About this preparation
Math diagnostic test, Grade 10: Year 9 Mixed Review. 11 questions with answers and explanations. Topics: Fractions and decimals, Percentages, Linear equations, Angles and geometry, Area and perimeter, Ratios and proportions, Exponents and roots, Data interpretation. Duration: 25 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 3/4 + 2/5?
11/20
23/20
5/9
1/20
Explanation: Find a common denominator of 20: 3/4 = 15/20 and 2/5 = 8/20, so the sum is 23/20.
2
A jacket costs $80 and is reduced by 15%. What is the sale price?
$68
$72
$65
$75
Explanation: 15% of 80 is 12, so the sale price is 80 - 12 = 68.
3
Solve for x: 2x + 7 = 19
x = 5
x = 6
x = 7
x = 8
Explanation: Subtract 7 from both sides to get 2x = 12, then divide by 2 to get x = 6? Wait, check carefully: 19 - 7 = 12, and 12 ÷ 2 = 6, so the correct answer is x = 6.
4
A triangle has angles 48° and 67°. What is the third angle?
55°
65°
75°
85°
Explanation: Angles in a triangle add to 180°. So 180 - 48 - 67 = 65.
5
Simplify: 4^2 × 4^3
4^5
4^6
16^5
8^5
Explanation: When multiplying powers with the same base, add the exponents: 2 + 3 = 5.
6
If 5 notebooks cost $12.50, how much do 8 notebooks cost at the same rate?
$18.00
$19.50
$20.00
$21.00
Explanation: One notebook costs $12.50 ÷ 5 = $2.50, so 8 notebooks cost 8 × $2.50 = $20.00.
7
What is the area of a rectangle with length 9 cm and width 6 cm?
15 cm²
30 cm²
54 cm²
60 cm²
Explanation: Area of a rectangle is length × width: 9 × 6 = 54.
8
A number is increased by 20% and becomes 84. What was the original number?
66
68
70
72
Explanation: If the final amount is 120% of the original, then original = 84 ÷ 1.2 = 70.
9
Solve: 3(x - 4) = 18
x = 2
x = 6
x = 8
x = 10
Explanation: Divide both sides by 3 to get x - 4 = 6, then add 4 to get x = 10? Check carefully: 18 ÷ 3 = 6, so x - 4 = 6 and x = 10.
10
A data set has values 4, 7, 7, 9, 13. What is the median?
7
8
9
13
Explanation: The numbers are already in order, and the middle value is 7.
11
What is the value of √81 + 2^3?
11
13
17
19
Explanation: √81 = 9 and 2^3 = 8, so the total is 17.
