Page 11 - 新思维数学活动用书8 样章

1 Integers

9 Here is an equation: x − x = 120
3
a Is x = 5 a solution? Give a reason for your answer.
b Is x = −5 a solution? Give a reason for your answer.
10 a Write 64 as a product of its prime factors.
b Show that 64 is a square number and a cube number.

c Write 729 as a product of prime numbers.
d Show that 729 is both a square number and a cube number.
e Find another integer that is both a square number and a cube number.

11 Look at the following solution of the equation x = 64
6

x = 64
6
so x = 8
3
so x = 2

There is an error in this solution. Write a corrected version.

1.4 Indices

Exercise 1.4 Key words

index
Focus power
1 Write as a single power

a 3 × 3 b 7 × 7 3 c 12 × 12 5 d 15 × 15
2
4
2 Write as a single power
a 6 × 6 3 b 10 × 10 2 c 3 × 3 3 d 14 × 14 4
3
6
5
3
3 a Show that 2 + 2 + 2 + 2 = 2 – 1
4
3
0
1
2
b Can you find a similar expression for 2 + 2 + 2 + 2 + 2 + 2 ?
2
1
3
5
4
0
c Read what Zara says:
3 + 3 + 3 + 3 = 3 − 1
1
0
2
3
4

Is she correct? Give a reason for your answer.
10