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GCSE · Number

1.9D Powers and Roots: Fluency and Exam Drill

EDEXCEL Edexcel 1MA1 · Calculator allowed · about 40 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Work out 9².

(Total for Question 1 is 1 mark)

Work out 4³.

(Total for Question 2 is 1 mark)

Work out √121.

(Total for Question 3 is 1 mark)

Work out the cube root of 27.

(Total for Question 4 is 1 mark)

Write 5 x 5 x 5 in index form.

(Total for Question 5 is 1 mark)

Work out 2⁵.

(Total for Question 6 is 1 mark)

Simplify 3² x 3³.

(Total for Question 7 is 2 marks)

Simplify (10²) / (10⁴). Give your answer in ordinary number form.

(Total for Question 8 is 2 marks)

Work out 2⁰.

(Total for Question 9 is 1 mark)

Which two consecutive integers does √7 lie between?

(Total for Question 10 is 1 mark)

Which two consecutive integers does the cube root of 50 lie between?

(Total for Question 11 is 1 mark)

Simplify √180 giving your answer in simplest form.

(Total for Question 12 is 2 marks)

Write 0.0004 in index form (standard form with a power of 10).

(Total for Question 13 is 2 marks)

Simplify (4²)³ and give your answer as an ordinary number.

(Total for Question 14 is 2 marks)

Show that √3⁵ = 3^5/2.

(Total for Question 15 is 2 marks)

Solve 2^x = 32. Give the value of x.

(Total for Question 16 is 2 marks)

The area of a square is 256 cm². Work out the length of one side in cm.

(Total for Question 17 is 2 marks)

Express cube root(54) in simplest form.

(Total for Question 18 is 2 marks)

Mark scheme · 1.9D Powers and Roots: Fluency and Exam Drill

Question 1

B1 81 cao
Answer:81
(9 times 9 = 81).

Question 2

B1 64 cao
Answer:64
(4 x 4 x 4 = 64).

Question 3

B1 11 cao
Answer:11
(√121 = 11).

Question 4

B1 3 cao
Answer:3
(3³ = 27).

Question 5

B1 5³ cao
Answer: 5³

Question 6

B1 32 cao
Answer:32
(2⁵ = 32).

Question 7

M1 use index law: add powers (3² x 3³ = 3²⁺³)
A1 243 cao
Answer:243
(3²⁺³ = 3⁵ = 243).

Question 8

M1 use index law: subtract powers to get 10^2-4 = 10^-2
A1 0.01 cao
Answer:0.01
(10^-2 = 0.01).

Question 9

B1 1 cao
Answer:1
(any non-zero number to the power 0 equals 1).

Question 10

B1 2 and 3 cao
Answer:Between 2 and 3
(since 2² = 4 and 3² = 9, and 4 < 7 < 9).

Question 11

B1 3 and 4 cao
Answer:Between 3 and 4
(since 3³ = 27 and 4³ = 64, and 27 < 50 < 64).

Question 12

M1 factor 180 as 36 x 5 and take square root of square factor
A1 6 √5 cao
Answer:6 √5
(√180 = √36 x 5 = 6 √5).

Question 13

M1 move decimal point 4 places to write as 4 x 10ⁿ
A1 4 x 10^-4 cao
Answer:4 x 10^-4
(0.0004 = 4 x 10^-4).

Question 14

M1 use index law (a^m)ⁿ = a^mn to get 4^2x3 = 4⁶
A1 4096 cao
Answer:4096
((4²)³ = 4⁶ = 4096).

Question 15

M1 rewrite sqrt as power 1/2: √3⁵ = (3⁵)^1/2
A1 3^5/2 cso
Answer:3^5/2
((3⁵)^1/2 = 3^{5 x 1/2} = 3^5/2).

Question 16

M1 recognise 32 = 2⁵ or use logs to show x = 5
A1 x = 5 cao
Answer:x = 5
(2⁵ = 32).

Question 17

M1 take square root of 256 to find side length
A1 16 cm cao
Answer:16 cm
(side = √256 = 16 cm).

Question 18

M1 factor 54 as 27 x 2 and take cube root of cube factor
A1 3 cube root(2) cao
Answer:3 cube root(2)
(cube root(54) = cube root(27 x 2) = 3 cube root(2)).

Powers and Roots: Fluency and Exam Drill - Worksheets, Questions and Revision