About this preparation
Math diagnostic test, Year 6: Number and place value. 11 questions with answers and explanations. Topics: Number and place value, Fractions, decimals and percentages, Ratio and proportion, Measurement, Geometry, Algebraic reasoning, Problem solving and reasoning. 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
Which number is 3,000 + 400 + 20 + 5?
3,425
3,045
3,245
3,402
Explanation: 3,000 + 400 + 20 + 5 = 3,425? Wait carefully: 400 + 20 + 5 = 425, so the number is 3,425.
2
A shop sells pencils in packs of 6. How many packs are needed to buy 42 pencils?
6
7
8
9
Explanation: 42 ÷ 6 = 7, so 7 packs are needed.
3
Which of these numbers are multiples of 9?
18
27
32
45
Explanation: 18, 27, and 45 are divisible by 9 with no remainder.
4
What is 3/4 of 20?
10
12
15
18
Explanation: 1/4 of 20 is 5, so 3/4 of 20 is 15? Check carefully: 5 × 3 = 15. Therefore the correct answer is 15.
5
A rectangle has a length of 8 cm and a width of 5 cm. What is its perimeter?
13 cm
26 cm
40 cm
20 cm
Explanation: Perimeter = 2 × (8 + 5) = 2 × 13 = 26 cm.
6
Which statements are true?
0.5 is the same as 1/2
0.25 is greater than 1/2
3/10 is the same as 0.3
0.75 is the same as 3/4
Explanation: 0.5 = 1/2, 0.3 = 3/10, and 0.75 = 3/4.
7
A bag has red and blue marbles in the ratio 2:3. If there are 15 marbles altogether, how many are red?
5
6
9
10
Explanation: The ratio has 5 equal parts in total. 15 ÷ 5 = 3 per part, and red is 2 parts: 2 × 3 = 6? Recheck: 2:3 means red is 2 parts, blue is 3 parts, total 5 parts. 15 ÷ 5 = 3, so red = 2 × 3 = 6.
8
A number is rounded to the nearest 10 and becomes 70. Which number could it be?
64
66
73
79
Explanation: Numbers from 65 to 74 round to 70 to the nearest 10. 73 is one of them.
9
A class collected 48 cans. They packed them equally into 6 boxes. Which statements are true?
Each box has 8 cans
48 ÷ 6 = 8
Each box has 6 cans
The remainder is 2
Explanation: 48 ÷ 6 = 8, so each box has 8 cans and there is no remainder.
10
What is the next number in the pattern: 4, 9, 14, 19, __ ?
22
23
24
25
Explanation: The pattern increases by 5 each time, so 19 + 5 = 24? Check the sequence carefully: 4, 9, 14, 19, 24. The correct answer is 24.
11
A jug contains 1.5 litres of water. How many millilitres is this?
150 ml
1500 ml
15 ml
1050 ml
Explanation: 1 litre = 1000 ml, so 1.5 litres = 1500 ml.
