🖩 Grade 8 Practice Paper 2

Cambridge Lower Secondary Stage 8 — Calculator Allowed

⏱ 45 Minutes
📊 50 Marks
✅ Calculator Permitted
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⏱ 45:00 — Click to start
Section A — Number & Proportion (15 marks)
1 [1]

Write 3.6 × 104 as an ordinary number.

36000
2 [2]

Write 0.000047 in standard form.

4.7 × 10−5
3 [2]

A coat costs $125. It is reduced by 12%. Find the sale price.

$125 × 0.88 = $110
4 [2]

A population of bacteria doubles every 3 hours. Starting at 500, how many after 12 hours?

500 × 24 = 8000
5 [2]

y is inversely proportional to x. When x = 4, y = 15. Find y when x = 10.

k = 60, y = 6
6 [2]

Divide 450 kg in the ratio 4 : 5. Give both shares.

kg and kg
200 kg and 250 kg
7 [2]

A car travels 270 km in 3.5 hours. Find its average speed in km/h. (1 d.p.)

270/3.5 ≈ 77.1 km/h
8 [2]

An alloy is 35% copper. If a sample has 84 g of copper, what is the total mass of the alloy?

84/0.35 = 240 g
Section B — Algebra & Graphs (15 marks)
9 [2]

Expand and simplify: (x + 3)(x + 5)

x² + 8x + 15
10 [2]

Solve the simultaneous equations: 2x + y = 10 and x − y = 2

x =   y =
x = 4, y = 2
11 [2]

A line has equation y = 3x − 2. What is its gradient and y-intercept?

Gradient:   y-intercept:
Gradient = 3, y-intercept = −2
12 [2]

What is the equation of a line perpendicular to y = 2x + 1 that passes through (0, 3)?

y = −½x + 3
13 [3]

A ball is dropped. Its height h (m) at time t (s) is h = 20 − 5t².

(a) What is h when t = 0?  (b) When does the ball hit the ground?  (c) What is h at t = 1?

h(0) =   t =   h(1) =
h(0)=20, t=2 (when 5t²=20), h(1)=15
14 [2]

f(x) = 2x + 5. Find f−1(x).

f⁻¹(x) = (x − 5)/2
15 [2]

A distance-time graph shows a car travels 120 km in 2 hours, stops for 30 minutes, then returns 120 km in 1.5 hours. Find the speed on the return journey.

120/1.5 = 80 km/h
Section C — Geometry & Measures (12 marks)
16 [2]

Find the total surface area of a sphere with radius 5 cm. (Give answer in terms of π.)

4π × 25 = 100π cm²
17 [2]

A cone has base radius 3 cm and height 4 cm. Find the slant height, then the total surface area. (2 d.p., use π = 3.14)

Slant h:   SA:
l = 5, SA = π×9 + π×3×5 = 3.14×(9+15) = 3.14×24 = 75.36 cm²
18 [2]

Two similar triangles have areas 16 cm² and 100 cm². Find the linear scale factor.

k² = 100/16 = 6.25, k = 2.5
19 [2]

A sector has radius 8 cm and angle 135°. Find the arc length. (2 d.p.)

(135/360) × 2π × 8 = 18.85 cm
20 [2]

A cuboid has volume 360 cm³. The base is 6 cm by 10 cm. Find the height.

360/(6×10) = 6 cm
21 [2]

Shape A has vertices at (2,1), (5,1), (5,4). It is reflected in the line y = x. Give the new coordinates of the vertex originally at (5,1).

Reflection in y=x: (x,y)→(y,x) → (5,1)→(1,5)
Section D — Statistics & Probability (8 marks)
22 [2]

A spinner is spun 200 times. P(red) = 0.45. How many reds are expected? How many non-reds?

Red:   Non-red:
Red = 90, Non-red = 110
23 [2]

Two fair dice are rolled. Find P(sum ≥ 10). Give as a fraction.

(4,6),(5,5),(6,4),(5,6),(6,5),(6,6) = 6 outcomes → 6/36 = 1/6
24 [2]

The quarterly sales (£000s) of a shop are: Q1=45, Q2=62, Q3=58, Q4=70, Q1=50, Q2=65. Calculate the first two 4-point moving averages.

MA1:   MA2:
MA1=(45+62+58+70)/4=58.75, MA2=(62+58+70+50)/4=60
25 [2]

P(A) = 0.4, P(B) = 0.35, P(A∩B) = 0.1. A and B are not mutually exclusive. Find P(A or B).

P(A or B) = 0.4 + 0.35 − 0.1 = 0.65

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