Simplifying Algebra: Fluency and Exam Drill (Part 2) - Worksheets, Questions and Revision

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

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GCSE · Algebra

2.6DB Simplifying Algebra: Fluency and Exam Drill (Part 2)

EDEXCEL 1MA1 · Calculator allowed · about 50 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Priya has 4x football stickers. Her friend gives her 6x more stickers. Write down an expression, in its simplest form, for the number of stickers Priya has now.

(Total for Question 1 is 1 mark)

Simplify 9h - 3h - 2h.

(Total for Question 2 is 1 mark)

Simplify 5p + 4q - 2p + q.

(Total for Question 3 is 1 mark)

Simplify 3m + 2n - 5m - 6n.

(Total for Question 4 is 2 marks)

Expand and simplify 4(2x + 3) - 9.

(Total for Question 5 is 2 marks)

Expand and simplify 15 - 2(3y - 4).

(Total for Question 6 is 2 marks)

A rectangle has length (3x + 2) cm and width (x - 1) cm. Find an expression, in its simplest form, for the perimeter of the rectangle.

(Total for Question 7 is 2 marks)

Simplify 5a² b x 3ab³.

(Total for Question 8 is 2 marks)

Simplify (x³)⁴.

(Total for Question 9 is 1 mark)

Simplify (12x⁵ y³) / (4x² y).

(Total for Question 10 is 2 marks)

Show that 6t⁰ = 6 for any non-zero value of t.

(Total for Question 11 is 2 marks)

Simplify (2x⁴ y^-2) x (3x^-1 y⁵).

(Total for Question 12 is 2 marks)

Simplify (2x)² + 3x(x - 1).

(Total for Question 13 is 3 marks)

Given g(x) = 5x² - 2x + 3,

(a)Simplify g(x) - (2x² - 3x + 1).(2)

(b)The table below shows two values of x. Use your answer to part (a) to complete the table, giving each value of 3x² + x + 2.

x	-2	3
3x² + x + 2	___	___

(2)

(Total for Question 14 is 4 marks)

Erin was asked to simplify 5x - 3(x - 2). Her working is shown below:
5x - 3(x - 2) = 5x - 3x - 6 = 2x - 6
The answer 2x - 6 is incorrect. Explain the error in Erin's working and work out the correct simplified expression.

(Total for Question 15 is 2 marks)

Simplify (8x^-3 y⁴) / (2x² y^-1). Give your answer with positive indices.

(Total for Question 16 is 3 marks)

Mark scheme · 2.6DB Simplifying Algebra: Fluency and Exam Drill (Part 2)

Question 1

B1 10x cao
Answer: 10x (cao)

Question 2

B1 4h cao
Answer: 4h (cao)

Question 3

B1 3p + 5q cao
Answer: 3p + 5q (cao)

Question 4

M1 collects m terms and n terms separately, e.g. 3m - 5m and 2n - 6n identified
A1 -2m - 4n oe cao
Answer: -2m - 4n (oe cao)

Question 5

M1 correct expansion 8x + 12 shown
A1 8x + 3 cao
Answer: 8x + 3 (cao)

Question 6

M1 correct expansion -6y + 8 shown, i.e. -2 x 3y = -6y and -2 x (-4) = +8
A1 23 - 6y oe cao
Answer: 23 - 6y (oe cao)

Question 7

M1 correct method for perimeter, e.g. (3x + 2) + (x - 1) + (3x + 2) + (x - 1) or 2[(3x + 2) + (x - 1)]
A1 8x + 2 cao (cm)
Answer: 8x + 2 (cm) (cao)

Question 8

M1 multiply coefficients 5 x 3 = 15 and add indices for a (2 + 1) and for b (1 + 3)
A1 15a³ b⁴ cao
Answer: 15a³ b⁴ (cao)

Question 9

B1 x¹² cao (use of index law 3 x 4 = 12)
Answer: x¹² (cao)

Question 10

M1 divide coefficients 12/4 = 3 and subtract indices for x (5 - 2) and for y (3 - 1)
A1 3x³ y² cao
Answer: 3x³ y² (cao)

Question 11

B1 states or uses t⁰ = 1 for t not equal to 0
B1 6 x 1 = 6 (cso)
Answer: 6 (shown, cso)

Question 12

M1 multiply coefficients 2 x 3 = 6 and add indices for x (4 + (-1)) and for y (-2 + 5)
A1 6x³ y³ cao
Answer: 6x³ y³ (cao)

Question 13

M1 squares the term (2x)² = 4x²
M1 expand 3x(x - 1) to 3x² - 3x and add to the previous term
A1 7x² - 3x cao
Answer: 7x² - 3x (cao)

Question 14

(a) M1 subtracts like terms: 5x² - 2x² and -2x - (-3x) and 3 - 1
(a) A1 3x² + x + 2 cao
(a) Answer: 3x² + x + 2 (cao)
(b) B1 12 cao (when x = -2)
(b) B1 32 cao (when x = 3)
(b) Answer: 12 and 32 (cao)

Question 15

M1 identifies the error: -3 x (-2) = +6, not -6 (sign error when multiplying two negative numbers) oe
A1 2x + 6 cao
Answer: Erin's error: -3 x (-2) = +6, not -6 (a sign error). Correct answer: 2x + 6

Question 16

M1 divide coefficients 8/2 = 4 and subtract indices for x: -3 - 2 = -5
M1 subtract indices for y: 4 - (-1) = 5, obtaining 4x^-5 y⁵
A1 4y⁵ / x⁵ cao (positive indices)
Answer: 4y⁵ / x⁵ (cao)

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Simplifying Algebra: Fluency and Exam Drill (Part 2) - Worksheets, Questions and Revision

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2.6DB Simplifying Algebra: Fluency and Exam Drill (Part 2)

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