Download Chapter 9 Exercise 9.1

Chapter 9 Exercise 9.1
Q. 1.
(i) 25
(ix) (−1)6
(ii) 8
= 16 (even power)
(iii) 9
= 16
(iv) −343
Q. 3. −(−4)7 = (4)7?
(v) 1
= −(−47)
(vi) 1
Q. 2.
= 47
(i) 43
=
(odd power)
(i) (7.8)3
Q. 4.
(22)3
= 474.55
= 26
= 220 (even power)
6.55
(ii) ____2
2.3
= 2,193.37
= 220
(iii) (2.53)5
(ii) (−2)20
= 931,322.57
(iii) 619
(iv) 12.450
(iv) (−3)3
=1
= −33 (odd power)
(v) 2.53 × 3.84
(v) (−5)12
= 3,258.03
= 512 (even power)
(vi) ((5.1)2)3 × (2.8)2
(vi) −(−1)100
= 137,954.9
= −(1100)
(6.2)2
(vii) _____3
(5.8)
= 0.2
= −1100
(vii) −(7)3
= −73
(viii) (2.4)3 × (3.7)2 × (5.2)5
(viii) −(−11)3
= −(−113)
= 719,538.26
(odd power)
= 113
Q. 5.
Index notation
2
22
23
24
25
26
27
Whole number
2
4
8
16
32
64
128
Index notation
3
32
33
34
35
36
Whole number
3
9
27
81
Index notation
4
42
43
44
45
46
Whole number
4
16
64
246
1,024
4,096
Index notation
9
92
93
94
95
96
Whole number
9
81
729
6,561
59,049
531,441
243 729
Active Maths 2 (Strands 1–5): Ch 9 Solutions
1
(a) x = 2
or
x=4
y=1
y=2
(b) x = 1
or
x=2
y=2
or
x=3
y=1
or
x=2
y=1
Q. 7.
or
x=3
y=6
or
y=2
(d) x = 1
x=6
y=3
y=4
(c) x = 1
Q. 6.
or
x=5
or
x=7
y=3
or
y=2
y=4
x=3
y=3
(i) 55
(iv) 48
(ii) 810
(v) 221
(ii) 26
(iii) 63
(vi) 37
(iii) 103
Q. 8.
(iv) 77
(i) (−5)10
(v) 106
= 510 (even power)
(vi) 8−6
(ii) (−2)9
= −29 (odd power)
Q. 9.
(iii) (−3)7
(iii) 1025
(iv) (−5)5
(iv) 430
= −55 (odd power)
(v) 742
(v) (−7)8
=
(i) 315
(ii) 620
= −37 (odd power)
78
(i) 31
(vi) 536
(even power)
(vi) (−4)5
= −45 (odd power)
Q. 10.
Index notation
5
52
Whole number
5
25
53
54
125 625
55
56
3,125
15,625
(v) 253 × 6255
(i) 25 × 125
(iii) 625 × 25
= 52 × 53
= 54 × 52
= (52)3 × (54)5
= 55
= 56
= 56 × 520
= 526
(ii) 3,125 × 15,625
2
(iv) (15,625)11
= 55 × 56
= (56)11
= 511
= 566
Active Maths 2 (Strands 1–5): Ch 9 Solutions
(15,625)4
(vi) _________
(125)3
(56)4
= ____
(53)3
524
= ___
59
= 515
Q. 11.
(i) 26
Q. 2.
( )
(ii) 43
(iii) 641
1
= 6 __3
4
6
= ___
64
3
= ___
32
1
__
(iv) 4,0962
There are only 4 other ways.
(ii) 2(7−2)
Exercise 9.2
Q. 1.
(i)
( )
1
= 2 __2
7
2
= ___
49
3−3
1
= __3
3
1
___
=
27
(ii)
(iii) 6(3−2)
( )
1
= 6 __2
3
6
= __
9
2
= __
3
5−2
1
= __2
5
1
___
=
25
(iv) 5(2−4)
(iii) 9−2
( )
1
= 5 __4
2
5
= ___
16
1
= __2
9
1
___
=
81
(v) 2(8−2)
(iv) 7−3
( )
1
= 2 __2
8
2
= ___
64
1
= ___
32
1
= __3
7
1
____
=
343
(v) 4−1
1
= __1
4
1
__
=
4
(vi) 3(6−2)
( )
1
= 3 __2
6
3
= ___
36
1
= ___
12
(vi) 2−5
1
= __5
2
1
___
=
32
(i) 6(4−3)
