Cambridge IGCSE · Mathematics (0580)

Types of number: Practice Questions

5 multiple-choice questions marked as you go, and 5 written questions with worked solutions. All on Types of number.

10 questions22 marksFree, no account

Question 1

1 mark

Which of the following numbers is an irrational number?

Question 2

1 mark

Identify the rational number from the list below.

Question 3

1 mark

Simplify the expression involving surds:
\( \sqrt{48} - \sqrt{12} \)

Question 4

1 mark

Find the Highest Common Factor (HCF) of \( 36 \) and \( 54 \).

Question 5

1 mark

Two buses, Route X and Route Y, leave the central station at the same time. Route X buses leave every \( 15 \) minutes and Route Y buses leave every \( 25 \) minutes. After how many minutes will both buses next leave the station at the same time?

Question 6

2 marks

List all the prime numbers that are between \( 10 \) and \( 20 \).

Write your answer out first, then check it against the worked solution.

Question 7

3 marks

State whether \( \sqrt{8} \) is rational or irrational and give a brief reason for your answer.

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Question 8

5 marks

Given the set of numbers \( S = \{ -4, \sqrt{2}, 0, \frac{22}{7}, \pi, 9 \} \):
(a) List all the integers in the set.
(b) List all the rational numbers in the set.

Write your answer out first, then check it against the worked solution.

Question 9

3 marks

From the following list of numbers:
\( 4, 9, 15, 21, 25, 27 \)

(a) Find the highest common factor (HCF) of \( 24 \) and \( 60 \).
(b) From the list provided, identify all numbers that are square numbers and also odd numbers.

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Question 10

4 marks

Triangle numbers follow the pattern 1, 3, 6, 10, ... where the \(n\)-th term is given by the formula \(T_n = \frac{n(n+1)}{2}\).

(a) Show that the 5th triangle number is 15.
(b) Find the 10th triangle number.
(c) Determine if the sum of the 3rd and 4th triangle numbers is a square number. Show your working.

Write your answer out first, then check it against the worked solution.

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