Name:
Class:
Mathematics
2 Hours
Year 8
Jan FE 2021
Additional Materials
Electronic Calculator
READ THESE INSTRUCTIONS FIRST
Write in dark blue or black pen.
You may use a soft pencil for any diagrams or graphs.
Do not use paper clips, highlighters, glue, or correction fluid.
Answer all questions.
If working is needed for any question it must be shown clearly.
Electronic calculators should be used.
If the degree of accuracy is not specified in the question, and if the answer is not exact, give
the answer to three significant figures. Give answers in degrees to one decimal place.
For 𝜋, use either your calculator value or 3.142.
At the end of the examination, fasten all your work securely together.
The number of marks is given in brackets [ ] at the end of each question or part question.
The total number of marks for this paper is 80.
Parent’s Signature:
___________________________
Date:
This document consists of 12 printed pages
ACE5722
Maths – Y8 – FE –2021
ACE EdVenture
1 As shown in the diagram, the parallel lines 𝑃𝑄 and 𝑅𝑆 are cut by the transversals 𝐴𝐵 and 𝐶𝐷.
If ∠𝑄𝑊𝐵= 113° and ∠𝑃𝑋𝐷= 129°, find
113°
129°
NOT TO SCALE
(a) ∠𝐴𝑌𝑆
………………………………° [2]
(b) ∠𝑆𝑍𝐷
………………………………° [2]
2 A solid square pyramid has a mass of 274 g. It is made of a material with a density of 2.74g/cm3.
Given that the height of the pyramid is 12 cm, find the length of its square base.
!
[Volume of a pyramid = " × area of base × ℎ]
……………………………...cm [3]
Page 2 of 12
Maths – Y8 – FE –2021
ACE EdVenture
3 𝐴𝐵𝐶𝐷𝐸 is a pentagon. Given that ∠𝐴𝐵𝐶 = 2∠𝐵𝐶𝐷 and ∠𝐵𝐶𝐷 = ∠𝐶𝐷𝐸. Find ∠𝐶𝐷𝐸.
°
°
NOT TO SCALE
……………………………° [3]
4 The body mass index, 𝐵 for a person of mass, 𝑚 (kg) and height, ℎ (metres) is given by the
formula
2𝑚
𝐵 = #
ℎ
Work out the body mass index of a person weighs 53 kg and has a height of 1.67 m.
………………………………. [2]
Page 3 of 12
Maths – Y8 – FE –2021
ACE EdVenture
5 The figure shows a structure made up of a solid cone and a solid hemisphere. The hemisphere
has a radius of 2.5 cm. The cone has a base radius of 3 cm and a height of 9 cm. Find
$
[The volume, V, of a sphere with radius r is 𝑉 = " 𝜋𝑟 " ]
[Surface area of a sphere = 4𝜋𝑟 # ]
!
[The volume, V, of a cone with radius r and height h is 𝑉 = " 𝜋𝑟 # ℎ]
[Curved surface area of a cone = 𝜋𝑟𝑙]
2.5 cm
9 cm
NOT TO SCALE
3 cm
(a) the volume of the structure,
…………………………cm" [3]
(b) the slant height of the cone,
……………………………cm [2]
Page 4 of 12
Maths – Y8 – FE –2021
ACE EdVenture
(c) the total surface area of the structure.
…………………………cm# [3]
6 A square 𝐴𝐵𝐶𝐷 with each side of 18 cm has another square 𝑃𝑄𝑅𝑆 inside it. 𝑃, 𝑄, 𝑅 and 𝑆 are
the midpoints of each side of square 𝐴𝐵𝐶𝐷, as shown in the diagram. Calculate the length of
𝑆𝑅.