Q. 3.
____
(i) √ 100
= 10
____
(ii) √ 144
= 12
Active Maths 2 (Strands 1–5): Ch 9 Solutions
3
3
___
(iii) √ 27
(vii)
√ 1,000
=3
= 10
4
___
___
(viii) √ 81
=2
=3
5
6
___
=2
10
___
(ix) √ 64
(v) √ 32
=2
__
3
____
(x) √ 125
(vi) √ 1
=1
=5
x
1
2
3
4
5
6
7
8
9
10
x2
1
4
9
16
25
36
49
64
81
100
x
1
4
9
16
25
36
49
64
81
100
√x
1
2
3
4
5
6
7
8
9
10
x
1
2
3
4
5
6
7
8
9
10
x3
1
8
27
64
125
216
343
512
729
1,000
x
1
8
27
64
125
216
343
512
729
1,000
1
2
3
4
5
6
7
8
9
10
__
Q. 5.
3
__
√x
Q. 6.
______
4
(iv) √ 16
Q. 4.
3
1
__
(i) 1002
____
= √ 100
= 10
1
__
1
__
(vi) 83
3
__
= √8
=2
1
__
(ii) 64 2
___
= √ 64
=8
(vii) 92
__
= √9
=3
1
__
(iii) 216 3
____
3
= √ 216
=6
(iv) 5123
____
= √ 512
=8
______
√ 1,000
1
__
(ix) 643
3
___
= √ 64
1
__
___
= √ 16
=4
4
3
=4
1
__
(v) 162
=
= 10
1
__
3
1
__
(viii) 1,0003
Active Maths 2 (Strands 1–5): Ch 9 Solutions
(x) 362
___
= √ 36
=6
Q. 7.
1
__
(i) 164
Q. 8.
___
4
1
= _______1
1002
= √ 16
=2
1
____
= _____
√ 100
2
__
(ii) 273
(
___
3
= √ 27
)
2
1
= ___
10
=9
1
– __
2
(ii) 36
2
__
(iii) 643
(
___
3
= √ 64
1
= ______1
362
)
2
= 16
1
___
= ____
√ 36
3
__
(iv) 164
(
___
4
= √ 16
1
= __
6
)
3
=8
1
− __
4
(iii) 16
3
__
(v) 1002
____
= ( √ 100 )
3
= 1,000
2
__
(vi) 1253
(
3
____
= √ 125
= 25
4
___
= √ 16
)
5
= 32
3
__
(viii) 814
(
4
___
= √ 81
)
3
= 27
__
( )
2
3
4
__
___
= √ 64
1
= _____3
92
1__
= _____
3
( √9 )
1
= ___
27
3
−__
4
(v) 81
(
(x) 643
3
3
−__
2
1
= ______
4 ___ 3
√ 81
= 27
(
2
1
= ____
4 ___
√ 16
1
= __
2
1
= ______3
814
3
__
(ix) 92
= √9
)
1
= ______1
164
(iv) 9
5
__
(vii) 164
(
1
– __
2
(i) 100
)
4
)
1
= ___
27
= 256
Active Maths 2 (Strands 1–5): Ch 9 Solutions
5
2
− __
3
(vi) 8
Q. 9.
= 54 × 44
1
= _____2
83
=
(i) 204 = (5 × 4)4
(ii) 156 = (3 × 5)6
= 36 × 56
1
_____
__
1
__
( √8 )
3
2
1
__
1
= __
4
(vii)
1
__
1
___
5
__
Q. 10.
()
68
6
(i) __8 = __
8
8
243
(ix)
( )
1
__
1
_______
____
(iii)
( √ 125 )
2
9
( )
182
____
18
= ___
32
1
__
322
( )
9
= ___
16
5
− __
16 4
75 2
_______
1
= ______
4 ___ 5
√ 16
)
