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Homework Sheet – Indices and Standard Form
1.
Work out:
(a) 7 squared
2.
5.
(c) 142
(d)
(c) 5x = 125
(d) 7x = 1
(b) x3 = -8
5
1
 4
2
2
(a) 27 x 22
(b) 35 x 3-2
(c) 4
(e) 75 ÷ 73
(f) 2-3 ÷ 2
(g) 10-3 ÷ 10-2
(h)
(c) (2a2b3)4
(d)
(d)
(23)4
3 4  3 2
35
Simplify fully:
(b) y10 ÷ y6
10c 8
2c 5
Copy and complete the following table. The first row has been completed for you.
Ordinary
Number
3500
1470000
7.
49
Simplify the following. Leave your answers in index form.
(a) x5 × x7
6.
(b) 53
(d) Cube root of 64
Solve the following equations:
(a) x2 = 9
4.
(c) Negative square root of 16
Work out:
(a) (-5)2
3.
(b) 3 cubed
20.2
0.0376
0.00404
Standard
Index Form
3.5 x 103
7.
Copy and complete the following table. The first row has been completed for you.
Standard
Index Form
3.5 x 103
Ordinary
Number
3500
2.7 x 104
1.06 x 107
1.7 x 10-3
2 x 10-5
6.9 x 10-1
8.
Write the following numbers in ascending order:
3.5 x 10-3
9.
P = 1.56 x 103
2.7 x 10
1.3 x 102
Q = 7.8 x 106
Work out:
(a) P + Q
(b) P – Q
(c) P x Q
(d) P ÷ Q
Indices and Standard Form
Q
Answer
Answers and Mark Scheme
Mark
1(a)
49
B1
1(b)
27
B1
1(c)
-4
B1
1(d)
4
B1
2(a)
25
B1
2(b)
125
B1
2(c)
196
B1
2(d)
7
B1
3(a)
x=3
B1
3(b)
x = -2
B1
3(c)
x=3
B1
3(d)
x=0
B1
4(a)
29
B1
4(b)
33
B1
4(c)
43
B1
4(d)
212
B1
4(e)
72
B1
4(f)
2-4
B1
4(g)
10-1
B1
4(h)
3-3
B1
5(a)
x12
B1
5(b)
y4
B1
5(c)
16a8b12
B1
5(d)
5c3
B1
Comments
Q
Answer
Mark
6.
Ordinary Number
Standard Index
Form
3500
3.5 x 103
1470000
1.47 x 106
20.2
2.02 x 10
0.0376
3.76 x 10-2
0.00404
4.04 x 10-3
B1
B1
B1
B1
7.
Standard
Index Form
8.
3.5 x 103
3500
2.7 x 104
27000
1.06 x 107
10600000
1.7 x 10-3
0.0017
2 x 10-5
0.00002
6.9 x 10-1
0.69
3.5 x 10-3
=
2.7 x 10
= 27
1.3 x 102
B1
B1
B1
B1
B1
M1
0.0035
M1
M1
= 130
Order is 3.5 x 10-3
9(a)
Ordinary
Number
2.7 x 10
1.3 x 102
A1
P = 1.56 x 103
=
Q = 7.8 x 106
= 7800000
M1
P+Q
= 7801560
M1
= 7.80156 x 106
A1
1560
Comments
Q
9(b)
9(c)
9(d)
Answer
P = 1.56 x 103 =
Mark
1560
Q = 7.8 x 106 = 7800000
M1
P-Q
= -7798440
M1
= -7.79844 x 106
A1
P x Q = 1.56 x 103 x 7.8 x 106
M1
= 12.168 x 109
M1
= 1.2168 x 1010
A1
P ÷ Q = 1.56 × 103 ÷ 7.8 × 106
M1
= 0.2 × 10-3
M1
= 2 × 10-4
A1
Comments