About this preparation
Хочу зробити діагностичний тест з математики для учня 10 класу, на 55 хвилин, середньої складності. Потрібні завдання рівня GCSE без алгебраїчних питань.
Reid Rachel
Preparation author
Diagnostic tasks
Below is the full list of tasks with correct answers and explanations. In a lesson the tutor can hide the answers and reveal them after the student tries.
1
What is 3/5 as a percentage?
15%
30%
60%
80%
Explanation: To convert 3/5 to a percentage, first write it as a decimal: 3 ÷ 5 = 0.6. Then multiply by 100 to get 60%.
2
Work out 18% of 250.
32
36
45
54
Explanation: 18% of 250 = 0.18 × 250 = 45? Wait carefully: 10% is 25, 5% is 12.5, and 3% is 7.5, so 18% = 25 + 12.5 + 7.5 = 45.
3
A recipe uses flour and sugar in the ratio 4:1. If there are 20 g of sugar, how much flour is needed?
16 g
20 g
40 g
80 g
Explanation: The ratio flour:sugar is 4:1. If 1 part is 20 g, then flour is 4 parts = 4 × 20 = 80 g? Check carefully: flour is 4 parts and sugar is 1 part, so if sugar is 20 g, flour is 80 g.
4
A triangle has angles 48° and 67°. What is the third angle?
55°
65°
75°
85°
Explanation: The angles in a triangle add to 180°. So the third angle is 180 - 48 - 67 = 65? Recalculate: 48 + 67 = 115, and 180 - 115 = 65.
5
A bag contains 5 red counters, 3 blue counters and 2 green counters. What is the probability of picking a blue counter?
1/10
3/10
2/5
3/5
Explanation: There are 10 counters in total and 3 are blue. So the probability is 3/10.
6
A rectangle has length 12 cm and width 7 cm. What is its area?
19 cm²
38 cm²
84 cm²
96 cm²
Explanation: Area of a rectangle = length × width = 12 × 7 = 84 cm².
7
A car travels 150 km in 3 hours. What is its average speed?
45 km/h
50 km/h
60 km/h
75 km/h
Explanation: Average speed = distance ÷ time = 150 ÷ 3 = 50 km/h.
8
The mean of 4, 7, 9, 10 and 10 is:
8
8.5
9
10
Explanation: Add the numbers: 4 + 7 + 9 + 10 + 10 = 40. Then divide by 5: 40 ÷ 5 = 8.
9
A circle has radius 6 cm. What is its circumference? Use π ≈ 3.14.
18.84 cm
37.68 cm
56.52 cm
113.04 cm
Explanation: Circumference = 2πr = 2 × 3.14 × 6 = 37.68 cm.
10
Which of the following are equivalent to 0.25?
1/4
25%
2/5
0.2
0.50
Explanation: 0.25 is equal to 1/4 and 25%. The other options are not equivalent to 0.25.
11
Which statements about a right-angled triangle are true?
It has one angle of 90°
The longest side is opposite the right angle
All three sides are always equal
The angles always add to 90°
It can have two right angles
Explanation: A right-angled triangle has one 90° angle, and the side opposite that angle is the longest side. The angles in any triangle add to 180°.
