Number Sense – AP Book 8, Part 2: Unit 5
11.
a)
i)
page 137
1.
b)
3, 2
c)
7, 4
2.
b)
7×7×7
c)
8×8×8×8
3.
a)
3
3
b)
4
4
c)
9
2
d)
8
4
a)
8
b)
81
c)
16
d)
25
e)
16
f)
125
4.
5.
6
ii)
2
iii)
4
iv) = 4 × 32
= 128
7
=2
2+5=7
iv) 14
b)
i)
6 × 6 × 6 = 216
ii)
4×4×4×4×4
= 1 024
iii)
12.
Circle: c) and e)
v)
6 + 4 = 10
7×7×7×7
= 2 401
b)
3 × 8 = 24
vi) = 32 × 16
= 512
9
=2
c)
16 ÷ 2 = 8
5+4=9
d)
2 × 25 = 50
e)
4 × 9 = 36
f)
9 × 8 = 72
g)
100 ÷ 25 = 4
h)
4 + 9 = 13
i)
49 + 36 = 85
j)
64 ‒ 4 = 60
The answer’s exponent
equals the sum of the
exponents in the question.
3.
INVESTIGATION
A.
i)
ii)
iii)
B.
Yes
6.
a)
7.
8.
9.
10.
8, 9
AP Book NS8-105
243, 125
page 139
100, 1 024
1.
5
c)
8
b)
Gaps:
+2, +4, +8, +16, +32,
+64, +128
13
e)
2 057
a)
3×3×3×3
b)
3×3×3×3×3
c)
3×3×3×3×3×3
d)
5×5×5×5
e)
4×4×4×4×4
f)
8×8×8×8×8×8×8
a)
8 × 8 = 64
b)
3 × 3 × 3 = 27
2.
c)
2 × 2 × 2 × 2 × 2 = 32
4
a)
1
2
b)
1
3
c)
1
4
d)
1
5
a)
1
b)
1
c)
1
d)
1
e)
1
4.
Sequence:
2, 4, 8, 16, 32, 128,
256
d)
V‐32 2, 4, 8, 16, 32
9
c)
8
d)
2
12
5.
or
12
11
11
2 =2 +2
= 2 048 + 2 048
= 4 096
6.
a)
5
6
7
8
9
10
16 32 64 128 256 512 1 024
b)
i)
5
ii)
= 8 × 16
= 128
7
=2
3+4=7
iii)
= 2 × 32
= 64
6
=2
1+5=6
x=8
j)
x=4
k)
x=7
l)
x=2
a)
2 (even number)
b)
5 (ends in 0 or 5)
c)
7 (long division)
d)
3 (sum of digits is
divisible by 3)
b)
3
c)
7
2
3
d)
2
6
c)
3
6
e)
2
8
d)
6
9
f)
5
e)
5
10
g)
7
3
f)
8
9
h)
3
5
g)
7
7
a)
64 = 2 = 4 = 8
h)
4
10
b)
729 = 3 = 9 = 27
11.
=9×9×9
=3×3×3×3×3×3
6
=3
c)
3
8
d)
3
10
e)
3
12
5
1.
2.
16
6
3.
d)
100 000
e)
10 000 000
2
3
f)
100 000 000
b)
10
6
c)
10
7
b)
10 000 000 000
10
= 10
c)
10 000 = 10
d)
100 000 000 = 10
b)
= 3 × 10 000 +
6 × 1 000 +
9 × 100 +
8 × 10 + 2
250
3
7
12
17
20
3,3,3,3 ,3 ,3 ;
given the same base (3),
the larger the exponent,
the larger the number.
a)
2
14
b)
2
15
c)
(2 ) = 2
d)
(2 ) = 2
3
3
2
page 141
3
4
6
AP Book NS8-106
14
3
5
22
5
b)
g)
11
x=4
i)
8
BONUS
=2 ×2
= 2 048 × 2
= 4 096
10.
h)
4
f)
2 =2 ×2
or
9
8
8
2 =2 +2
9.
x=2
b)
BONUS
a)
3
b)
= 64 × 16
= 1 024
10
=2
g)
4 3
12
5 4
20
7
5
4.
