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GCSE · Algebra

2.6D Simplifying Algebra: Fluency and Exam Drill

EDEXCEL Edexcel 1MA1 · Calculator allowed · about 50 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Simplify 5x + 3x.

(Total for Question 1 is 1 mark)

Simplify 7y - 2y + 4y.

(Total for Question 2 is 1 mark)

Simplify 3a + 2 - a + 5.

(Total for Question 3 is 1 mark)

Simplify 4x - 3 + 2x + 9.

(Total for Question 4 is 1 mark)

Expand and simplify 2(3x + 4).

(Total for Question 5 is 2 marks)

Expand and simplify -3(2y - 5).

(Total for Question 6 is 2 marks)

Simplify (2x)(3x).

(Total for Question 7 is 2 marks)

Simplify 4x² * 3x³.

(Total for Question 8 is 2 marks)

Simplify x⁵ / x².

(Total for Question 9 is 1 mark)

Simplify (6x³) / (3x).

(Total for Question 10 is 2 marks)

Simplify (2a³ * a²) / a.

(Total for Question 11 is 2 marks)

Simplify (x⁴ * x^-2) / x.

(Total for Question 12 is 2 marks)

Simplify 2x(3x - 4) - x(x - 5).

(Total for Question 13 is 3 marks)

Given f(t) = 4t² - 3t + 6,

(a)Simplify f(t) - (t² + 2t - 1).(2)

(b)Evaluate your result from part (a) at t = 2.(1)

(Total for Question 14 is 3 marks)

Simplify (1/2)x³ * 4x^-1.

(Total for Question 15 is 2 marks)

Simplify (6x² y^-1) / (2x^-1 y²). Give your answer with positive indices.

(Total for Question 16 is 3 marks)

Mark scheme · 2.6D Simplifying Algebra: Fluency and Exam Drill

Question 1

B1 8x cao
Answer: 8x (cao)

Question 2

B1 9y cao
Answer: 9y (cao)

Question 3

B1 2a + 7 cao
Answer: 2a + 7 (cao)

Question 4

B1 6x + 6 cao
Answer: 6x + 6 (cao)

Question 5

M1 correct multiplication of both terms, e.g. 2*3x and 2*4 shown
A1 6x + 8 cao
Answer: 6x + 8 (cao)

Question 6

M1 multiply each term by -3, e.g. -3*2y and -3*(-5) shown
A1 -6y + 15 cao
Answer: -6y + 15 (cao)

Question 7

M1 multiply coefficients and use index law x¹ * x¹ = x²
A1 6x² cao
Answer: 6x² (cao)

Question 8

M1 multiply coefficients 4*3 and add indices 2+3
A1 12x⁵ cao
Answer: 12x⁵ (cao)

Question 9

B1 x³ cao (use of index subtraction 5 - 2)
Answer: x³ (cao)

Question 10

M1 divide coefficients 6/3 and subtract indices 3 - 1
A1 2x² cao
Answer: 2x² (cao)

Question 11

M1 multiply indices for a: 3 + 2 = 5 then divide by a (subtract 1)
A1 2a⁴ cao
Answer: 2a⁴ (cao)

Question 12

M1 use index laws: x⁴ * x^-2 = x^{4 + (-2)} = x², then divide by x (subtract 1)
A1 x cao
Answer: x (cao)

Question 13

M1 expand 2x(3x - 4) to 6x² - 8x
M1 expand x(x - 5) to x² - 5x and subtract from previous expression
A1 5x² - 3x cao
Answer: 5x² - 3x (cao)

Question 14

(a) M1 subtract like terms: 4t² - t² and -3t - 2t and 6 - (-1)
(a) A1 3t² - 5t + 7 cao
(a) Answer: 3t² - 5t + 7 (cao)
(b) B1 9 cao
(b) Answer: 9 (cao)

Question 15

M1 multiply coefficients (1/2)*4 = 2 and add indices 3 + (-1) = 2
A1 2x² cao
Answer: 2x² (cao)

Question 16

M1 divide coefficients 6/2 = 3 and subtract indices: x^{2 - (-1)} and y^{-1 - 2}
M1 obtain 3x³ y^-3 (showing correct indices)
A1 3x³ / y³ cao
Answer: 3x³ / y³ (cao)

Simplifying Algebra: Fluency and Exam Drill - Worksheets, Questions and Revision