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4.8F Expanding and Factorising: Foundation Tier Practice

EDEXCEL Edexcel 1MA1 · Calculator allowed · about 55 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Expand and simplify: 3(2x + 4).

(Total for Question 1 is 2 marks)

Expand fully: (x + 5) + (2x + 3).

(Total for Question 2 is 2 marks)

Expand and simplify: 4( x - 2 ) - 2x.

(Total for Question 3 is 2 marks)

Factorise fully: 6y + 9.

(Total for Question 4 is 3 marks)

Factorise fully: 8m - 12n.

(Total for Question 5 is 3 marks)

Factorise the quadratic: x² + 5x + 6.

(Total for Question 6 is 4 marks)

Factorise the quadratic: x² + 7x + 12. Give the answer in bracket form.

(Total for Question 7 is 4 marks)

A small charity sells charity bags. The cost to make each bag is given by the expression 2x + 3, where x is the number of special stickers used. The charity makes 5 identical bags. Write an expression for the total cost for the 5 bags and then expand and simplify it.

(a)Write an expression for the total cost for the 5 bags.(2)

(b)Expand and simplify the expression from part (a).(4)

(Total for Question 8 is 6 marks)

A rectangular label has length (3x + 2) cm and width (x - 1) cm. Find an expression for the area of the label and then expand and simplify it.

(a)Write an expression for the area of the rectangle.(2)

(b)Expand and simplify the expression from part (a).(4)

(Total for Question 9 is 6 marks)

Remove common factors and factorise fully: 12p²q - 8pq² + 4pq.

(a)Write down the highest common factor that can be removed from all three terms.(2)

(b)Factorise the expression fully after removing the common factor.(6)

(Total for Question 10 is 8 marks)

Mark scheme · 4.8F Expanding and Factorising: Foundation Tier Practice

Question 1

M1 multiply each term by 3: 3*2x and 3*4 shown
A1 6x + 12 cao
Answer: 6x + 12

Question 2

M1 collect like terms shown: x + 2x and 5 + 3
A1 3x + 8 cao
Answer: 3x + 8

Question 3

M1 expand 4(x - 2) to 4x - 8 or equivalent
A1 2x - 8 cao
Answer: 2x - 8

Question 4

M1 identify common factor 3 and show factoring step: 3(2y + 3) or equivalent
A1 3(2y + 3) cao
B1 final answer written in fully factorised form, 3(2y + 3) oe
Answer: 3(2y + 3)

Question 5

M1 identify common factor 4 and show factoring step: 4(2m - 3n) or equivalent
A1 4(2m - 3n) cao
B1 final answer written in fully factorised form, 4(2m - 3n) oe
Answer: 4(2m - 3n)

Question 6

M1 find two numbers multiplying to 6 and adding to 5 (2 and 3) shown
M1 split middle term or show factors used: x² + 2x + 3x + 6
A1 (x + 2)(x + 3) cao
B1 final answer given in bracket form (x + 2)(x + 3) oe
Answer: (x + 2)(x + 3)

Question 7

M1 identify pair 3 and 4 that multiply to 12 and add to 7
M1 split middle term or show factors: x² + 3x + 4x + 12
A1 (x + 3)(x + 4) cao
B1 final answer presented in bracket form (x + 3)(x + 4) oe
Answer: (x + 3)(x + 4)

Question 8

(a) M1 show 5 times the cost of one bag: 5(2x + 3) or equivalent
(a) A1 5(2x + 3) cao
(a) Answer: 5(2x + 3)
(b) M1 show multiplication by 5 applied to both terms: 5*2x and 5*3 shown
(b) M1 state the intermediate expanded terms 10x and 15 explicitly
(b) A1 10x + 15 cao
(b) B1 final simplified expression given as 10x + 15 oe
(b) Answer: 10x + 15

Question 9

(a) M1 area = length * width shown: (3x + 2)(x - 1)
(a) A1 (3x + 2)(x - 1) cao
(a) Answer: (3x + 2)(x - 1)
(b) M1 multiply out brackets correctly: 3x*x, 3x*(-1), 2*x, 2*(-1) shown
(b) M1 write each term found: 3x², -3x, 2x, -2
(b) A1 combine like terms correctly to give 3x² - x - 2 cao
(b) B1 final simplified form presented as 3x² - x - 2 oe
(b) Answer: 3x² - x - 2

Question 10

(a) M1 identify common factor 4pq or equivalent shown
(a) A1 4pq cao
(a) Answer: 4pq
(b) M1 factor out 4pq from each term and show intermediate division: 12p²q ÷ 4pq = 3p, -8pq² ÷ 4pq = -2q, 4pq ÷ 4pq = 1
(b) M1 write the expression as 4pq(3p - 2q + 1) or equivalent bracket contents shown
(b) M1 show multiplication back check for at least one term, e.g. 4pq * 3p = 12p²q
(b) A1 4pq(3p - 2q + 1) cao
(b) B1 correct ordering of terms in the brackets (3p - 2q + 1) oe
(b) B1 final answer presented in fully factorised form 4pq(3p - 2q + 1) oe
(b) Answer: 4pq(3p - 2q + 1)

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