Page 19 - ACE YR IGCSE A TOP APPR' TO MATHS

4 Express 160 as a product of its prime factors, give your answer in index notation.
Hence, find the smallest possible value of x such that 160x is a perfect cube.

[2]

5 (a) It is given that 400 = 2 × 5 . Express 9000 as a product of its prime factors, give your answer in index
4
2
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notation.

[2]

(b) Find the smallest positive integer m for which 400m is a multiple of 9000.

[2]

4
(c) Find the smallest positive integer n for which √9000n is a whole number.

[2]

6 Wei Wei bought a cardboard measuring 95 cm and 285 cm. She wants to cut out square cards of identical
size from the cardboard such that there is no wastage.
(a) Calculate the largest possible perimeter of each square that she can cut out.

[2]

(b) Find the total number of square cards she can cut out.

[2]

Three traffic lights at different locations are changing from green to red every 45, 48 and 60 seconds
respectively. If all three lights changed concurrently at 11:59 p.m., when would be the next time that
all three lights change at the same time again?

[3]

Cambridge IGCSE
TM
14 Ace Your Mathematics

Chapter 1A.indd 14 15/03/2022 10:27 AM