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GCSE · Number

4.2 Indices

EDEXCEL 1MA1 · Calculator allowed · about 90 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

1

Work out the value of each of the following.

(a)6²(1)

(b)2⁵(1)

(c)9⁰(1)

(Total for Question 1 is 3 marks)

2

Write each of the following as a single power.

(a)4 x 4 x 4 x 4 x 4(1)

(b)7 x 7 x 7(1)

(c)2 x 2 x 2 x 2 x 2 x 2 x 2(1)

(Total for Question 2 is 3 marks)

3

Simplify each of the following, giving your answer as a single power.

(a)5³ x 5⁴(1)

(b)8⁹ / 8⁶(1)

(c)(3²)⁴(1)

(Total for Question 3 is 3 marks)

4

Simplify each of the following.

(a)a⁵ x a²(1)

(b)b⁹ / b⁴(1)

(c)(c³)³(1)

(Total for Question 4 is 3 marks)

5

Work out the value of each of the following. Give each answer as a fraction or a decimal.

(a)4^-2(1)

(b)10^-3(1)

(c)3^-2(1)

(Total for Question 5 is 3 marks)

6

Work out the value of each of the following.

(a)8⁰(1)

(b)3 x 4⁰(1)

(c)(7⁰)⁵(1)

(Total for Question 6 is 3 marks)

7

Simplify each of the following.

(a)p^-3 x p⁵(2)

(b)q² / q⁵(2)

(Total for Question 7 is 4 marks)

8

Simplify each of the following.

(a)(a³ x a⁵) / a⁴(2)

(b)(2c²)³ x c(2)

(Total for Question 8 is 4 marks)

9

A rectangle has a width of 3² cm and a length of 3⁵ cm.

Diagram NOT accurately drawn

(a)Work out the area of the rectangle, giving your answer as a single power of 3.(2)

(b)A second rectangle has the same area as the rectangle in part (a). Its width is 3³ cm. Work out its length, giving your answer as a single power of 3.(3)

(Total for Question 9 is 5 marks)

10

Work out the value of each of the following.

(a)25^1/2(1)

(b)8^1/3(1)

(c)81^1/4(1)

(Total for Question 10 is 3 marks)

11

Simplify each of the following.

(a)(2x³)²(2)

(b)(5y²)³(2)

(Total for Question 11 is 4 marks)

12

Solve each of the following equations.

(a)2^x = 32(2)

(b)3^x+1 = 81(2)

(Total for Question 12 is 4 marks)

13

Answer each of the following.

(a)Given that 2^a x 2⁵ = 2¹², work out the value of a.(2)

(b)Given that (3^b)² = 3¹⁰, work out the value of b.(2)

(Total for Question 13 is 4 marks)

14

Simplify fully (6x⁵ y³) / (2x² y⁵)

(Total for Question 14 is 4 marks)

15

Which of these is equal to 5^-2 ?

A) 1/25
B) -25
C) 25
D) -1/25

(Total for Question 15 is 1 mark)

16

Show that (3⁴ x 3^-2) / 3 = 3

(Total for Question 16 is 3 marks)

17

Work out the value of each of the following.

(a)8^2/3(2)

(b)4^3/2(2)

(Total for Question 17 is 4 marks)

18

Work out the value of each of the following.

(a)16^-1/2(2)

(b)27^-2/3(2)

(Total for Question 18 is 4 marks)

19

Simplify fully (4n^3/2 x 2n^1/2) / (8n^-1)

(Total for Question 19 is 3 marks)

20

Answer each of the following.

(a)Solve x^2/3 = 25(3)

(b)Simplify fully (27x⁶)^-2/3(4)

(Total for Question 20 is 7 marks)

Mark scheme · 4.2 Indices

Question 1

(a) B1 36 cao
(a) Answer: 36
(b) B1 32 cao
(b) Answer: 32
(c) B1 1 cao
(c) Answer: 1

Question 2

(a) B1 4⁵ cao
(a) Answer: 4⁵
(b) B1 7³ cao
(b) Answer: 7³
(c) B1 2⁷ cao
(c) Answer: 2⁷

Question 3

(a) B1 5⁷ cao
(a) Answer: 5⁷
(b) B1 8³ cao
(b) Answer: 8³
(c) B1 3⁸ cao
(c) Answer: 3⁸

