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HIGHER

4.8H Expanding and Factorising: Higher Tier Practice

EDEXCEL Edexcel 1MA1 · Calculator allowed · about 75 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Expand and simplify: 3(x + 4).

(Total for Question 1 is 2 marks)

Expand and simplify: (2x - 5)(x + 3).

(Total for Question 2 is 2 marks)

Factorise fully: 6y + 15.

(Total for Question 3 is 2 marks)

Factorise fully: x² + 5x + 6.

(Total for Question 4 is 3 marks)

Expand and simplify. Give your answer in the form ax² + bx + c.
0.5x(x - 6) + x(2x + 1)

(Total for Question 5 is 3 marks)

Factorise by grouping: 3x² + 6x - 2x - 4.

(Total for Question 6 is 4 marks)

Show that (x + 4)(2x - 1) = 2x² + 7x - 4. You must show your steps.

(Total for Question 7 is 3 marks)

Factorise fully: 4x² + 7x - 15.

(Total for Question 8 is 5 marks)

A rectangle has length (3x + 2) cm and width (x - 4) cm. The area is given by A = (3x + 2)(x - 4).
(a) Expand and simplify A in the form ax² + bx + c. (3 marks)
(b) Hence factorise the expression from part (a) and use your factorised form to work out the value of the expression when x = 6. (2 marks)

(a)Expand and simplify A in the form ax² + bx + c.(3)

(b)Hence factorise the expression from part (a) and use your factorised form to work out the value of the expression when x = 6.(2)

(Total for Question 9 is 5 marks)

Completely factorise: x³ + 2x² - 9x - 18.

(Total for Question 10 is 6 marks)

Mark scheme · 4.8H Expanding and Factorising: Higher Tier Practice

Question 1

M1 multiply 3 by each term in the bracket, e.g. 3x + 12 or equivalent method
A1 3x + 12 cao
Answer: 3x + 12

Question 2

M1 multiply out brackets correctly, e.g. 2x*x, 2x*3, -5*x, -5*3
A1 2x² + x - 15 cao
Answer: 2x² + x - 15

Question 3

M1 identify highest common factor 3 (or show grouping) and divide each term
A1 3(2y + 5) cao
Answer: 3(2y + 5)

Question 4

M1 identify two numbers that multiply to 6 and add to 5 (2 and 3) or equivalent method
M1 write factors (x + 2)(x + 3) or show splitting the middle term
A1 (x + 2)(x + 3) cao
Answer: (x + 2)(x + 3)

Question 5

M1 expand 0.5x(x - 6) to 0.5x² - 3x and expand x(2x + 1) to 2x² + x
M1 combine like terms correctly
A1 2.5x² - 2x + 0 cao
Answer: 2.5x² - 2x

Question 6

M1 group first two and last two terms: (3x² + 6x) + (-2x - 4)
M1 factor common factors from each group: 3x(x + 2) -2(x + 2)
A1 (x + 2) as common factor identified
A1 (x + 2)(3x - 2) cao
Answer: (x + 2)(3x - 2)

Question 7

C1 expand brackets correctly: x*2x, x*(-1), 4*2x, 4*(-1) shown
C1 combine the four terms to form 2x² + 7x - 4
C1 final statement equal to 2x² + 7x - 4 with clear workings (cso)
Answer: 2x² + 7x - 4

Question 8

M1 multiply 4 * -15 = -60 and look for pair summing to 7
M1 find pair 12 and -5 that give -60 and sum 7
M1 split middle term and factor by grouping
A1 (4x - 5)(x + 3) cao
A1 final factorisation shown correctly
Answer: (4x - 5)(x + 3)

Question 9

(a) M1 multiply out brackets: 3x*x, 3x*(-4), 2*x, 2*(-4)
(a) M1 combine like terms correctly
(a) A1 3x² - 10x - 8 cao
(a) Answer: 3x² - 10x - 8
(b) M1 factorise 3x² - 10x - 8 to (3x + 2)(x - 4) or equivalent
(b) A1 substitute x = 6 into the factorised form: (3*6 + 2)(6 - 4) = 20 * 2 = 40 cao
(b) Answer: Factorised form (3x + 2)(x - 4); when x = 6 the expression equals 40

Question 10

M1 attempt factorisation by grouping or test integer roots (e.g. x = -3) to find a linear factor
M1 divide polynomial by (x + 3) or use grouping to obtain quadratic x² - x - 6
M1 factor quadratic x² - x - 6 into (x + 2)(x - 3)
A1 state intermediate factorisation (x + 3)(x² - x - 6) cao
A1 complete factorisation (x + 3)(x + 2)(x - 3) cao
A1 final answer fully factorised cao
Answer: (x + 3)(x + 2)(x - 3)

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