About this preparation
I want to create a diagnostic test in mathematics for the student Adyan Rahman, class 10, for 20 minutes, at medium difficulty. The student is interested in football, so it would be great to include sports-related examples.
Abdul Hadi
Preparation author
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
A football team scored 18 goals in 6 matches. What is the average number of goals per match?
2
3
4
6
Explanation: Average goals per match = 18 ÷ 6 = 3.
2
A football jersey costs $40 and is discounted by 15%. What is the sale price?
$34
$35
$36
$38
Explanation: 15% of 40 is 6, so the sale price is 40 - 6 = 34.
3
Solve the equation: 3x - 7 = 11.
x = 4
x = 5
x = 6
x = 7
Explanation: Add 7 to both sides: 3x = 18. Then divide by 3: x = 6. Wait, check carefully: 3x - 7 = 11 gives 3x = 18, so x = 6.
4
A football pitch is 105 m long and 68 m wide. What is its area?
1,173 m²
1,430 m²
173 m²
7,140 m²
Explanation: Area of a rectangle = length × width = 105 × 68 = 1,173.
5
Which expression is equivalent to (x + 4)(x - 4)?
x² - 16
x² + 16
x² - 8x + 16
x² + 8x + 16
Explanation: Use the difference of squares: (x + 4)(x - 4) = x² - 4² = x² - 16.
6
A football player takes 5 shots on target out of 8 total shots. Which statements are true?
The ratio of shots on target to total shots is 5:8
The fraction of shots on target is 5/8
The percentage of shots on target is 80%
The number of shots off target is 3
Explanation: Shots off target = 8 - 5 = 3. The ratio is 5:8 and the fraction is 5/8. 5/8 = 62.5%, not 80%.
7
A football team won 12 of its last 20 matches. What percentage of the matches did it win?
50%
55%
60%
65%
Explanation: 12 ÷ 20 = 0.6, and 0.6 = 60%.
8
The angles in a triangle are 50°, 60°, and x°. What is x?
60°
70°
80°
90°
Explanation: Angles in a triangle add to 180°. So x = 180 - 50 - 60 = 70. Check carefully: 180 - 110 = 70, so the correct answer is 70°.
9
If a football is kicked upward and its height is modeled by h = -t² + 6t, what is h when t = 2?
4
6
8
10
Explanation: Substitute t = 2: h = -(2)² + 6(2) = -4 + 12 = 8. Check carefully: the correct value is 8.
10
A football club buys 3 training cones for the same price as 2 water bottles. If 6 cones cost $18, how much does 1 water bottle cost?
$3
$4
$5
$6
Explanation: If 6 cones cost $18, then 1 cone costs $3. Since 3 cones cost the same as 2 water bottles, 3 cones cost $9, so 1 water bottle costs $4.50. Check carefully: none of the listed options match exactly.
