🧮 Grade 7 Practice Paper 2

✅ Calculator Allowed ⏱ 45 Minutes 📝 50 Marks 38 Questions Cambridge Lower Secondary Stage 7
Instructions: Answer all questions. Write your answers in the boxes provided. A calculator is allowed for this paper. Show your working where asked — you may get marks for working even if your final answer is wrong. Marks for each question are shown in brackets.
Name:
Class:
Date:
Section A: Number & Calculation (10 questions)
1
Write 5.84 × 10−3 as an ordinary number.
[1]
2
Work out: √529
[1]
3
Work out: ∛216
[1]
4
Find 3.7% of £820.
£
[2]
5
Work out: 5.83 × 2.7, giving your answer to 2 decimal places.
[2]
6
The population of a city is 2.4 × 106. Write this as an ordinary number.
[1]
7
Write 0.000067 in standard form.
[1]
8
Find the LCM of 15, 20, and 12.
[2]
9
A number rounded to 2 significant figures gives 4800. Write down the upper bound.
[1]
10
Work out: (−5)3
[1]
Section B: Algebra (10 questions)
11
Factorise: 12x − 8
[1]
12
Expand and simplify: 3(2x + 4) − 2(x − 1)
[2]
13
Solve: 2(3x − 1) = 4x + 8
x =
[2]
14
A = ½bh. Find h when A = 45 and b = 9.
h =
[2]
15
Solve the inequality: 4x − 3 > 13
[2]
16
The nth term of a sequence is 3n² − 1. Find the 5th term.
[1]
17
Two consecutive even numbers sum to 54. Form and solve an equation to find the two numbers.
[2]
18
For the graph of y = 2x − 3, state the gradient and the y-intercept.
Gradient:   y-intercept:
[2]
19
Simplify: x5 ÷ x2
[1]
20
Find the value of 3x² − 2x + 1 when x = −3.
[2]
Section C: Fractions, Decimals & Percentages (8 questions)
21
Work out: 4/7 ÷ 2/3. Give your answer in its simplest form.
[2]
22
Convert 2 5/6 to an improper fraction.
[1]
23
A shirt originally costs £45. It is reduced by 35%. Find the sale price.
£
[2]
24
VAT at 15% is added to a price of £60. Find the total price.
£
[1]
25
The price after a 12% increase is £112. Find the original price.
£
[2]
26
Write 7/12 as a decimal, correct to 3 decimal places.
[1]
27
Work out: 3⅓ × 1⅘. Give your answer as a mixed number in its simplest form.
[2]
28
Which is greater: 5/8 or 62%? Show your working.
[2]
Section D: Geometry (6 questions)
29
Find the circumference of a circle with radius 8.5 cm. Give your answer to 1 decimal place.
cm
[2]
30
Find the area of a semicircle with diameter 14 cm. Give your answer to 1 decimal place.
cm²
[2]
31
A cylinder has radius 4 cm and height 10 cm. Find its volume to 1 decimal place.
cm³
[2]
32
Find the surface area of a cylinder with radius 3 cm and height 7 cm, to 1 decimal place.
cm²
[2]
33
Corresponding angles: one is (3x + 10)° and the other is (5x − 14)°. Find x.
x =
[2]
34
A scale drawing uses a scale of 1 : 25 000. A road measures 4.5 cm on the map. Find the real length of the road in kilometres.
km
[2]
Section E: Ratio, Proportion & Statistics (4 questions)
35
y is directly proportional to x. When x = 4, y = 20. Find y when x = 7.
y =
[2]
36
Three workers can paint a fence in 6 hours. How long would it take 2 workers? (Assume all workers work at the same rate.)
hours
[2]
37
The mean of a dataset is 14.2. The dataset is: 8, 11, 14, x, 22, 20. Find the value of x.
x =
[2]
38
40 students were surveyed about pets. 15 boys and 10 girls own a dog. 5 boys and 10 girls do not own a dog. Find P(girl | owns a dog). Give your answer as a fraction in its simplest form.
[2]
45:00

✅ Mark Scheme — Paper 2

10.00584 move decimal 3 places left
223 23² = 529
36 6³ = 216
4£30.34 [2] 820 × 0.037
515.74 [2] 5.83 × 2.7 = 15.741
62,400,000
76.7 × 10⁻⁵
860 [2] LCM(15,20,12)
94850 4800 + half of 100
10−125
114(3x − 2)
124x + 14 [2] 6x+12−2x+2
13x = 5 [2] 6x−2=4x+8; 2x=10
14h = 10 [2] 45=½×9×h; h=10
15x > 4 [2] 4x > 16
1674 3(25)−1=74
1726 and 28 [2] n+(n+2)=54; n=26
18gradient = 2, y-intercept = −3 [1+1]
19x³ index law: subtract powers
2034 [2] 3(9)−2(−3)+1=27+6+1
216/7 [2] 4/7 × 3/2 = 12/14 = 6/7
2217/6 2×6+5=17
23£29.25 [2] 45 × 0.65
24£69 60 × 1.15
25£100 [2] 112 ÷ 1.12
260.583 7÷12=0.5833…
276 [2] 10/3 × 9/5 = 90/15 = 6
285/8 [2] 5/8 = 0.625 = 62.5% > 62%
2953.4 cm [2] 2π × 8.5
3077.0 cm² [2] ½π × 7² = 76.97…
31502.7 cm³ [2] π × 4² × 10
32188.5 cm² [2] 2πr²+2πrh = 2π(9)+2π(21)
33x = 12 [2] 3x+10=5x−14; 24=2x
341.125 km [2] 4.5×25000=112500 cm=1.125 km
35y = 35 [2] k=5; y=5×7
369 hours [2] total work=18 man-hrs; 18÷2=9
37x = 10.2 [2] sum=85.2; 8+11+14+22+20=75; x=10.2
382/5 [2] P(girl|dog)=10/25=2/5