About this preparation
Math diagnostic test, Grade 8: Arithmetic, Fractions. 10 questions with answers and explanations. Topics: Arithmetic, Fractions, Decimals, Basic Algebra, Geometry. Duration: 10 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 48 + 27?
65
75
85
95
Explanation: Add the tens and ones: 40 + 20 = 60, and 8 + 7 = 15, so 60 + 15 = 75.
2
What is 96 − 39?
47
57
67
69
Explanation: Subtract 40 from 96 to get 56, then add 1 back because 39 is 1 less than 40: 57.
3
Which fraction is equivalent to 1/2?
2/3
3/6
4/5
5/8
Explanation: Multiply the numerator and denominator of 1/2 by the same number, such as 3, to get 3/6.
4
What is 3/4 of 20?
10
12
15
18
Explanation: Find 1/4 of 20, which is 5, then multiply by 3: 5 × 3 = 12.
5
What is 0.7 + 0.2?
0.9
0.8
0.10
1.9
Explanation: Add the tenths: 7 tenths + 2 tenths = 9 tenths, which is 0.9.
6
Solve for x: x + 9 = 14
3
4
5
6
Explanation: Subtract 9 from both sides: x = 14 − 9 = 5.
7
A rectangle has length 8 cm and width 5 cm. What is its area?
13 cm²
26 cm²
40 cm²
45 cm²
Explanation: Area of a rectangle is length × width: 8 × 5 = 40 cm².
8
Which number is a prime number?
21
29
33
39
Explanation: 29 has exactly two factors, 1 and 29, so it is prime.
9
What is 6 × 7 − 8?
34
36
42
48
Explanation: First multiply: 6 × 7 = 42. Then subtract 8: 42 − 8 = 34? Wait, check carefully. The correct result is 34.
10
A number is divisible by 3 if the sum of its digits is divisible by 3. Is 246 divisible by 3?
Yes
No
Only if it is even
Only if it ends in 0
Explanation: 2 + 4 + 6 = 12, and 12 is divisible by 3, so 246 is divisible by 3.
