = 3x - 2

3

Solve for x: 5x - 2 = 3x + 6

x = 4

Volume of a sphere with radius 6 cm

4/3 π (6)³ = 288π cm³

Calculate 6!

720

Equation of a line parallel to y = 4x + 1

y = 4x + c, where c is any constant

Find 25/100 as a decimal

0.25

Gradient between points (1,2) and (4,8)

(8 - 2)/(4 - 1) = 2

What is log₂ 8?

3

Find sin 45°

√2/2

Quadratic formula solution for ax² + bx + c = 0

x = (-b ± √(b² - 4ac))/2a

Derivative of f(x) = x³ + 2x² - x + 5

3x² + 4x - 1

Sum of the first 10 terms of an arithmetic sequence where a = 2 and d = 3

S₁₀ = 10/2 (2(2) + 9(3)) = 155

Simplify 4√2 + 2√2

6√2

Solve 3x + 5 = 2x + 12

x = 7

Volume of a cylinder with radius 3 cm and height 10 cm

π(3²)(10) = 90π cm³

Express 0.8 as a fraction

4/5

Perimeter of a rectangle with length 8 cm and width 3 cm

22 cm

Perimeter of a rectangle

Find the perimeter of a rectangle with length 8 cm and width 3 cm. 2(8 + 3) = 22 cm

Square root of 121

Find the square root of 121. 11

Simplify (x² - 4x + 4) ÷ (x - 2)

x - 2

Gradient of the line

Find the gradient of the line passing through the points (2, 3) and (5, 11). (11 - 3)/(5 - 2) = 8/3

Solve for x: 4x - 7 = 13

x = 5

Solve x² + 6x + 9 = 0 by factorising

(x + 3)(x + 3) = 0, so x = -3

Simplify 5(3x - 4) - 2(x + 6)

13x - 38

Area of a triangle

Find the area of a triangle with base 6 cm and height 4 cm. 1/2 × 6 × 4 = 12 cm²

Surface area of a sphere

Find the surface area of a sphere with radius 7 cm. 4π(7)² = 196π cm²

Nth term of the sequence

Find the nth term of the sequence 2, 4, 8, 16, ... 2ⁿ

Simplify 12 ÷ 3 × 2

8

Solve x + 3 = 7

x = 4

Area of a trapezoid

Find the area of a trapezoid with bases 5 cm and 7 cm, and height 4 cm. 1/2 × (5 + 7) × 4 = 24 cm²

Solve for x: x/3 = 5

x = 15

Sum of interior angles of a quadrilateral

Find the sum of the interior angles of a quadrilateral. (4 - 2) × 180 = 360°

Hypotenuse of a right-angled triangle

Find the hypotenuse of a right-angled triangle with sides 6 cm and 8 cm. √(6² + 8²) = √(36 + 64) = √100 = 10 cm

Solve for x: 3x + 2 = 14

x = 4

Simplify (2x - 3)(x + 4)

2x² + 5x - 12

Volume of a cone

Find the volume of a cone with radius 4 cm and height 9 cm. 1/3π(4²)(9) = 48π cm³

Convert 0.375 to a fraction

3/8

Mean of numbers

Find the mean of 2, 6, 7, 10. (2 + 6 + 7 + 10) / 4 = 6.25

Expand (x - 3)(x + 5)

x² + 5x - 3x - 15 = x² + 2x - 15

Simplify 8x - 2x + 5

6x + 5

Solve 2x - 3 = 11

x = 7

Perimeter of a circle

Find the perimeter of a circle with radius 4 cm. 2π(4) = 8π cm

Convert 3.25 to a fraction

13/4

Volume of a rectangular prism

Find the volume of a rectangular prism with length 2 cm, width 4 cm, and height 6 cm. 2 × 4 × 6 = 48 cm³

Solve x² + 8x + 15 = 0 by factorising

(x + 3)(x + 5) = 0, so x = -3 or x = -5

Area of a square

Find the area of a square with side length 5 cm. 5² = 25 cm²

Solve x² - 4x - 21 = 0 by factorising

(x - 7)(x + 3) = 0, so x = 7 or x = -3

Distance between points

Find the distance between the points (1, 1) and (4, 5). √((4 - 1)² + (5 - 1)²) = √(9 + 16) = √25 = 5

Solve for x: 5x - 4 = 11

x = 3

Area of a circle

Find the area of a circle with radius 8 cm. π(8)² = 64π cm²

Solve 2x + 3 = 11

x = 4

Mode of numbers

Find the mode of the numbers 1, 1, 2, 2, 3, 4. 1 and 2 (bimodal)

Simplify √18

3√2

Solve 6x + 2 = 20

x = 3

Equation of a line perpendicular to y = 2x + 1

Find the equation of a line perpendicular to y = 2x + 1. y = -1/2x + c (where c is any constant)

Simplify (x - 2)²

x² - 4x + 4

Solve for x: x² - 9 = 0

x = ±3

Surface area of a cylinder

Find the surface area of a cylinder with radius 3 cm and height 5 cm. 2π(3)² + 2π(3)(5) = 18π + 30π = 48π cm²

Volume of a rectangular prism

Find the volume of a rectangular prism with length 3 cm, width 2 cm, and height 4 cm. 3 × 2 × 4 = 24 cm³

Express 0.625 as a fraction

5/8

Solve x/4 = 6

x = 24

Area of a parallelogram

Find the area of a parallelogram with base 5 cm and height 7 cm. 5 × 7 = 35 cm²

Simplify 7(2x + 3)

14x + 21

Perimeter of a triangle

Find the perimeter of a triangle with sides 3 cm, 4 cm, and 5 cm. 3 + 4 + 5 = 12 cm

Solve 7x - 5 = 19

x = 3.43 (rounded to 2 decimal places)