About this preparation
Math diagnostic test, Year 7: Integers and rational numbers. 11 questions with answers and explanations. Topics: Integers and rational numbers, Fractions, decimals, and percentages, Algebraic expressions and equations, Ratios and proportions, Geometry and measurement. 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 greater than -3 but less than 2?
-5
-1
3
2
Explanation: The number must be between -3 and 2. Only -1 fits this condition.
2
What is the value of 7 - 12 + 5?
0
10
-10
2
Explanation: Compute from left to right: 7 - 12 = -5, then -5 + 5 = 0.
3
Which fraction is equivalent to 3/4?
6/8
3/8
4/3
9/16
Explanation: Multiply numerator and denominator by the same number: 3/4 = 6/8.
4
What is 25% of 80?
10
15
20
25
Explanation: 25% means one quarter. One quarter of 80 is 20.
5
Simplify the expression 3x + 5x - 2.
8x - 2
8x
2x - 2
15x - 2
Explanation: Combine like terms: 3x + 5x = 8x, so the expression becomes 8x - 2.
6
Solve the equation x + 9 = 14.
x = 3
x = 5
x = 23
x = -5
Explanation: Subtract 9 from both sides: x = 14 - 9 = 5.
7
A recipe uses 2 cups of flour for 3 cakes. How many cups of flour are needed for 6 cakes?
3 cups
4 cups
6 cups
12 cups
Explanation: 6 cakes is twice as many as 3 cakes, so the flour amount also doubles: 2 × 2 = 4 cups.
8
What is the area of a rectangle with length 8 cm and width 5 cm?
13 cm²
20 cm²
26 cm²
40 cm²
Explanation: Area of a rectangle = length × width = 8 × 5 = 20 cm².
9
Which expression is equal to 4(2 + x)?
8 + x
8 + 4x
6x
4 + 2x
Explanation: Distribute 4 across the parentheses: 4 × 2 + 4 × x = 8 + 4x.
10
A number is increased by 15% and becomes 92. What was the original number?
75
80
85
107
Explanation: If the original number is x, then 1.15x = 92. So x = 92 ÷ 1.15 = 80.
11
Which of the following are rational numbers?
-7
0.25
√2
3/5
Explanation: Rational numbers can be written as a fraction. Integers, terminating decimals, and fractions are rational; √2 is not rational.
