Number and Numeration

Which ONE of these numbers is irrational? 0.75, √16, √10, 2/3

ECZ Paper 1 · 1 mark · Foundation level

Express 60 as a product of its prime factors, in index form.

ECZ Paper 1 · 2 marks · Foundation level

Write down the lowest common multiple (LCM) of 6 and 8.

ECZ Paper 1 · 1 mark · Foundation level

Which ONE of these numbers is a prime number? 9, 15, 23, 51

ECZ Paper 1 · 1 mark · Foundation level

Find the highest common factor (HCF) of 18 and 24.

ECZ Paper 1 · 2 marks · Foundation level

Answer (a) and (b) on separate lines, true or false: (a) Every integer is a rational number. (b) 0.333… (recurring) is an irrational number.

ECZ Paper 1 · 2 marks · Foundation level

A carpenter has two planks, one 96 cm long and one 144 cm long. He cuts both into pieces of the same length, with no wood left over, and the pieces must be as long as possible. Find the length of one piece.

ECZ Paper 1 · 3 marks · Application level

Buses to Ndola leave a station every 12 minutes and buses to Livingstone leave every 18 minutes. At 08:00, one bus to each town leaves at the same time. At what time do they next leave together?

ECZ Paper 1 · 2 marks · Application level

(a) List ALL the factors of 72. (b) Write down the largest prime factor of 72.

ECZ Paper 1 · 3 marks · Application level

A number is multiplied by itself and the result is 196. Find the number.

ECZ Paper 1 · 2 marks · Application level

A teacher can arrange a group of learners in rows of 15 or in rows of 21, with no learner left over in either case. What is the least number of learners the group could contain?

ECZ Paper 1 · 2 marks · Application level

A rectangular floor measures 4.05 m by 2.85 m. It is to be tiled completely with identical square tiles of the largest possible size. (a) Find the side length of one tile, in centimetres. (b) Find how many tiles are needed.

ECZ Paper 2 · 4 marks · Analysis level

Put each of these numbers under the correct heading, on separate lines: integers; rational but NOT an integer; irrational −3, 0, 2/5, √25, √7, π

ECZ Paper 2 · 3 marks · Analysis level

Find the smallest whole number that leaves a remainder of 3 when it is divided by 8 and also when it is divided by 11.

ECZ Paper 2 · 3 marks · Analysis level

The red light on a billboard flashes every 12 seconds and the blue light flashes every 18 seconds. At 06:00 exactly, the two lights flash together. (a) After how many seconds do the two lights next flash together? (b) How many times do the two lights flash together in the first 10 minutes after 06:00?

ECZ Paper 2 · 4 marks · Mastery level

A shopkeeper packs 84 oranges and 126 mangoes into identical baskets. Each basket contains the same number of oranges and the same number of mangoes, with no fruit left over, and she wants to use the greatest possible number of baskets. (a) Find the greatest number of baskets she can use. (b) State how many oranges and how many mangoes are in each basket.

ECZ Paper 2 · 5 marks · Mastery level