CAIE IGCSE Mathematics Extended Percentage Questions

Practise percentage amounts and change, reverse percentages and repeated growth or decay in financial, population and measurement contexts.

Exam points

calculate a percentage amount or express a part as a percentage of the correct original total
apply increase or decrease multipliers and divide by a multiplier for a reverse percentage
use repeated multipliers for compound interest, growth or depreciation over several periods

Covered syllabus points

E1.13.1 Calculate a given percentage of a quantity.E1.13.2 Express one quantity as a percentage of another.E1.13.3 Calculate percentage increase or decrease.E1.13.4 Calculate with simple and compound interest.E1.13.5 Calculate using reverse percentages

[Maximum number: 6]

(a)

Table for Question (a) — CAIE IGCSE Mathematics Extended

The table shows information about some of the planets in the solar system.

Planet	Diameter (km)	Average distance from the Sun (km)
Earth	12800	$1.496\times10^8$
Mars	6800	$2.279\times10^8$
Jupiter	143000	$7.786\times10^8$
Saturn	120500	$1.434\times10^9$
Neptune	49500	$4.495\times10^9$

[ 6 ]

(i)

The planet Uranus has a diameter that is 35.8% of the diameter of Jupiter.

Calculate the diameter of Uranus.

[ 2 ]

51200 or 51190 or 51194
M1 for $\frac{35.8}{100}\times143000$
After 0 scored, SC1 for answer figs 512 or figs 5119 or figs 51194

(ii)

Find the average distance of Neptune from the Sun as a percentage of the average distance of the Earth from the Sun.

[ 2 ]

3000 or 3004 to 3005
M1 for $\frac{4.495\times10^9}{1.496\times10^8}\times100$ oe
After 0 scored, SC1 for answer figs 3 or figs 3004... or figs 3005

(iii)

The diameter of Mars is 39.2% greater than the diameter of Mercury.

Calculate the diameter of Mercury.

[ 2 ]

4890 or 4885...
M1 for $d\left(1+\frac{39.2}{100}\right)=6800$ oe

[Maximum number: 3]

Dhanu has a model railway.

(a)

He has a train that consists of a locomotive and 4 coaches. The mass of the locomotive is 87 g and the mass of each coach is 52 g .

[ 1 ]

(i)

Work out the mass of the locomotive as a percentage of the total mass of the train.

[ 1 ]

29.5 or $29.49 \ldots$

1

FT $\frac{87}{\text { their }(\mathbf{a})(\mathbf{i})} \times 100$

(b)

The cost of a railway magazine increases by $12.5 \%$ to $\$ 2.70$ .

Calculate the cost of the magazine before this increase.
$

[ 2 ]

2.4[0] nfww
M1 for $\left(1+\frac{12.5}{100}\right)x=2.7[0]$ oe.

[Maximum number: 4]

(a)

In 2021, the value of the team's players was $2.65 million.
In 2022 this value has decreased by 12%.
Find the value in 2022.
$ million

[ 2 ]

2.332 oe
M1 for $2.65\left(1-\frac{12}{100}\right)$ oe
or B1 for 0.318 [million] seen

(b)

The number of people at a football match is 1455.

This is 6.25% of the total number of people allowed in the stadium.
Find the total number of people allowed in the stadium.

[ 2 ]

23280 cao
M1 for $\frac{6.25}{100}\times x=1455$ or better

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Covered syllabus points

E1.13 Percentages question 1

Question (a)

Question (i)

Question (ii)

Question (iii)

E1.13 Percentages question 2

Question (a)

Question (i)

Question (b)

E1.13 Percentages question 3

Question (a)

Question (b)