πŸ“ Grade 8 Practice Paper 1

Cambridge Lower Secondary Stage 8 β€” Non-Calculator

⏱ 45 Minutes
πŸ“Š 50 Marks
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Section A β€” Number (14 marks)
1 [1]

Write 23 Γ— 24 as a single power of 2.

Answer: 27
2 [1]

Calculate: 3 + 4 Γ— (5 βˆ’ 2)2

Answer: 39
3 [2]

Find the HCF and LCM of 24 and 36.

HCF:   LCM:
HCF = 12, LCM = 72
4 [2]

A television costs $360. The price is reduced by 15%. What is the sale price?

Answer: $306
5 [2]

After a 20% increase, a price is $84. What was the original price?

Answer: $70
6 [2]

Divide $240 in the ratio 3 : 5. Give the larger share.

Answer: $150
7 [2]

Write 4.5 Γ— 103 and 2 Γ— 10βˆ’2 as ordinary numbers. Then find their sum.

4500 + 0.02 = 4500.02
8 [2]

y is directly proportional to x. When x = 5, y = 35. Find y when x = 9.

k = 7, y = 63
Section B β€” Algebra (14 marks)
9 [1]

Expand and simplify: 3(2x βˆ’ 4) + 5x

11x βˆ’ 12
10 [2]

Factorise fully: 12x2 βˆ’ 8x

4x(3x βˆ’ 2)
11 [2]

Solve: 5x + 3 = 2x + 15

x = 4
12 [2]

Solve: 3(2x βˆ’ 1) = 4x + 9

6x βˆ’ 3 = 4x + 9 β†’ 2x = 12 β†’ x = 6
13 [2]

Find the nth term of the sequence: 5, 8, 11, 14, …

3n + 2
14 [2]

Solve the inequality: 4x βˆ’ 3 β‰₯ 9. List the first three positive integer solutions.

x β‰₯ 3 β†’ solutions: 3, 4, 5
15 [3]

f(x) = 3x + 1 and g(x) = x2. Find: (a) f(5)  (b) g(4)  (c) fg(2)

f(5) =   g(4) =   fg(2) =
f(5)=16, g(4)=16, fg(2)=f(4)=13
Section C β€” Geometry & Measures (13 marks)
16 [2]

Find the interior angle of a regular hexagon.

(6βˆ’2)Γ—180/6 = 120Β°
17 [2]

A cylinder has radius 4 cm and height 10 cm. Find its volume in terms of Ο€.

160Ο€ cmΒ³
18 [2]

A cube has side 3 cm. Find its total surface area.

6 Γ— 9 = 54 cmΒ²
19 [2]

Triangle ABC is enlarged by scale factor 3. If AB = 4 cm, what is the length of A'B'?

12 cm
20 [2]

A prism has a cross-sectional area of 15 cmΒ² and length 8 cm. Find its volume.

120 cmΒ³
21 [3]

A is at (1, 2) and B is at (7, 10). Find: (a) midpoint of AB  (b) length of AB  (c) gradient of AB

Mid:   Length:   Grad:
Midpoint (4,6), Length = 10, Gradient = 4/3 β‰ˆ 1.33
Section D β€” Statistics (9 marks)
22 [2]

The ages of 7 students are: 13, 14, 12, 15, 13, 14, 13. Find the mean and median.

Mean:   Median:
Mean = 94/7 β‰ˆ 13.4, Median = 13
23 [2]

A pie chart has sector angles: Red = 90Β°, Blue = 120Β°, Green = ?, Yellow = 60Β°. Total survey = 120 people. How many chose Green?

Green angle = 360βˆ’90βˆ’120βˆ’60=90Β°, freq = (90/360)Γ—120 = 30
24 [2]

A die is biased. P(6) = 0.25. The die is rolled 200 times. What is the expected number of 6s?

0.25 Γ— 200 = 50
25 [3]

The frequency table shows heights of plants:

Height (cm)Frequency
0 – 104
10 – 209
20 – 3012
30 – 405

Find: (a) total frequency  (b) modal class  (c) estimated mean (to 1 d.p.)

Total:   Modal class:   Mean:
Total = 30, Modal class: 20–30, Mean = (4Γ—5+9Γ—15+12Γ—25+5Γ—35)/30 = (20+135+300+175)/30 = 630/30 = 21.0

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