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)251/2(1)
(b)81/3(1)
(c)811/4(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)2x = 32(2)
(b)3x+1 = 81(2)
(Total for Question 12 is 4 marks)
13
Answer each of the following.
(a)Given that 2a x 25 = 212, work out the value of a.(2)
(b)Given that (3b)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)82/3(2)
(b)43/2(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 (4n3/2 x 2n1/2) / (8n-1)
(Total for Question 19 is 3 marks)
20
Answer each of the following.
(a)Solve x2/3 = 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 q2-5 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