About this preparation
Math diagnostic test, Grade 8: Integers and rational numbers. 10 questions with answers and explanations. Topics: Integers and rational numbers, Linear equations, Proportions and percentages, Geometry: angles and triangles, Area and volume, Data interpretation. 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: Adding 12 to -7 gives 5.
2
Which expression is equal to 3(2x - 5)?
6x - 15
6x - 5
3x - 15
5x - 6
Explanation: Distribute 3 to both terms: 3 × 2x = 6x and 3 × -5 = -15.
3
Solve for x: x + 9 = 17.
6
8
9
26
Explanation: Subtract 9 from both sides: x = 17 - 9 = 8.
4
A shirt costs $40 and is discounted by 15%. What is the sale price?
$6
$34
$35
$45
Explanation: 15% of 40 is 6, so the sale price is 40 - 6 = 34.
5
If 5 notebooks cost $12.50, how much do 8 notebooks cost at the same rate?
$15.00
$18.00
$20.00
$22.50
Explanation: One notebook costs $12.50 ÷ 5 = $2.50, so 8 notebooks cost 8 × $2.50 = $20.00.
6
Two angles of a triangle measure 48° and 67°. What is the measure of the third angle?
65°
75°
85°
95°
Explanation: The angles in a triangle add to 180°. 180 - 48 - 67 = 65.
7
What is the area of a rectangle with length 9 cm and width 4 cm?
13 cm²
18 cm²
36 cm²
40 cm²
Explanation: Area of a rectangle is length × width, so 9 × 4 = 36 cm².
8
Which number is a rational number?
√2
0.75
π
√5
Explanation: 0.75 can be written as the fraction 3/4, so it is rational.
9
Which of the following statements about a data set are true? Select all that apply.
The mean is found by adding all values and dividing by the number of values.
The median is always the largest value.
The mode is the value that appears most often.
The range is the difference between the greatest and least values.
Explanation: Mean, mode, and range are defined correctly in options a, c, and d.
10
Which of the following equations have x = 4 as a solution? Select all that apply.
x - 1 = 3
2x = 6
3x - 8 = 4
x + 5 = 10
Explanation: Substitute x = 4: a gives 3 = 3, c gives 12 - 8 = 4. The others are not true for x = 4.
