Factorising into Single Brackets - Worksheets, Questions and Revision

18 original exam-style questions - 5 pages of questions with a full mark scheme - free printable PDF.

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KS3 · Algebra

KS3.M-A9 Factorising into Single Brackets

AQA KS3.M-A9 · Calculators not allowed · about 60 minutes
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
Write down the greatest common factor for each pair of numbers.
(a)GCF of 18 and 30(1)
(b)GCF of 14 and 35(1)
(c)GCF of 24 and 40(1)
2
Factorise each integer by taking out the greatest common factor.
(a)Factorise 28 + 70(1)
(b)Factorise 45 - 15(1)
3
Factorise each algebraic expression by taking out the common factor.
(a)Factorise 6x + 15x(1)
(b)Factorise 4y - 10y(1)
(c)Factorise 9a + 6b(1)
4
Factorise each expression by taking out the highest numeric factor.
(a)Factorise 63p + 21q(1)
(b)Factorise 50m - 20n(1)
5
Factorise each expression fully, taking out common algebraic factors.
(a)Factorise 12x2 + 18x(1)
(b)Factorise 7x - 21x2(1)
(c)Factorise 15y2 - 10y(1)
6
Factorise each expression where one term is negative.
(a)Factorise -6x + 18(1)
(b)Factorise 8 - 12p(1)
7
Factorise each expression completely. Show any common algebraic factors taken out.
(a)Factorise 18x2 - 24x(2)
(b)Factorise 14ab - 21a(2)
8
Factorise each expression where every term has a number and a letter in common.
(a)Factorise 21mn + 14m(1)
(b)Factorise 30xy - 10y(1)
9
Factorise each expression and then check by expanding your answer.
(a)Factorise 16x + 24 and expand your factorised form to check(3)
10
Factorise each expression where the coefficients are small primes.
(a)Factorise 5x + 15(1)
(b)Factorise 11y - 33(1)
11
Apply factorising to simplify an expression used in a context.
(a)A recipe needs 12ab + 6b grams of an ingredient. Factorise to write the amount as a product.(3)
12
Factorise each pair where one term has a squared letter and the other does not.
(a)Factorise x2 + 5x(1)
(b)Factorise 6z2 - 12z(1)
13
Factorise each expression with three terms where a single common factor exists.
(a)Factorise 9x + 3y + 6(2)
(b)Factorise 12a - 8b + 4c(2)
14
Factorise each expression then give the sign of the bracket so that the expression inside is positive where possible.
(a)Factorise -15p + 5 and give factor with positive bracket(3)
15
Solve each equation by factorising. Show your steps.
(a)Solve 6x - 18 = 0(4)
16
Factorise each expression that includes a decimal coefficient.
(a)Factorise 0.6x + 1.8(1)
(b)Factorise 2.5y - 7.5(1)
17
A school buys 18 identical packs and 24 identical rulers. The total cost is 18p + 24r. Factorise the total cost to show the cost of one set containing a pack and a ruler.
(a)Write the total cost 18p + 24r as a product showing the cost of one pack and one ruler.(3)
18
Stretch: Factorise fully and then indicate whether the bracket contains only positive terms. Explain how you know.
(a)Factorise -12k + 8 - 16k and say whether the bracket has only positive terms.(3)
Mark scheme · KS3.M-A9 Factorising into Single Brackets

Question 1

Question 2

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Question 9

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Question 11

Question 12

Question 13

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Question 15

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Question 18