4
8
4
4
7.
16 < 4 < 8 < 32
8.
b)
3; 9; 27; 81;
x=4
c)
1; 16; 81;
x=3
d)
1; 8; 27; 64; 125
x=5
e)
x=2
f)
x=3
3
= 3 × 10 + 6 × 10
2
+ 9 × 10 + 8 × 10
+2
c)
= 4 × 1 000 000 +
2 × 10 000 +
5 × 1 000 +
9 × 100 + 1
6
4
= 4 × 10 + 2 × 10
3
2
+ 5 × 10 + 9 × 10
+1
5.
b)
434 519
c)
3 050
d)
905 037
AnswerKeysforAPBook8.2
COPYRIGHT©2011JUMPMATH:NOTTOBECOPIED
AP Book NS8-104
Number Sense – AP Book 8, Part 2: Unit 5
5
(‒ 2)
= (‒ 2)
= ‒ 32
a)
‒ 24
b)
‒6
c)
‒ 22
AP Book NS8-107
d)
30
page 142
e)
10
1.
f)
‒4
3
g)
2
4
h)
9
i)
4
6
j)
‒ 12
7
k)
‒5
l)
4
m)
3
n)
‒ 11
o)
‒ 16
a)
(3 ‒ 5) × 2 = ‒ 4
b)
(2 ‒ 5) × 3 + 4 = ‒ 5
c)
[ 5 + (‒ 2)] × (‒ 3)
= ‒9
6.
900 307
f)
790 000 000
a)
>
b)
<
3.
a)
3
2 =8
(‒ 2) = 16
4
2 = 16
5
2 = 32
(‒ 2) = ‒ 8
5
(‒ 2) = ‒ 32
6
(‒ 2) = 64
2 = 64
7
(‒ 2) = ‒ 128
b)
2 = 128
2, 4, 6
c)
8
d)
(‒ 2) = 2
when n is even.
n
n
n
4.
n
(‒ 2) = ‒ (2 )
when n is odd.
2.
3.
4.
e)
‒ 8 192; 16 384
a)
‒ 1, 1, ‒ 1, 1, ‒ 1, 1
b)
(‒ 1) = ‒ 1 since
973 is odd.
d)
973
7
5
3
1
(‒ 2) , (‒ 2) , (‒ 2) , (‒ 2) ,
2
4
6
(‒ 2) , (‒ 2) , (‒ 2)
a)
b)
f)
(3 ‒ 5) = 4
(‒ 2) + 2 × 4 = 0
(‒ 3) , (‒ 3) , (‒ 3) , (‒
1
2
4
3) , (‒ 3) , (‒ 3) , (‒ 3)
j)
(‒ 2)
6
k)
(2 – 5) = 9
2.
d)
81 + 81 = 162
4
f)
32 ‒ 32 = 0
g)
(‒ 2) = ‒ 8
h)
‒ 5 + 27 = 22
b)
7
c)
d)
3
2÷2
1
(‒ 2)
= ‒8
= (‒ 2)
3
6 ÷ (3 – 1)
= ‒8
4.
2
5
[(‒ 6 ‒ 9) + 7]
2
= (‒ 15 + 7)
2
= (‒ 8)
= 64
3
AnswerKeysforAPBook8.2
6.
a)
2
[ 6 ÷ (‒ 3)] + (‒ 10)
– (‒ 12)
= ‒ 2 – 10 + 12
=0
( [ 2 + (‒ 8)] ÷ 3)
= [ (‒ 6) ÷ 3]
4
= (‒ 2)
= 16
=7 =7
6÷2
a)
4
4
3
2
4
9 → if n = 4x – 2;
3 → if n = 4x – 3.
d)
c)
i)
4
ii)
8
5, 25, 125, 625, 3 125,
15 625;
20
The ones digit of 5 is 5;
This is true of all powers
of 5.
a)
n
e)
i)
3
14
ii)
3
18
iii)
3
98
Since 1000 is a
multiple of 4, the
ones digit is 1.
