Factorising into Single Brackets - Worksheets, Questions and Revision

31 original exam-style questions - 7 pages of questions with a full mark scheme - free printable PDF.

Download PDF Jump to mark scheme (page 8)Factorising into Single Brackets revision guide

This topic is chapter 6 of KS3 Maths: Algebra Practice Book 1.

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2.9 Factorising into Single Brackets

AQA KS3.M-A9 · Calculators not allowed · about 95 minutes

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Factorise each expression where the coefficients are small primes.

(a)Factorise 5x + 15(1)

(b)Factorise 11y - 33(1)

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)

Factorise each expression with three terms where a single common factor exists.

(a)Factorise 9x + 3y + 6(2)

(b)Factorise 12a - 8b + 4c(2)

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)

Solve each equation by factorising. Show your steps.

(a)Solve 6x - 18 = 0(4)

Factorise each expression that includes a decimal coefficient.

(a)Factorise 0.6x + 1.8(1)

(b)Factorise 2.5y - 7.5(1)

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)

Factorise each integer by taking out the greatest common factor.

(a)Factorise 28 + 70(1)

(b)Factorise 45 - 15(1)

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)

Factorise each expression by taking out the highest numeric factor.

(a)Factorise 63p + 21q(1)

(b)Factorise 50m - 20n(1)

Factorise each expression fully, taking out common algebraic factors.

(a)Factorise 12x² + 18x(1)

(b)Factorise 7x - 21x²(1)

(c)Factorise 15y² - 10y(1)

Factorise each expression where one term is negative.

(a)Factorise -6x + 18(1)

(b)Factorise 8 - 12p(1)

Factorise each expression completely. Show any common algebraic factors taken out.

(a)Factorise 18x² - 24x(2)

(b)Factorise 14ab - 21a(2)

Factorise each expression where every term has a number and a letter in common.

(a)Factorise 21mn + 14m(1)

(b)Factorise 30xy - 10y(1)

Factorise each expression and then check by expanding your answer.

(a)Factorise 16x + 24 and expand your factorised form to check(3)

Factorise 8x + 12.

(1)

Factorise fully -14x + 21.

(2)

Factorise fully 24mn - 16m.

(2)

Factorise fully 1.2x + 3.6.

(2)

Factorise fully 15x² + 25x.

(2)

Factorise fully 12x²y - 18xy + 6xy².

(3)

A market stall sells 16 apples and 24 pears for a total of (16p + 24q) pounds, where p is the price of an apple and q is the price of a pear. Factorise the total to show the cost of one bundle containing a fixed number of apples and pears.

(3)

Factorise fully -18k - 30, giving your answer with a positive number outside the bracket. State whether the terms inside the bracket are both positive.

(3)

A rectangle has area 24x + 36 square cm, where the width is a whole number of cm common to both terms and is as large as possible.

(a)Factorise 24x + 36 fully to find the greatest possible width and the length of the rectangle.(2)

(b)Given that x = 3, work out the width and the length of the rectangle.(2)

Factorise 9y - 15.

(1)

Factorise 7a + 7b.

(1)

Factorise x² + 9x.

(1)

Factorise 6m² - 8m.

(1)

Factorise 16xy + 12x.

(1)

Factorise fully 20x + 30y + 10.

(2)

Factorise fully 18a² - 27a.

(2)

Mark scheme · 2.9 Factorising into Single Brackets

Question 1

(a) B1 5(x + 3) cao
(a) Answer: 5(x + 3)
(b) B1 11(y - 3) cao
(b) Answer: 11(y - 3)

Question 2

(a) B1 x(x + 5) cao
(a) Answer: x(x + 5)
(b) B1 6z(z - 2) cao
(b) Answer: 6z(z - 2)

Question 3

(a) M1 identify GCF 3
(a) A1 3(3x + y + 2) cao
(a) Answer: 3(3x + y + 2)
(b) M1 identify GCF 4
(b) A1 4(3a - 2b + c) cao
(b) Answer: 4(3a - 2b + c)

Question 4

(a) M1 take out -5 or 5 and change signs correctly
(a) M1 write factor form -5(3p - 1) or 5( -3p + 1) method
(a) A1 -5(3p - 1) cao
(a) Answer: -5(3p - 1)

Question 5

(a) M1 factor out 6 to give 6(x - 3) = 0
(a) M1 use zero product principle or divide both sides by 6
(a) M1 isolate x showing x - 3 = 0
(a) A1 x = 3 cao
(a) Answer: 3

