CAIE IGCSE Mathematics Extended E1.13 Percentages 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: 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

[Maximum number: 12]

(a)

Write $ 1.92 as a percentage of $ 1.60. \%

[ 1 ]

(b)

In a sale the original prices are reduced by 15%.

[ 4 ]

(i)

Calculate the sale price of a book that has an original price of $\$ 12$ .
$

[ 2 ]

10.2[0]
M1 for $\frac{15}{100}\times12$ .

(ii)

Calculate the original price of a jacket that has a sale price of $\$ 38.25$ .
$

[ 2 ]

45
M1 for $38.25\div\left(1-\frac{15}{100}\right)$ .

(c)

Dean invests $\$ 500$ for 10 years at a rate of $1.7 \%$ per year simple interest.

Calculate the total interest earned during the 10 years.
$

[ 2 ]

85
M1 for $\frac{500\times1.7\times10}{100}$ .

(d)

Ollie invests $\$ 200$ at a rate of $0.0035 \%$ per day compound interest.

Calculate the value of Ollie's investment at the end of 1 year.
[1 year = 365 days.]
$

[ 2 ]

203 or 202.5 to 202.6
M1 for $200\left(1+\frac{0.0035}{100}\right)^{365}$ .

(e)

Edna invests $500 at a rate of r % per year compound interest.

At the end of 6 years, the value of Edna's investment is $ 559.78.
Find the value of r.

[ 3 ]

1.9
M2 for $\sqrt[6]{\frac{559.78}{500}}$ oe, or M1 for $500\left(1+\frac{r}{100}\right)^6=559.78$ .

[Maximum number: 2]

Table for Question 4 — 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	$4.495\times10^9$

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

Calculate the diameter of Uranus.

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

[Maximum number: 1]

Dhanu has a model railway.

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 .

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

29.5 or $29.49 \ldots$

1

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

[Maximum number: 2]

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

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

[Maximum number: 2]

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.

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

All question bank results loaded

Covered syllabus points

Question 1

Question (a)

Question (i)

Question (b)

Question 2

Question (a)

Question (b)

Question 3

Question (a)

Question (b)

Question (i)

Question (ii)

Question (c)

Question (d)

Question (e)

Question 4

Question 5

Question 6

Question 7