Factorise 5x - 20 completely, then use your factorised form to solve the equation 5x - 20 = 0.
(3)
16
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)
17
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)
18
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)
19
The area of a path is given by the expression 9x2 - 6x, where x is a length in metres.
(a)Factorise 9x2 - 6x fully.(2)
(b)Given that the path is 3x metres wide, write down an expression for its length, using your factorised form.(1)
(c)Given that x = 5, work out the area of the path in square metres.(2)
Mark scheme · KS3.M-A9D Factorising into Single Brackets: Fluency and Exam Drill
Question 1
B1 4(2x + 3) cao
Answer: 4(2x + 3)
Question 2
B1 3(3y - 5) cao
Answer: 3(3y - 5)
Question 3
B1 7(a + b) cao
Answer: 7(a + b)
Question 4
B1 x(x + 9) cao
Answer: x(x + 9)
Question 5
B1 5(2p - 5) cao
Answer: 5(2p - 5)
Question 6
B1 2m(3m - 4) cao
Answer: 2m(3m - 4)
Question 7
B1 4x(4y + 3) cao
Answer: 4x(4y + 3)
Question 8
M1 identify GCF 10
A1 10(2x + 3y + 1) cao
Answer: 10(2x + 3y + 1)
Question 9
M1 identify GCF 9a
A1 9a(2a - 3) cao
Answer: 9a(2a - 3)
Question 10
M1 identify GCF 7 and take it out with correct signs
A1 -7(2x - 3) cao
Answer: -7(2x - 3)
Question 11
M1 identify GCF 8m
A1 8m(3n - 2) cao
Answer: 8m(3n - 2)
Question 12
M1 identify GCF 1.2
A1 1.2(x + 3) cao
Answer: 1.2(x + 3)
Question 13
M1 identify GCF 5x
A1 5x(3x + 5) cao
Answer: 5x(3x + 5)
Question 14
M1 identify GCF 6xy
M1 divide each term correctly by 6xy
A1 6xy(2x - 3 + y) cao
Answer: 6xy(2x - 3 + y)
Question 15
M1 factorise to 5(x - 4)
M1 use zero product, x - 4 = 0
A1 x = 4 cao
Answer: 5(x - 4); x = 4
Question 16
M1 identify common factor 8
M1 write 8(2p + 3q)
A1 8(2p + 3q) cao
Answer: 8(2p + 3q)
Question 17
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 18
(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 19
(a) M1 identify GCF 3x
(a) A1 3x(3x - 2) cao
(a) Answer: 3x(3x - 2)
(b) B1 (3x - 2) metres cao
(b) Answer: (3x - 2) metres
(c) M1 substitute x = 5 into 9x2 - 6x or into 3x(3x-2)