Question 6

(a) B1 0.6(x + 3) oe
(a) Answer: 0.6(x + 3)
(b) B1 2.5(y - 3) cao
(b) Answer: 2.5(y - 3)

Question 7

(a) M1 correct factor taken out, e.g. -4
(a) M1 correct factorised form -4(3k - 2 + 4k) or simplified -4(7k - 2)
(a) A1 state that the bracket 7k - 2 is not all positive for small k and explain oe
(a) Answer: -4(7k - 2)

Question 8

(a) B1 2(14 + 35) or 14(2 + 5) oe
(a) Answer: 14(2 + 5)
(b) B1 15(3 - 1) oe
(b) Answer: 15(3 - 1)

Question 9

(a) B1 3x(2 + 5) or 3x(7) not required but factor form 3x(2+5) oe
(a) Answer: 3x(2 + 5)
(b) B1 2y(2 - 5) oe
(b) Answer: 2y(2 - 5)
(c) B1 3(3a + 2b) oe
(c) Answer: 3(3a + 2b)

Question 10

(a) B1 21(3p + q) cao
(a) Answer: 21(3p + q)
(b) B1 10(5m - 2n) cao
(b) Answer: 10(5m - 2n)

Question 11

(a) B1 6x(2x + 3) cao
(a) Answer: 6x(2x + 3)
(b) B1 7x(1 - 3x) oe
(b) Answer: 7x(1 - 3x)
(c) B1 5y(3y - 2) cao
(c) Answer: 5y(3y - 2)

Question 12

(a) B1 -6(x - 3) or 6( -x + 3) oe
(a) Answer: -6(x - 3)
(b) B1 4(2 - 3p) cao
(b) Answer: 4(2 - 3p)

Question 13

(a) M1 method: factor common number and x, e.g. 6x taken out
(a) A1 6x(3x - 4) cao
(a) Answer: 6x(3x - 4)
(b) M1 method: take out 7a
(b) A1 7a(2b - 3) cao
(b) Answer: 7a(2b - 3)

Question 14

(a) B1 7m(3n + 2) cao
(a) Answer: 7m(3n + 2)
(b) B1 10y(3x - 1) cao
(b) Answer: 10y(3x - 1)

Question 15

(a) M1 factor method, take out 8
(a) M1 correct factorised form 8(2x + 3)
(a) A1 expansion 16x + 24 cao
(a) Answer: 8(2x + 3)

Question 16

B1 4(2x + 3) cao
Answer: 4(2x + 3)

Question 17

M1 identify GCF 7 and take it out with correct signs
A1 -7(2x - 3) cao
Answer: -7(2x - 3)

Question 18

M1 identify GCF 8m
A1 8m(3n - 2) cao
Answer: 8m(3n - 2)

Question 19

M1 identify GCF 1.2
A1 1.2(x + 3) cao
Answer: 1.2(x + 3)

Question 20

M1 identify GCF 5x
A1 5x(3x + 5) cao
Answer: 5x(3x + 5)

Question 21

M1 identify GCF 6xy
M1 divide each term correctly by 6xy
A1 6xy(2x - 3 + y) cao
Answer: 6xy(2x - 3 + y)

Question 22

M1 identify common factor 8
M1 write 8(2p + 3q)
A1 8(2p + 3q) cao
Answer: 8(2p + 3q)

Question 23

M1 take out -6, correctly changing both signs
M1 correct factorised form -6(3k + 5)
A1 state that both terms inside the bracket (3k and 5) are positive, so cao explanation
Answer: -6(3k + 5); yes, both terms inside the bracket are positive

Question 24

(a) M1 identify GCF 12
(a) A1 12(2x + 3) cao
(a) Answer: 12(2x + 3)
(b) M1 substitute x = 3 into (2x + 3) to get the length
(b) A1 width 12 cm, length 9 cm cao
(b) Answer: width 12 cm, length 9 cm

Question 25

B1 3(3y - 5) cao
Answer: 3(3y - 5)

Question 26

B1 7(a + b) cao
Answer: 7(a + b)

Question 27

B1 x(x + 9) cao
Answer: x(x + 9)

Question 28

B1 2m(3m - 4) cao
Answer: 2m(3m - 4)

Question 29

B1 4x(4y + 3) cao
Answer: 4x(4y + 3)

Question 30

M1 identify GCF 10
A1 10(2x + 3y + 1) cao
Answer: 10(2x + 3y + 1)

Question 31

M1 identify GCF 9a
A1 9a(2a - 3) cao
Answer: 9a(2a - 3)

Factorising into Single Brackets - Worksheets, Questions and Revision

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Related topics

2.9 Factorising into Single Brackets

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