About this preparation
Math diagnostic test, Year 11: Factorising Expressions and Core Algebra. 10 questions with answers and explanations. Topics: Factorising expressions, Common factors, Difference of squares, Quadratic expressions, Algebraic simplification. 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
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.
