About this preparation
Хочу зробити діагностичний тест з математики для учня Edison Thomas, 11 клас, на 55 хвилин, середньої складності. Потрібно включити factorising expressions.
Reid Rachel
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
What is the factorised form of 6x + 12?
6(x + 2)
3(2x + 4)
2(3x + 12)
6x(1 + 2)
Explanation: The greatest common factor is 6, so 6x + 12 = 6(x + 2).
2
Which expression is fully factorised?
x(x + 5)
x^2 + 5x
x^2 + x + 5
5x + x^2
Explanation: x(x + 5) is already written as a product of factors.
3
Factorise: 9y^2 - 16
(3y - 4)(3y + 4)
(9y - 4)(y + 4)
(3y - 8)(3y + 2)
(y - 4)(y + 4)
Explanation: This is a difference of squares: a^2 - b^2 = (a - b)(a + b).
4
Factorise: x^2 + 7x + 12
(x + 3)(x + 4)
(x + 1)(x + 12)
(x - 3)(x - 4)
(x + 2)(x + 6)
Explanation: We need two numbers that multiply to 12 and add to 7: 3 and 4.
5
Factorise: 4a^2 - 12a
4a(a - 3)
2a(2a - 12)
a(4a - 12)
4(a^2 - 3a)
Explanation: The common factor is 4a, so 4a^2 - 12a = 4a(a - 3).
6
Which expression is equivalent to 2x^2 + 8x?
2x(x + 4)
x(2x + 8)
2(x^2 + 4x)
(2x + 4)(x + 2)
Explanation: Factor out the common factor 2x: 2x^2 + 8x = 2x(x + 4).
7
Factorise: x^2 - 5x - 24
(x - 8)(x + 3)
(x - 6)(x + 4)
(x + 8)(x - 3)
(x - 12)(x + 2)
Explanation: We need two numbers that multiply to -24 and add to -5: -8 and 3.
8
Which of the following expressions are factorised correctly? Select all that apply.
3x(x - 2)
x^2 - 2x
(x + 5)(x - 5)
x^2 - 25
Explanation: A factorised form is written as a product. Options a and c are factorised; b and d are expanded forms.
9
Factorise: 15m^2n - 10mn^2
5mn(3m - 2n)
5m(3mn - 2n^2)
10mn(1.5m - n)
5n(3m^2 - 2mn)
Explanation: The greatest common factor is 5mn, giving 15m^2n - 10mn^2 = 5mn(3m - 2n).
10
What is the factorised form of x^2 + 2x - 15?
(x + 5)(x - 3)
(x - 5)(x - 3)
(x + 15)(x - 1)
(x + 3)(x - 5)
Explanation: We need two numbers that multiply to -15 and add to 2: 5 and -3.
