NAME:
CLASS:
G9 Final Maths Exams 1.0
SHOW ALL WORKINGS (30marks) Time allowed: 50minutes
Question 1
Factorise 𝑥 2 + 2𝑥 − 15 .
..........................
(3 marks)
Question 2
Factorise
6𝑥 2 − 23𝑥 − 4
..........................
(3 marks)
Question 3
Factorise
4𝑥 2 − 9
..........................
(3 mark)
2
Question 4
Find the volume of the cylinder.
[ ]
12𝜋
[ ]
120𝜋
[ ]
64𝜋
[ ]
32𝜋
(3 mark)
Question 5
Sam is going to cover a tank completely with paint.
The tank is in the shape of a cylinder with a top and a bottom as shown below.
Paint is sold in tins.
A tin of paint costs £41.99 Each tin of paint covers 6 m 2
Calculate the cost of the paint needed to cover the tank completely with paint.
£ ..........................
(4 mark)
3
Question 6
Work out the volume of this pyramid.
.......................... cm 3
(3 mark)
Question 7
Owen collects the heights of some toys and puts the data in the stem-and-leaf diagram below.
4
5
6
7
0
0
1
1
3
1
3
4
5
2
3
4
9
3
6
7
9
9
Key: 4 | 3 = 43 cm
Find the median of the data in the stem-and-leaf diagram.
.......................... cm
(3 mark)
Question 8
A cone has a diameter of 44 cm and a height of 40 cm.
Work out the volume of the cone.
Give your answer correct to 1 decimal place.
1
Volume of cone = 3 𝜋 𝑟 2 ℎ
.......................... cm 3
(3 mark)
4
Question 9
The diagram shows a shape made from a solid cube and a solid cylinder.
The cube has sides of length 8.7 cm.
The cylinder has a radius of 2.7 cm and a height of 4.9 cm.
Calculate the total surface area of the solid shape.
Give your answer correct to 3 significant figures.
.......................... 𝑐𝑚2
(5 marks)
5
Answers
Question 1
(𝑥 − 3)(𝑥 + 5)
Question 2
(6𝑥 + 1)(𝑥 − 4)
Question 3
(2𝑥 − 3)(2𝑥 + 3)
Question 4
32𝜋
Question 5
£ 167.96
① Calculate the surface area of the cylinder:
𝐴 = 2 × 𝜋 × 1.052 + 2𝜋 × 1.05 × 2.2
= 21.4414 m2
② Find how many tins of paint are needed:
𝑛 = 21.4414 ÷ 6
Therefore 4 tins are needed.
= 3.57
③ Calculate the cost of 4 tins:
𝐶 = 4 × 41.99
= £167.96
6
Question 6
14 cm 3
1
The volume of a pyramid is 3 × base × height , therefore the volume is:
1
3
× 6 × 1 × 7 = 14 cm 3
Question 7
any value in the range 248.7 𝑚2 to 248.9 𝑚2
Question 8
62 cm
Put the data in order:
40
77
43
79
45
49
50
51
52
53
61
63
63
66
69
71
74
74
As there is an even number of values, you can split the data set in two:
40
77
43
79
45
49
50
51
52
53
61
63
The median is the mean of the 9th and 10th values
Median =
61+63
2
= 62
Question 9
20273.7 cm 3
The radius is half the diameter, so 𝑟 = 44 ÷ 2 = 22
1
3
Substitute 𝑟 = 22 and ℎ = 40 into the formula 𝑉 = 𝜋 𝑟 2 ℎ
𝑉 =
1
𝜋
3
× 222 × 40
= 20273.7 cm3
Question 10
537 𝑐𝑚2
63
66
69
71
74
74