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5.7F Expanding and Factorising Quadratics: Foundation Tier Practice

EDEXCEL Edexcel 1MA1 · Calculator allowed · about 60 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Expand the single bracket 3(x + 4).

(Total for Question 1 is 1 mark)

Expand and simplify 2(2x - 5).

(Total for Question 2 is 1 mark)

Expand the brackets and simplify: (x + 2)(x + 3).

(Total for Question 3 is 1 mark)

Expand and simplify (x + 5)(x - 1).

(Total for Question 4 is 2 marks)

Factorise fully: 2x² + 6x.

(Total for Question 5 is 2 marks)

Factorise the quadratic x² + 7x + 10.

(Total for Question 6 is 3 marks)

Factorise x² - 4x - 12.

(Total for Question 7 is 3 marks)

A toy company sells k² + 5k + 6 toys at a fair. They pack the toys into groups so the number of toys is (k + 2)(k + 3).
Explain briefly why the two expressions are equal.

(Total for Question 8 is 3 marks)

Expand and simplify 3(x - 2)(x + 1). Show all steps.

(Total for Question 9 is 4 marks)

Factorise fully 4x² + 2x - 12.

(Total for Question 10 is 4 marks)

The area of a rectangle is given by x² + 6x + 8 square cm. The length is (x + 2) cm.
Find the width in terms of x. Show your working. Then find the width when x = 3.

(a)Factorise the expression for the area x² + 6x + 8.(2)

(b)Use part (a) to find the width of the rectangle in terms of x.(2)

(c)Find the width when x = 3.(2)

(Total for Question 11 is 6 marks)

A rectangular flower bed has length (x + 3) metres and width (2x + 1) metres.
(a) Expand and simplify the expression for the area.
(b) Given the area is 2x² + 7x + 3, show how this can be written as a product of two linear brackets.

(a)Expand and simplify (x + 3)(2x + 1).(2)

(b)Factorise 2x² + 7x + 3 to write it as a product of two linear brackets.(4)

(Total for Question 12 is 6 marks)

Mark scheme · 5.7F Expanding and Factorising Quadratics: Foundation Tier Practice

Question 1

B1 3x + 12 cao
Answer: 3x + 12 (or 12 + 3x).

Question 2

B1 4x - 10 cao
Answer: 4x - 10.

Question 3

B1 x² + 5x + 6 cao
Answer: x² + 5x + 6.

Question 4

M1 multiply terms correctly, e.g. x*x, x*(-1), 5*x, 5*(-1) or show full FOIL
A1 x² + 4x - 5 cao
Answer: x² + 4x - 5.

Question 5

M1 factor out common factor 2x
A1 2x(x + 3) cao
Answer: 2x(x + 3).

Question 6

M1 identify two numbers that multiply to 10 and add to 7 (2 and 5) or show splitting the middle term
A1 (x + 2)(x + 5) cao
B1 correct checking statement e.g. expand to get x² + 7x + 10 oe
Answer: (x + 2)(x + 5).

Question 7

M1 identify two numbers that multiply to -12 and add to -4 ( -6 and 2 ) or show splitting the middle term
A1 (x - 6)(x + 2) cao
B1 correct check, e.g. expand to x² - 4x - 12 oe
Answer: (x - 6)(x + 2).

Question 8

M1 expand (k + 2)(k + 3) to show method, e.g. k² + 2k + 3k + 6
A1 correctly simplify to k² + 5k + 6
B1 conclude that this matches the given expression k² + 5k + 6, so the two expressions are equal oe
Answer: Expanding gives (k + 2)(k + 3) = k² + 2k + 3k + 6 = k² + 5k + 6, which matches the given expression k² + 5k + 6 exactly, so the two expressions are equal for all k.

Question 9

M1 expand (x - 2)(x + 1) to x² - x - 2 or show partial expansion
M1 multiply by 3 correctly to get 3x² - 3x - 6
A1 3x² - 3x - 6 cao
B1 clear and correct working shown or check via substitution
Answer: 3x² - 3x - 6.

Question 10

M1 factor out common factor 2 first to give 2(2x² + x - 6)
M1 factorise the quadratic inside correctly or show splitting the middle term
A1 2(2x - 3)(x + 2) cao or equivalent correct factorisation
B1 correct check by expansion or statement
Answer: 2(2x - 3)(x + 2).

Question 11

(a) M1 identify two numbers that multiply to 8 and add to 6 (2 and 4) or show splitting the middle term
(a) A1 (x + 2)(x + 4) cao
(a) Answer: (x + 2)(x + 4).
(b) M1 divide the area expression by length (x + 2) or cancel a factor to show method
(b) A1 width = x + 4 cao
(b) Answer: x + 4
(c) M1 substitute x = 3 into width expression or show calculation 3 + 4
(c) A1 7 cm cao
(c) Answer: 7 cm

Question 12

(a) M1 multiply out brackets correctly, e.g. use distributive law
(a) A1 2x² + 7x + 3 cao
(a) Answer: 2x² + 7x + 3
(b) M1 identify pair of numbers or use splitting the middle term: find factors of 2*3 = 6 that add to 7 (1 and 6)
(b) M1 split middle term and factor by grouping or show rearrangement to (2x² + x) + (6x + 3)
(b) A1 (x + 3)(2x + 1) cao
(b) B1 correct check by expanding to 2x² + 7x + 3 oe
(b) Answer: (x + 3)(2x + 1)

Expanding and Factorising Quadratics: Foundation Tier Practice - Worksheets, Questions and Revision