Simplifying Algebra (Part 2) - Worksheets, Questions and Revision

20 original exam-style questions - 4 pages of questions with a full mark scheme - free printable PDF.

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2.6B Simplifying Algebra (Part 2)

EDEXCEL 1MA1 · Calculator allowed · about 50 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Simplify 8g + 3g - 2g

(Total for Question 1 is 1 mark)

Simplify 15h - 9h - 3h

(Total for Question 2 is 1 mark)

Simplify -6k + 11k

(Total for Question 3 is 1 mark)

Simplify 4p + 3q - r - p + 2r - q

(Total for Question 4 is 2 marks)

Simplify 5x² + 3x - 2x² + 4x

(Total for Question 5 is 2 marks)

Simplify each expression.

(a)3a² x 4a³(1)

(b)(b³)²(1)

(Total for Question 6 is 2 marks)

Simplify each expression.

(a)15xy / 5x(1)

(b)24pq / 6p(1)

(Total for Question 7 is 2 marks)

Simplify each expression.

(a)(4x)²(1)

(b)(2y)³(1)

(Total for Question 8 is 2 marks)

Expand -3(2x - 5)

(Total for Question 9 is 2 marks)

Expand and simplify 6x - (x - 7)

(Total for Question 10 is 2 marks)

Which of these expressions is equivalent to 3(2x - 5)?

A) 6x - 5
B) 6x - 15
C) 5x - 15
D) 6x - 2

(Total for Question 11 is 1 mark)

Show that 4(x - 3) - 2(x - 5) = 2x - 2

(Total for Question 12 is 2 marks)

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

(Total for Question 13 is 3 marks)

Expand and simplify -2(3x - 1) - (x - 5)

(Total for Question 14 is 3 marks)

A student was asked to simplify 5(2x - 3) + 4x. Their working is shown below.
5(2x - 3) + 4x = 10x - 3 + 4x = 14x - 3
Identify the mistake in the student's working, and give the correct simplified expression.

(Total for Question 15 is 2 marks)

Three consecutive integers can be written as n, n + 1 and n + 2. Write and simplify an expression, in terms of n, for the sum of three consecutive integers.

(Total for Question 16 is 2 marks)

Three consecutive even numbers can be written as 2n, 2n + 2 and 2n + 4, where n is an integer. Show that the sum of three consecutive even numbers is always a multiple of 6.

(Total for Question 17 is 3 marks)

The diagram shows an isosceles triangle. The two equal sides are each (x + 4) cm and the base is (3x - 2) cm. Write down and simplify an expression, in terms of x, for the perimeter of the triangle.

Figure (to be drawn): An isosceles triangle with the two equal (slanting) sides each labelled (x + 4) cm and the base labelled (3x - 2) cm.

(Total for Question 18 is 2 marks)

Simplify fully 3x(x + 2) - 2x(x - 5)

(Total for Question 19 is 3 marks)

Simplify (12a⁵ b³) / (4a² b)

(Total for Question 20 is 2 marks)

Mark scheme · 2.6B Simplifying Algebra (Part 2)

Question 1

B1 9g cao
Answer: 9g

Question 2

B1 3h cao
Answer: 3h

Question 3

B1 5k cao
Answer: 5k

Question 4

M1 3p, 2q or r seen (at least one letter correctly collected)
A1 3p + 2q + r oe cao
Answer: 3p + 2q + r

Question 5

M1 3x² or 7x seen (x² terms and x terms correctly collected separately)
A1 3x² + 7x oe cao
Answer: 3x² + 7x

Question 6

(a) B1 12a⁵ cao
(a) Answer: 12a⁵
(b) B1 b⁶ cao
(b) Answer: b⁶

Question 7

(a) B1 3y cao
(a) Answer: 3y
(b) B1 4q cao
(b) Answer: 4q

Question 8

(a) B1 16x² cao
(a) Answer: 16x²
(b) B1 8y³ cao
(b) Answer: 8y³

Question 9

M1 -6x or +15 seen (one term correctly multiplied out, including its sign)
A1 -6x + 15 oe cao
Answer: -6x + 15

Question 10

M1 -x + 7 seen (bracket correctly expanded, treating the missing coefficient as -1)
A1 5x + 7 oe cao
Answer: 5x + 7

Question 11

B1 B) 6x - 15
Answer: B) 6x - 15

Question 12

M1 4x - 12 and -2x + 10 (or 2x - 10) both seen (both brackets correctly expanded)
A1 4x - 12 - 2x + 10 = 2x - 2 shown correctly, cso
Answer: 2x - 2 (shown)

Question 13

M1 2x + 10 seen (first bracket expanded correctly)
M1 3x - 6 seen (second bracket expanded correctly)
A1 5x + 4 oe cao
Answer: 5x + 4

Question 14

M1 -6x + 2 seen (first bracket correctly expanded, including its sign)
M1 -x + 5 seen (second bracket correctly expanded, treating the missing coefficient as -1)
A1 -7x + 7 oe cao
Answer: -7x + 7

Question 15

C1 correctly identifies the error: the -3 was not multiplied by 5, so the constant term should be -15, not -3, oe
B1 14x - 15 oe cao
Answer: Error: -3 was not multiplied by 5 (it should become -15). Correct answer: 14x - 15

Question 16

M1 n + (n + 1) + (n + 2) oe seen
A1 3n + 3 oe cao
Answer: 3n + 3

Question 17

M1 2n + (2n + 2) + (2n + 4) oe seen
M1 6n + 6 correctly obtained and written as 6(n + 1) oe
A1 valid conclusion given, e.g. n + 1 is an integer so 6(n + 1) is a multiple of 6, cso
Answer: 6(n + 1), a multiple of 6 (shown)

Question 18

M1 (x + 4) + (x + 4) + (3x - 2) oe seen
A1 5x + 6 oe cao
Answer: 5x + 6

Question 19

M1 3x² + 6x seen (first bracket correctly expanded)
M1 -2x² + 10x seen (second bracket correctly expanded and subtracted)
A1 x² + 16x oe cao
Answer: x² + 16x

Question 20

M1 3, a³ or b² seen (at least one part of the answer correctly simplified)
A1 3a³b² oe cao
Answer: 3a³b²

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Simplifying Algebra (Part 2) - Worksheets, Questions and Revision

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2.6B Simplifying Algebra (Part 2)

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Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20

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Question 11

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Question 17

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Question 19

Question 20