About this preparation
Math diagnostic test, Year 11: Number, Algebra. 10 questions with answers and explanations. Topics: Number, Algebra, Ratio and proportion, Geometry, Statistics. 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
Work out 3/4 of 28.
18
21
24
25
Explanation: To find 3/4 of 28, divide 28 by 4 to get 7, then multiply by 3: 7 × 3 = 21.
2
Simplify 5x + 3x - 2.
8x - 2
8x + 2
15x - 2
2x - 2
Explanation: Combine like terms: 5x + 3x = 8x, so the expression simplifies to 8x - 2.
3
Solve 2x + 7 = 19.
x = 5
x = 6
x = 7
x = 9
Explanation: Subtract 7 from both sides to get 2x = 12, then divide by 2: x = 6. Wait, check carefully: 2x + 7 = 19 gives 2x = 12, so x = 6.
4
A shirt costs £24 and is reduced by 25%. What is the sale price?
£6
£12
£18
£20
Explanation: 25% of £24 is £6. Subtract £6 from £24 to get £18.
5
The ratio of boys to girls in a class is 3:5. There are 24 boys. How many girls are there?
32
36
40
48
Explanation: 3 parts correspond to 24 boys, so 1 part is 8. Girls are 5 parts, so 5 × 8 = 40. Check the ratio carefully: 3:5 means girls = 5 parts, so the correct answer is 40.
6
Find the area of a triangle with base 12 cm and height 9 cm.
54 cm²
108 cm²
21 cm²
36 cm²
Explanation: Area of a triangle = 1/2 × base × height = 1/2 × 12 × 9 = 54 cm².
7
A number is rounded to 1 decimal place as 4.7. Which of these could be the original number?
4.64
4.73
4.79
4.85
Explanation: A number rounds to 4.7 to 1 decimal place if it is at least 4.65 and less than 4.75. 4.73 fits this range.
8
Expand and simplify (x + 4)(x + 2).
x² + 6x + 8
x² + 8x + 6
x² + 2x + 8
x² + 6x + 2
Explanation: Multiply each term: x·x = x², x·2 = 2x, 4·x = 4x, and 4·2 = 8. Then combine like terms to get x² + 6x + 8.
9
The mean of 4 numbers is 7. Three of the numbers are 5, 8, and 9. What is the fourth number?
4
6
7
8
Explanation: If the mean of 4 numbers is 7, their total is 4 × 7 = 28. The known numbers add to 5 + 8 + 9 = 22, so the missing number is 28 - 22 = 6.
10
Solve the equation x² = 49.
x = 7 only
x = -7 only
x = 7 or x = -7
x = 49
Explanation: Any number whose square is 49 is a solution. Both 7 and -7 work because 7² = 49 and (-7)² = 49.
