About this preparation
Math diagnostic test, Year 10: Number. 11 questions with answers and explanations. Topics: Number, Fractions, decimals and percentages, Ratio and proportion, Geometry, Measurement, Statistics, Probability. Duration: 55 min.
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°.
