About this preparation
Math diagnostic test, Grade 8: Integers and rational numbers. 11 questions with answers and explanations. Topics: Integers and rational numbers, Fractions, decimals, and percentages, Linear equations, Ratios and proportions, Geometry basics, Data and graphs. 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 the value of -7 + 12?
-19
-5
5
19
Explanation: Add 12 to -7. Moving 12 units right from -7 gives 5.
2
Which fraction is equivalent to 3/4?
6/8
3/8
4/3
9/16
Explanation: Multiply the numerator and denominator by the same number: 3/4 = 6/8.
3
What is 25% of 80?
10
20
25
40
Explanation: 25% means one quarter. One quarter of 80 is 20? Wait, 25% of 80 = 0.25 × 80 = 20.
4
Solve for x: x + 9 = 14
x = 5
x = 23
x = -5
x = 6
Explanation: Subtract 9 from both sides: x = 14 - 9 = 5.
5
A rectangle has length 8 cm and width 3 cm. What is its area?
11 cm²
24 cm²
22 cm²
48 cm²
Explanation: Area of a rectangle is length × width: 8 × 3 = 24.
6
Which number is greater?
-2
-5
They are equal
Cannot be determined
Explanation: On the number line, -2 is to the right of -5, so it is greater.
7
A bag has 3 red marbles and 5 blue marbles. What is the ratio of red to blue marbles?
5:3
3:5
8:3
3:8
Explanation: The ratio red to blue is 3 to 5.
8
Simplify: 2(4 + 3)
9
14
11
24
Explanation: First add inside the parentheses: 4 + 3 = 7. Then multiply: 2 × 7 = 14.
9
What is the value of 3/5 as a decimal?
0.35
0.6
1.5
0.03
Explanation: Divide 3 by 5 to get 0.6.
10
A line passes through the points (0, 2) and (0, 7). What can you say about the line?
It is horizontal
It is vertical
It has slope 1
It is a diagonal line
Explanation: Both points have the same x-coordinate, so the line is vertical.
11
Solve for x: 2x = 18
x = 9
x = 16
x = 20
x = 36
Explanation: Divide both sides by 2: x = 18 ÷ 2 = 9.