BONUS
Students can predict the
ones digit of the sum by
adding the ones digits of
the individual addends:
17
2 → ones digit = 2
17
3 → ones digit = 3
2, 4, 8, 16, 32, 64,
128, 256
2, 4, 8, 6, repeat
10
7 → if n = 4x – 1;
3
b)
3
5
0 =0
20 000 000;
follow the pattern
or notice that:
8
7
7
7
2 × 5 = 2 (2 × 5 )
7
= 2 (10 )
[(‒ 2) × (‒ 3)] ‒ 7 + 4
c)
e)
c)
a)
4
0 =0
2 ×5;2 ×5;
5
4
6
5
2 ×5;2 ×5
3
3
c)
b)
‒ 4 + (3 ‒ 2) = ‒ 3
2 =8
(‒ 2) = 16
200; 2 000;
20 000; 200 000
6
1 → if n = 4x (i.e.,
a multiple of 4);
Subtract 9 from 7.
Divide by 2.
Raise the result to
the third power.
a)
l)
b)
b)
3.
3
=6‒7+4
=3
page 143
a)
2 ÷ (4 ‒ 8) = ‒ 2
[(‒ 2) + 2] × 4 = ‒ 24
5.
Multiply ‒ 2 and ‒ 5.
Add 3.
Multiply by 4.
2
3
i)
‒ 2 187, ‒ 243, ‒ 27,
‒ 3, 9, 81, 729
2.
(2 ‒ 5) × (3 + 4)
= ‒ 21
2 – 5 × (3 + 4) = ‒ 33
AP Book NS8-108
1.
1.
h)
3
c)
2
3,3,3 ;
n
the nth exponent (3 )
will have a ones digit
of:
c)
page 144
Solution:
5
Subtract 3 from 5.
Multiply by 3.
Add ‒ 2.
AP Book NS8-109
e)
g)
b)
d)
Teacher to check
student predictions.
7
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4+1
d)
e)
(continued)
17
34
4 = 2 → ones digit = 4
17
5 → ones digit = 5
Since 2 + 3 + 4 + 5 = 14,
the ones digit of this sum
will be 4.
5.
6.
2
6
2
1
2
8
2
7
2
5
2
3
2
2
2
9
2
4
a)
i)
30
ii)
9
iii)
2
=
1s digit
4
81
1
3
5
243
3
3
6
729
9
3
7
2 187
7
3
8
6 561
1
3
9
19 683
3
Answers may vary –
teacher to check.
3
10
59 049
9
i)
3 ×3
3
11
177 147
7
ii)
3 ‒3
3
12
531 441
1
iii)
3 × (3 + 3)
b)
3, 9 , 7, 1, repeat
iv) 35 937
v)
729
vi) 3
b)
3
3
iv) 3 × 3 × 3
v)
3 × (3 ‒ 3)
Add 6 and ‒ 8.
Multiply by 3.
V‐33
Number Sense – AP Book 8, Part 2: Unit 5
(continued)
AP Book NS8-110
page 145
1.
b)
Teacher to check
marks.
8
8
10 ; 10
2.
3.
4.
Teacher to check marks.
a)
E, B, F, C, D, A, G
b)
G, A, D, C, F, B, E
c)
The lists are the
reverse of each
other.
Teacher to check number
line and marks.
A ‒ 2.8
4
B 5
2
C ‒5
3
D ‒4
a)
1
0.032, 8 , 0.134
b)
14
3
‒ 5 , ‒ 2 4 , ‒ 2.715
c)
1
‒ 9.126, ‒ 9 8 , ‒ 0.2,
1
0.3, 7 2 , 7.56
d)
1
1
‒ 3 3 , ‒ 3.257, ‒ 3 4 ,
1
1
COPYRIGHT©2011JUMPMATH:NOTTOBECOPIED
3 4 , 3.257, 3 3
V‐34 AnswerKeysforAPBook8.2