Cambridge IGCSE Mathematics: every topic, by paper

What is a prime number?

A number with exactly two factors: 1 and itself (e.g. 2, 3, 5, 7, 11).

Is 1 a prime number?

No; it has only one factor.

Write 60 as a product of prime factors.

60 = 2² × 3 × 5.

Simplify 18/24.

3/4.

Calculate 2/3 + 1/4.

8/12 + 3/12 = 11/12.

Calculate 3/5 × 10/9.

30/45 = 2/3.

Simplify the ratio 15 : 25.

3 : 5.

Share £60 in the ratio 2 : 3.

5 parts: £12 each; £24 and £36.

The ratio of boys to girls is 3 : 4. There are 21 boys. How many girls?

21 ÷ 3 = 7; 7 × 4 = 28 girls.

Simplify 3a + 5b − a + 2b.

2a + 7b.

Expand 4(2x − 3).

8x − 12.

Expand and simplify (x + 3)(x + 5).

x² + 8x + 15.

Solve 3x + 5 = 20.

3x = 15, so x = 5.

Solve 5x − 3 = 2x + 9.

3x = 12, so x = 4.

Solve 2(x + 4) = 18.

x + 4 = 9, so x = 5.

Find the next two terms: 3, 7, 11, 15, …

19, 23 (add 4 each time).

Find the nth term of 5, 8, 11, 14, …

3n + 2.

Find the nth term of 20, 17, 14, 11, …

23 − 3n.

What is the equation of a straight line in slope-intercept form?

y = mx + c, where m is the gradient and c the y-intercept.

Find the gradient and y-intercept of y = 3x − 4.

Gradient 3, y-intercept −4.

How do you find the gradient between two points?

Gradient = change in y ÷ change in x.

What does differentiation find?

The gradient function (derivative), giving the gradient of a curve at any point.

Differentiate y = xⁿ.

dy/dx = nxⁿ⁻¹.

Differentiate y = 5x³.

dy/dx = 15x².

What do angles on a straight line and around a point add up to?

180° and 360°.

What do the angles in a triangle and a quadrilateral add up to?

180° and 360°.

What are vertically opposite angles?

Angles opposite each other where two lines cross; they are equal.

Name the parts of a circle: the line from centre to edge, across through the centre, and around the edge.

Radius, diameter and circumference.

What is a chord, an arc, a sector and a segment?

Chord: line joining two points on the circle. Arc: part of the circumference. Sector: region between two radii. Segment: region between a chord and an arc.

What is the angle in a semicircle?

90°: the angle subtended by a diameter at the circumference is a right angle.

Give the formula for the area of a triangle.

½ × base × perpendicular height.

Give the formula for the area of a parallelogram.

Base × perpendicular height.

Give the formula for the area of a trapezium.

½(a + b)h, where a and b are the parallel sides.

State Pythagoras' theorem.

In a right-angled triangle, a² + b² = c², where c is the hypotenuse.

Find the hypotenuse of a right-angled triangle with shorter sides 6 cm and 8 cm.

√(36 + 64) = 10 cm.

Find the missing side: hypotenuse 13 cm, one side 5 cm.

√(169 − 25) = 12 cm.

Name the four transformations.

Translation, reflection, rotation and enlargement.

What information describes a translation?

A column vector giving the horizontal and vertical movement.

What information describes a rotation?

The angle, the direction (clockwise or anticlockwise) and the centre of rotation.

What is the probability scale?

From 0 (impossible) to 1 (certain).

A fair dice is rolled. What is P(even)?

3/6 = 1/2.

If P(rain) = 0.3, what is P(not rain)?

0.7.

How do you find the mean?

Add all the values and divide by how many there are.

What are the median and mode?

Median: the middle value when ordered. Mode: the most common value.

What is the range?

Largest value − smallest value.