3
4 Write down a multiple of 9 between 100 and 110.
................................................. [1]
5 (a) Tanvi rounds the number 4896.
She writes down 4900.
Rahul says Tanvi rounded 4896 correct to the nearest 100.
Explain why Rahul cannot be certain that Tanvi rounded 4896 correct to the nearest 100.
.....................................................................................................................................................
..................................................................................................................................................... [1]
(b) Calculate.
6.4 # 4 2
17.9 - 6.1
Give your answer correct to 3 decimal places.
................................................. [2]
6 These are the heights of four sisters.
1.61 m 1.65 m 1.53 m 1.58 m
(a) Work out the range of these heights.
Give your answer in centimetres.
............................................ cm [2]
(b) The four sisters have a brother.
The range of the five heights is 18 cm.
Work out the two possible heights of the brother.
.................... m or .................... m [2]
[Turn over
12 Factorise completely.
9t 2 w - 3t
................................................. [2]
1 (a) Find the lowest common multiple (LCM) of 30 and 75.
................................................. [2]
(b) Share $608 in the ratio 4 : 5 : 7.
$ ................................................
$ ................................................
$ ................................................ [3]
1
A ×120°
P
B
(a) Write down the bearing of B from P.
°
(1)
(b) Work out the bearing of A from P.
°
(1)
(Total for Question 1 is 2 marks)
North
Diagram NOT
accurately drawn
Y, aY,ship
The diagram shows the positions of a yacht S and
a ship a beacon
S and B. B.
a beacon
The bearing Boffrom Y isY228°
B from is 228°
Y from B.
(a) Find the bearing of Y from B.
....................................º
(2)
°
The bearing of S from Y is 118° ...............................
(2)
(b) Find the size of the angle BYS.
S from Y is 118°
BYS.
....................................º
(1)
(c) Given also that BY = SY, find the bearing of S from B.
...............................
°
(1)
8
16 (a) Write 567 000 000 in standard form.
................................................. [1]
(b) 6.5 # 10 -2 6.1 # 10 -1 6.2 # 10 2 6.79 # 10 1 6.18 # 10 2 6.35 # 10 -2
Calculate the product of the largest number and the smallest number from this list.
Give your answer in standard form.
................................................. [2]
17
P
A NOT TO
SCALE
x cm
1.61 cm
R 3.2 cm Q
C 2.8 cm B
Triangle ABC is mathematically similar to triangle PQR.
Find the value of x.
x = ................................................. [2]
9
18 (a) Simplify.
(i) x 12 ' x 3
................................................. [1]
5
(ii) ( y 2)
................................................. [1]
1
(b) 3p =
81
Find the value of p.
p = ................................................. [1]
1 2
19 Without using a calculator, work out 2 # 3 .
4 3
You must show all your working and give your answer as a mixed number in its simplest form.
................................................. [3]
© UCLES 2021 0580/12/F/M/21 [Turn over
10
20 Solve the simultaneous equations.
You must show all your working.
5x + 6y = 14
2x + 8y = 7
x = .................................................
y = ................................................. [4]
11
21
C
NOT TO
6 cm SCALE
O B
5 cm
The diagram shows a shape made from a quarter-circle, OAB, and a right-angled triangle OBC.
The radius of the circle is 5 cm and OC = 6 cm.
Calculate the area of the shape.
.......................................... cm 2 [3]
3
2 (a)
R
Q NOT TO
S SCALE
29°
The points P, Q, R and S lie on a circle with diameter PR.
Work out the size of angle PSQ, giving a geometrical reason for each step of your working.
.....................................................................................................................................................
.....................................................................................................................................................
..................................................................................................................................................... [3]
(b)
A
NOT TO
SCALE
98°
C T S
The points A, B and T lie on a circle and CTS is a tangent to the circle at T.
ABC is a straight line and AB = BT.
Angle ATS = 98°.
Work out the size of angle ACT.
8
6 (a) At a festival, 380 people out of 500 people questioned say that they are camping.
There are 55 300 people at the festival.
Calculate an estimate of the total number of people camping at the festival.
(b) 12 friends travel to the festival.
5 travel by car, 4 travel by bus and 3 travel by train.
Two people are chosen at random from the 12 friends.
Calculate the probability that they travel by different types of transport.
(c) Arno buys a student ticket for $43.68 .
This is a saving of 16% on the full price of a ticket.
Calculate the full price of a ticket.
(d) At a football match, there are 29 800 people, correct to the nearest 100.
(i) At the end of the football match, the people leave at a rate of 400 people per minute, correct
to the nearest 50 people.
Calculate the lower bound for the number of minutes it takes for all the people to leave.
.......................................... min [3]
(ii) At a cricket match there are 27 500 people, correct to the nearest 100.
Calculate the upper bound for the difference between the number of people at the football
match and at the cricket match.
................................................. [2]
10 (a) Find all the positive integers which satisfy the inequality.
3n - 8 2 5n - 15
................................................. [2]
(b)
y
x=4
9
8
7
6
5
4 10y + 8x = 80
2y = x - 4
3
R
2
1
0 x
0 1 2 3 4 5 6 7 8 9 10 11
–1
–2
–3
The region marked R is defined by three inequalities.
(i) Find these three inequalities.
.................................................
.................................................
................................................. [3]
11 (a)
A 28 cm D AD
NOT TO
SCALE
20 cm
N BC
B C
A rectangular sheet of paper ABCD is made into an open cylinder with the edge AB meeting the
edge DC.
AD = 28 cm and AB = 20 cm.
(i) Show that the radius of the cylinder is 4.46 cm, correct to 3 significant figures.
[2]
(ii) Calculate the volume of the cylinder.
......................................... cm 3 [2]
(iii) N is a point on the base of the cylinder, such that BN is a diameter.
Calculate the angle between AN and the base of the cylinder.
(b) The volume of a solid cone is 310 cm 3 .
The height of the cone is twice the radius of its base.
Calculate the slant height of the cone.
1
[The volume, V, of a cone with radius r and height h is V = rr 2 h .]
3
............................................ cm [5]