18 cm
18 cm
………………………….cm [3]
Page 5 of 12
ACE EdVenture
Maths – Y8 – FE –2021
7 Factorise the following expressions completely.
(a) 21𝑥𝑦 # − 49𝑥 # 𝑦
………………………………. [2]
(b) 1 − 121𝑝#
#
(c) 12𝑥 – 27𝑥 + 6
(d) 14𝑎𝑦 + 10𝑏𝑧 − 4𝑎𝑧 − 35𝑏𝑦
………………………………. [2]
………………………………. [3]
………………………………. [3]
Page 6 of 12
ACE EdVenture
Maths – Y8 – FE –2021
8 Given that 𝑥 satisfies the inequality 5𝑥 ≤ 125, find the greatest value of 𝒙 if 𝑥 is divisible by 12.
………………………………. [2]
9 Solve 𝑥 # − 3𝑥 − 10 = 0.
………………………………. [3]
10 State whether each of the following statements is true or false.
(a) An equilateral triangle has rotational symmetry of order 3.
(b) A parallelogram is a trapezium.
………………………………. [1]
………………………………. [1]
Page 7 of 12
Maths – Y8 – FE –2021
ACE EdVenture
11 Ben is 𝑥 # years old while his son is 𝑥 years old. In 4𝑥 years’ time, Ben will be twice as old as his
son.
(a) Form an equation in 𝑥 and show that it reduces to 𝑥 # − 6𝑥 = 0.
(b) Solve the equation 𝑥 # − 6𝑥 = 0.
(c) Find the age of Ben when his son was born.
………………………………. [3]
𝑥 = …………… or……………. [2]
………………. years old [2]
12 The exterior angle of a regular polygon is 15∘ .
Find the number of sides of this regular polygon.
………………………………. [2]
Page 8 of 12
ACE EdVenture
Maths – Y8 – FE –2021
13 𝐴𝐶𝐸 and 𝐵𝐶𝐷 are straight lines. 𝐴𝐵 is parallel to 𝐷𝐸. Calculate the length of 𝐶𝐷.
……………………………cm [3]
14 Write down the mathematical name for an angle that is more than 180° but less than 360°.
………………………………. [1]
Page 9 of 12
Maths – Y8 – FE –2021
ACE EdVenture
15 A map has a scale of 1 cm to 500 m.
(a) Express the scale of the map in the form 1 : 𝑛, where 𝑛 is an integer.
1: …………………………. [2]
(b) If the actual distance between two cities is 72 km, find the distance on the map.
……………………………cm [2]
(c) If a lake has an area of 120 cm2 on the map, what is the actual lake area in km2 ?
…………………………km2 [3]
16 From the word below, write down a letter that has
W
O
N
D
E
R
F
U
L
(a) two lines of symmetry,
(b) only one vertical line of symmetry,
(c) no line of symmetry.
………………………………. [1]
………………………………. [1]
………………………………. [1]
Page 10 of 12
Maths – Y8 – FE –2021
ACE EdVenture
17 If 𝑦 is inversely proportional to 2𝑥 + 4, and 𝑦 = 4 when 𝑥 = 3,
(a) find the equation connecting 𝑥 and 𝑦
………………………………. [3]
!
(b) find the values of 𝑦 when 𝑥 = #,
………………………………. [2]
(c) calculate the values of 𝑥 when 𝑦 = 10.
………………………………. [2]
18 Expand and simplify the following expression.
3(2𝑚 + 3𝑛)#
………………………………. [3]
Page 11 of 12
Maths – Y8 – FE –2021
ACE EdVenture
19 Expand and simplify the expression
(a) 𝑟 # − (𝑟 − 𝑝)(𝑟 + 𝑝)
………………………………. [2]
(b) Without using a calculator, evaluate by substituting a suitable value of 𝑟 and 𝑝. Show your
working clearly.
4495# − (4500)(4490)
………………………………. [3]
20 It is given that the quadrilateral 𝐴𝐵𝐶𝐷 is congruent to the quadrilateral 𝑃𝑄𝑅𝑆 , ∠𝐴 = 45°,
∠𝐵 = 153°, 𝑃𝑄 = 10 cm and 𝑅𝑆 = 15 cm.
(a) Find ∠𝑄.
………………………………° [1]
(b) Write down the length of 𝐶𝐷.
……………………………cm [1]
** End of Test ***
Page 12 of 12