Question 4

(a) B1 a⁷ cao
(a) Answer: a⁷
(b) B1 b⁵ cao
(b) Answer: b⁵
(c) B1 c⁹ cao
(c) Answer: c⁹

Question 5

(a) B1 1/16 oe (0.0625)
(a) Answer: 1/16
(b) B1 1/1000 oe (0.001)
(b) Answer: 1/1000
(c) B1 1/9 oe
(c) Answer: 1/9

Question 6

(a) B1 1 cao
(a) Answer: 1
(b) B1 3 cao
(b) Answer: 3
(c) B1 1 cao
(c) Answer: 1

Question 7

(a) M1 p^-3+5 or p² seen
(a) A1 p² cao
(a) Answer: p²
(b) M1 q^2-5 seen
(b) A1 q^-3 oe (1/q³) cao
(b) Answer: q^-3

Question 8

(a) M1 a⁸ seen (numerator combined)
(a) A1 a⁴ cao
(a) Answer: a⁴
(b) M1 8c⁶ seen
(b) A1 8c⁷ cao
(b) Answer: 8c⁷

Question 9

(a) M1 3² x 3⁵ seen (area = width x length)
(a) A1 3⁷ cao
(a) Answer: 3⁷
(b) P1 recognises length = area / width, i.e. 3⁷ / 3³ oe
(b) M1 3^7-3 seen
(b) A1 3⁴ cao
(b) Answer: 3⁴

Question 10

(a) B1 5 cao
(a) Answer: 5
(b) B1 2 cao
(b) Answer: 2
(c) B1 3 cao
(c) Answer: 3

Question 11

(a) M1 2² or x⁶ seen
(a) A1 4x⁶ cao
(a) Answer: 4x⁶
(b) M1 5³ or y⁶ seen
(b) A1 125y⁶ cao
(b) Answer: 125y⁶

Question 12

(a) M1 32 = 2⁵ seen oe
(a) A1 x = 5 cao
(a) Answer: x = 5
(b) M1 81 = 3⁴ seen oe, or x + 1 = 4
(b) A1 x = 3 cao
(b) Answer: x = 3

Question 13

(a) M1 a + 5 = 12 oe
(a) A1 a = 7 cao
(a) Answer: a = 7
(b) M1 2b = 10 oe
(b) A1 b = 5 cao
(b) Answer: b = 5

Question 14

M1 3 seen (coefficient 6/2 simplified)
M1 x³ seen (5-2)
A1 y^-2 oe (1/y²) seen (3-5)
A1 3x³/y² oe cao (fully simplified)
Answer: 3x³/y²

Question 15

B1 A identified, 1/25
Answer: A) 1/25

Question 16

M1 3⁴ x 3^-2 = 3² (or 9) seen
M1 3² / 3 = 3¹ (dependent on first M1)
A1 3 = 3 shown, cso (answer given, all steps correct)
Answer: 3 = 3 (shown)

Question 17

(a) M1 8^1/3 = 2 seen
(a) A1 4 cao
(a) Answer: 4
(b) M1 4^1/2 = 2 seen
(b) A1 8 cao
(b) Answer: 8

Question 18

(a) M1 16^1/2 = 4 seen
(a) A1 1/4 oe cao
(a) Answer: 1/4
(b) M1 27^1/3 = 3 seen, leading to 3² = 9
(b) A1 1/9 oe cao
(b) Answer: 1/9

Question 19

M1 8n² seen (numerator combined: 4x2=8, n^3/2+1/2=n²)
M1 n^2-(-1) seen (dependent on first M1, dividing by n^-1)
A1 n³ cao
Answer: n³

Question 20

(a) M1 x = 25^3/2 oe (raising both sides to the power 3/2)
(a) M1 25^1/2 = 5 seen, leading to 5³
(a) A1 x = 125 cao
(a) Answer: x = 125
(b) M1 x^-4 seen (6 x -2/3)
(b) M1 27^1/3 = 3 seen, leading to 27^2/3 = 9
(b) M1 27^-2/3 = 1/9 (dependent on second M1)
(b) A1 1/(9x⁴) oe cao
(b) Answer: 1/(9x⁴)

Indices - Worksheets, Questions and Revision

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4.2 Indices

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20