Grade 7 Practice Paper 1 — Non-Calculator

No Calculator 45 Minutes 50 Marks 40 Questions Cambridge Lower Secondary Stage 7
Instructions: Answer all questions. Write your answers in the boxes provided. Do not use a calculator 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 (Questions 1–12)
1
Write 4,507,000 in words.
[1]
2
Write 3.6 × 104 as an ordinary number.
[1]
3
Round 0.007463 to 2 significant figures.
[1]
4
Work out: (−3) × (−7)
[1]
5
Work out: (−24) ÷ 6
[1]
6
Find the LCM of 12 and 18.
[1]
7
Find the HCF of 36 and 48.
[1]
8
Write 60 as a product of its prime factors.
[2]
9
Work out: 3.7 × 0.04
[1]
10
Work out: 4.56 ÷ 0.8
[2]
11
Estimate: 48.6 × 19.7 by rounding each number to 1 significant figure.
[1]
12
Write the recurring decimal 0.3̄ as a fraction.
[1]
Section B: Algebra (Questions 13–22)
13
Simplify: 5x + 3y − 2x + y
[1]
14
Expand: 4(3x − 2)
[1]
15
Expand and simplify: 2(x + 5) + 3(2x − 1)
[2]
16
Solve: 3x + 7 = 22
x =
[1]
17
Solve: 5x − 3 = 2x + 9
x =
[2]
18
Using the formula v = u + at, find v when u = 5, a = 3, t = 4.
v =
[1]
19
Make x the subject of: y = 3x − 4
x =
[2]
20
List all integer values satisfying: −2 < x ≤ 3
[1]
21
Write an expression for the perimeter of a rectangle with length (2x + 3) and width x.
[1]
22
A sequence has nth term 4n − 3. Find the 10th term.
[1]
Section C: Fractions, Decimals & Percentages (Questions 23–30)
23
Work out: 3/4 × 8/9
[1]
24
Work out: 2⅓ ÷ 1/4
[2]
25
Work out: 1⅘ + 2⅔
[2]
26
Convert the recurring decimal 0.1̄2̄ (0.121212…) to a fraction in its simplest form.
[2]
27
Increase £240 by 15%.
£
[1]
28
After a 20% decrease, a price is £64. Find the original price.
£
[2]
29
Express 45 minutes as a percentage of 3 hours.
%
[1]
30
A coat costs £85 after a 15% discount. What was the original price?
£
[2]
Section D: Geometry (Questions 31–36)
31
Find the value of angle x in a triangle with angles 47° and 83°.
x = °
[1]
32
Two parallel lines are cut by a transversal. One co-interior angle is 112°. Find the other co-interior angle.
°
[1]
33
Find the circumference of a circle with diameter 10 cm. Give your answer in terms of π.
[1]
34
Find the area of a circle with radius 6 cm. Give your answer to 1 decimal place (use π ≈ 3.14159…).
cm²
[2]
35
A triangular prism has a triangular cross-section with base 8 cm and height 5 cm. The length of the prism is 12 cm. Find its volume.
cm³
[2]
36
Find the surface area of a cuboid measuring 3 cm × 4 cm × 5 cm.
cm²
[2]
Section E: Ratio, Proportion & Statistics (Questions 37–40)
37
Share £180 in the ratio 2 : 3 : 4.
[2]
38
A car travels 180 km on 15 litres of fuel. How far can it travel on 25 litres?
km
[1]
39
The mean of 5 numbers is 8. Four of the numbers are 6, 9, 11, 4. Find the fifth number.
[2]
40
A bag contains 3 red, 5 blue and 2 green balls. Find P(not red). Give your answer as a fraction in its simplest form.
[1]
45:00

Mark Scheme — Grade 7 Paper 1

1Four million five hundred and seven thousand
236,000
30.0075 2 s.f.
421 negative × negative = positive
5−4
636 LCM(12,18)
712 HCF(36,48)
82² × 3 × 5 [2 marks] accept 2 × 2 × 3 × 5
90.148
105.7 [2 marks] 4.56 ÷ 0.8 = 45.6 ÷ 8
111000 50 × 20 = 1000
121/3
133x + 4y
1412x − 8
158x + 7 [2 marks] 2x+10+6x−3
16x = 5 3x = 15
17x = 4 [2 marks] 3x = 12
18v = 17 5 + 3×4 = 5+12
19x = (y + 4) ÷ 3 [2 marks]
20−1, 0, 1, 2, 3
216x + 6 2(2x+3) + 2x
2237 4(10)−3
232/3 24/36 simplified
249⅓ or 28/3 [2 marks] 7/3 ÷ 1/4 = 7/3 × 4 = 28/3
254 7/15 or 67/15 [2 marks] 9/5 + 8/3 = 27/15 + 40/15
264/33 [2 marks] 100x − x = 12, x = 12/99 = 4/33
27£276 240 × 1.15
28£80 [2 marks] 64 ÷ 0.8
2925% 45 ÷ 180 × 100
30£100 [2 marks] 85 ÷ 0.85
3150° 180 − 47 − 83
3268° co-interior angles sum to 180°
3310π cm C = πd
34113.1 cm² [2 marks] π × 6² = 36π ≈ 113.097
35240 cm³ [2 marks] ½ × 8 × 5 × 12
3694 cm² [2 marks] 2(3×4 + 4×5 + 3×5) = 2(12+20+15) = 94
37£40 : £60 : £80 [2 marks] 9 parts, £20 each
38300 km 12 km/litre × 25
3910 [2 marks] total=40, 40−(6+9+11+4)=10
407/10 7 non-red out of 10