IGCSE Maths Types of number topical questions

From the list 1, 2, 15, 23, 33:

1. (a)Write down the two prime numbers.[2]
2. (b)Find the highest common factor of 18 and 24.[2]

In a class of 30 students, 18 walk to school, 12 cycle and 5 do both.

1. (a)Find the number who walk or cycle.[2]
2. (b)Find the number who do neither.[2]
3. (c)One student is picked at random. Find the probability that they cycle but do not walk.[2]

Write down the value of each of these.

1. (a)√144[1]
2. (b)2³[1]
3. (c)7²[1]

A = {multiples of 4 from 1 to 30 inclusive} and B = {multiples of 6 from 1 to 30 inclusive}.

1. (a)List the members of A.[2]
2. (b)Find A ∩ B.[2]
3. (c)Find n(A ∪ B).[2]

Here are four numbers: −3, 2, −7, 0.

1. (a)Write the four numbers in ascending order.[2]
2. (b)Work out 3² − 2³.[1]
3. (c)Copy and complete with < or >: −7 ⬜ 2.[1]

Use prime factorisation to compare 144 and 60.

1. (a)Express 144 and 60 each as a product of prime factors.[2]
2. (b)Write down the highest common factor of 144 and 60.[1]
3. (c)Find the lowest common multiple of 144 and 60.[2]

This question is about exact values.

1. (a)Find the reciprocal of 3¼, giving your answer as a fraction in its lowest terms.[2]
2. (b)Write 0.409, 0.44 and 7/16 in ascending order.[2]

Evaluate exactly. (Extended)

1. (a)16^(1/2) + 27^(1/3)[2]
2. (b)2⁻² × 2³[2]

220 = 2² × 5 × 11 and 280 = 2³ × 5 × 7.

1. (a)Write down the highest common factor of 220 and 280.[1]
2. (b)Find the lowest common multiple of 220 and 280.[2]
3. (c)Find the smallest positive integer k such that 220k is a perfect square.[2]

Of 200 travellers at an airport, 120 carry a passport card (P), 95 carry a visa document (V), and 40 carry neither.

1. (a)Find n(P ∩ V).[2]
2. (b)Find the number of travellers who carry P but not V.[2]
3. (c)One traveller is chosen at random. Find the probability that they carry P but not V, giving your answer as a fraction in its lowest terms.[1]

120 students were asked which of football (F), hockey (H) and tennis (T) they play. 65 play football, 60 play hockey, 45 play tennis, 25 play football and hockey, 20 play hockey and tennis, 15 play football and tennis, and 8 play all three. (Extended)

1. (a)Find the number who play football only.[2]
2. (b)Find the number who play hockey only.[2]
3. (c)Find the number who play tennis only.[1]
4. (d)Find the number who play none of the three sports.[2]

Two bus routes leave the same stop on the hour. Route A leaves every 12 minutes and route B leaves every 18 minutes.

1. (a)Find the number of minutes after the hour when both routes next leave together.[2]
2. (b)Two ropes are 84 cm and 126 cm long. They are each cut into pieces of the same length, as long as possible. Find the length of each piece and the total number of pieces.[3]

Answer this question without a calculator. (Extended)

1. (a)Write 2⁻⁴ as a fraction.[1]
2. (b)Find the reciprocal of 3⅗, giving your answer as a fraction in its lowest terms.[2]
3. (c)Find the smallest whole number n for which 3ⁿ is greater than 100.[1]

A school hall floor measures 480 cm by 360 cm. It is to be covered with identical square tiles, as large as possible, with no cutting and no gaps.

1. (a)Find the side length of the largest possible square tile.[3]
2. (b)Find the number of tiles needed.[2]
3. (c)Buses to the sports field leave school every 15 minutes and buses to the library every 20 minutes. Both leave at 08:00. Find the time of the next departure when both leave together.[2]