1
1 Write down an irrational number with a value between 10 and 20.
................................................... [1]
[Total: 1]
2 (a) Write 180 as a product of its prime factors.
................................................... [2]
(b) Find the lowest common multiple (LCM) of 160 and 180.
................................................... [2]
[Total: 4]
3 Write the recurring decimal as a fraction.
Show all your working.
................................................... [2]
[Total: 2]
2
4 The temperature on Monday was −7 °C.
The temperature on Tuesday was 5 °C lower than on Monday.
The temperature on Wednesday was 8 °C higher than on Tuesday.
Find the temperature on Wednesday.
................................................... °C [2]
[Total: 2]
5 Work out , giving your answer in standard form.
................................................... [2]
[Total: 2]
6 Without using a calculator, work out .
You must show all your working and give your answer as a mixed number in its simplest form.
................................................... [3]
[Total: 3]
3
7 The scale on a map is 1 : 50 000.
The area of a field on the map is 1.2 square centimetres.
Calculate the actual area of the field in square kilometres.
Answer ................................................... km2 [2]
[Total: 2]
8 Arjun and Gretal each pay rent.
In 2018, the ratio of the amount each paid in rent was Arjun : Gretal = 5 : 7.
In 2019, the ratio of the amount each paid in rent was Arjun : Gretal = 9 : 13.
Arjun paid the same amount of rent in both 2018 and 2019.
Gretal paid $290 more rent in 2019 than she did in 2018.
Work out the amount Arjun paid in rent in 2019.
$ ................................................... [4]
[Total: 4]
4
9 Sonia wants to invest $5000 for 6 years.
Bank A pays compound interest at a rate of 3.5% per year.
Bank B increases the $5000 by 22% at the end of 6 years.
Which bank will give Sonia the most money at the end of 6 years and by how much?
You must show all your working.
Bank A Bank B
Bank .................... will give $ .............................. more money. [5]
[Total: 5]
10 In a sale, a shop reduces all prices by 12%.
(a) Dina buys a book which has an original price of $6.50 .
Calculate how much Dina pays for the book.
$ ................................................... [2]
(b) Elu pays $11 for a toy.
Calculate the original price of the toy.
$ ................................................... [2]
[Total: 4]
5
11 Friedrich borrows $1200 for 3 years at a rate of 5.6% per year compound interest.
Work out the total amount he pays back at the end of the 3 years.
$ ................................................... [3]
[Total: 3]
12 $2600 is invested for 5 years at a rate of 4% per year simple interest.
Calculate the total interest at the end of the 5 years.
Answer $ ................................................... [2]
[Total: 2]
13 There are 30 000 lions in Africa.
The number of lions in Africa decreases exponentially by 2% each year.
Find the number of lions in Africa after 6 years.
Give your answer correct to the nearest hundred.
................................................... [2]
[Total: 2]
6
14 Two rectangular picture frames are mathematically similar.
The areas of the frames are 350 cm2 and 1134 cm2 .
The width of the smaller frame is 17.5 cm.
Calculate the width of the larger frame.
................................................... cm [3]
[Total: 3]
15
NOT TO
SCALE
The diagram shows two mathematically similar bowls.
The larger bowl has capacity 7.8 litres and height 11.5 cm.
The smaller bowl has capacity 4 litres.
Calculate the height of the smaller bowl.
................................................... cm [3]
[Total: 3]
7
16
The diagram shows an isosceles triangle ABC with AB = AC.
LCM and BCN are straight lines and LCM is parallel to AB.
Angle ACL = 56°.
Find the value of x and the value of y.
x = ...................................................
y = ................................................... [4]
[Total: 4]
8
17
NOT TO
59° 37° SCALE
a°
c°
b°
The diagram shows two parallel lines intersected by two straight lines.
Find the values of a, b and c.
a = ..................................
b = ..................................
c = .................................. [3]
[Total: 3]
18 Find the size of one interior angle of a regular 10-sided polygon.
................................................... [3]
[Total: 3]
9
19
A, B, C, D and E lie on the circle, centre O.
Angle AEB = 35°, angle ODE = 28° and angle ACD = 109°.
(a) Work out the following angles, giving reasons for your answers.
(i) Angle EBD = .............................. because ............................................................................
................................................................................................................................................
................................................................................................................................................ [3]
(ii) Angle EAD = .............................. because ............................................................................
................................................................................................................................................ [2]
(b) Work out angle BEO.
Angle BEO = ................................................... [3]
[Total: 8]
