About this preparation
Math diagnostic test, Grade 7: Integers and rational numbers. 10 questions with answers and explanations. Topics: Integers and rational numbers, Fractions, decimals, and percents, Ratios and proportions, Expressions and equations, Geometry and measurement, Statistics and 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 the value of -7 + 12?
-19
5
-5
19
Explanation: Adding 12 to -7 moves 12 units to the right on the number line, giving 5.
2
Which fraction is equivalent to 3/4?
6/8
3/8
9/16
12/20
Explanation: Multiply the numerator and denominator by the same number: 3/4 = 6/8.
3
Convert 0.35 to a percent.
3.5%
35%
350%
0.35%
Explanation: To convert a decimal to a percent, multiply by 100. 0.35 = 35%.
4
A recipe uses 2 cups of flour for every 3 cups of sugar. What is the ratio of flour to sugar?
3:2
2:3
2:5
5:2
Explanation: The ratio is written in the same order as the quantities given: flour to sugar = 2:3.
5
Solve for x: 4x = 28
x = 6
x = 7
x = 8
x = 24
Explanation: Divide both sides by 4: x = 28 ÷ 4 = 7.
6
Evaluate the expression 3(5 - 2) + 4.
9
13
19
25
Explanation: First evaluate the parentheses: 5 - 2 = 3. Then 3 × 3 + 4 = 13.
7
A rectangle has length 9 cm and width 4 cm. What is its area?
13 cm²
18 cm²
36 cm²
42 cm²
Explanation: Area of a rectangle = length × width = 9 × 4 = 36 cm².
8
The data set is 2, 4, 4, 6, 8. What is the median?
4
5
6
8
Explanation: The numbers are already in order, and the middle value is 4.
9
Which number is greater than -3?
-5
-4
-2
-7
Explanation: On the number line, numbers closer to zero are greater among negatives. -2 is greater than -3.
10
A shirt costs $20 and is discounted by 25%. What is the sale price?
$5
$10
$15
$25
Explanation: 25% of 20 is 5, so the sale price is 20 - 5 = 15.