Q. 11.
1
= ___
32
( )
1
(i) ( )
4
1
__
__ 2
1
= __
2
5
− __
2
( )
1
(ii) ___
25
1
= _______5
1002
1
_______
____
( √ 100 )
5
1
= ________
100,000
Active Maths 2 (Strands 1–5): Ch 9 Solutions
1
__
2
1
___
= ____
√ 25
1
= __
5
( )
75
= ____
192
1
− __
2
1__
= ___
√4
(x) 100
=
1
− __
2
192
25
= ___
64
2
2
1
− __
(iv)
1
__
1
__
1
= ___
25
(
9
()
3
= __
5
1
= ______5
164
6
8
99
9
(ii) ____9 = ___
15
15
1
= _______2
1253
3
8
()
3
= __
4
1
____
2
− __
125 3
=
1
__
= 83 . 273
1__
= _____
5
( √9 )
(viii)
1
__
1
__
(iv) 2162 = (8 × 27)3
92
=
1
__
= 92 . 42
5
− __
9 2
=
1
__
(iii) 362 = (9 × 4)2
1
−__
2
( )
()
4 __1
(iii) __ 2
9 __
4
√__
= ___
√9
4
(ii) ____
121
1__
= ______
4
√____
_____
√ 121
2
= __
3
( )
11
= ___
2
1
__
81
(iv) ___
25
2
( )
81 __
√___
9
= ____
=
5
√ 25
( )
1
= ______
3 __
√8
______
1
__
3
√ 125
5
= __
2
√8
____
= 3 ___
√ 27
2
= __
3
( )
(
27
(iv) ______
1,000
3
(
3
3
(
(
( )
4
___
1
= _______
3 ____ 2
√ 125
_______
(
)
)
3
√ 16
= ______
4 ___ 3
√ 81
8
= ___
27
( )
27
(viii) ___
64
(
(
()
4
(vi) __
9
)
)
2
__
( √9 )
9
= ___
16
( )
36
(i) ___
25
1
−__
2
1
___
= ____
36
√___
____
√ 25
5
= __
6
3
−__
2
1__
= _____
3
( √4 )
_____
√ 27
= ______
3 ___ 2
√ 64
Q. 12.
( √ 27 )
)
2
9
= ___
25
3
___
___
3
2
__
3
2
−__
3
125
(v) ____
27
3
__
4
2
100
= ____
9
2
= __
5
( )
)
______
( √ 1,000 )
__
√8
= ______
3 ____
√ 125
16
(vii) ___
81
)
2
−__
3
1
= _________
3 ___ 2
√ 27
_________
1
__
8
(vi) ____
125
____
3
__
3
1
−__
3
8
(iii) ____
125
___
8
(v) ___
27
1
– __
2
3
27
= ___
8
Q. 13.
(i) 4.36
(vi) 11.51
(ii) 57.19
(vii) 0.04
(iii) 1.9
(viii) 2.02
(iv) 15.61
(ix) 2.15
(v) 0.02
(x) 4.18
Active Maths 2 (Strands 1–5): Ch 9 Solutions
7
Q. 14.
(i) 24 = 2 × 2 × 2 × 3
(iii) 3 × 23 = 69
= 23 . 3
(ii)
(24)3
=
(23
Reason: The prime factorisation
of a square number must have
prime factors with even powers.
3)3
.
= (23)3 . 33
= 29 . 33
Q. 15.
Q. 18.
(ii) 23
282012
(iii) 24
28 = 2 × 2 × 7
(iv) 25
28 = 22 × 7
(v) 2−1
282012 = (22 . 7)2012
(vi) 2−2
= (22)2012 . 72012
=
Q. 16.
24024
.
1
__
(vii) 22
72012
1
__
(viii) 23
100 = 2 × 2 × 5 × 5
1
−__
2
(ix) 2
= 22 . 52
100 = 22 . 52
1001601 = (22 . 52)1601
Q. 17.
=
(22)1601
=
23202
.
.
Q. 19.
(iii) 33
53202
(iv) 34
(v) 3−1
(vi) 3−2
12 = 2 × 2 × 3
1
__
(vii) 32
122 = (22 × 3)2 = 24 . 32
2,500 =
3
__
(viii) 32
502
1
−__
2
(ix) 3
50 = 2 × 5 × 5
50 = 2 × 52
502
= (2 ×
22
52)2
Q. 20.
(i) 52
(ii) 53
. 54
(iii) 5−1
11,025 = 1052
(iv) 50
105 = 5 × 3 × 7
(v) 5−2
1052 = (3 × 5 × 7)2
(vi) 5−3
1052 = 32 . 52 . 72
(vii) 52
1,002,001 = 1,0012
(viii) 55
1
__
1
__
1
−__
2
1,001 = 7 × 11 × 13
(ix) 5
(1,001)2 = (7 × 11 × 13)2
(x) 5−1
(1,001)2 = 72 . 112 . 132
(ii) even
8
(i) 30
(ii) 32
(52)1601
(i) 144 = 122
=
(i) 22
Q. 21.
Active Maths 2 (Strands 1–5): Ch 9 Solutions
(i) 102
(iv) 104
(ii) 103
(v) 10−1
(iii) 10−2
(vi) 10−4
1
__
(vii) 102
Q. 2.
(32)x = 34
(viii) 102.5
(ix)
(x)
32x = 34
1
−__
10 2
2x = 4
1
__
106
x=2
3
__
(ii) 4x = 82
(xi) 102
(22)x = (23)2
(xii) 101.5
22x = 26
Exercise 9.3
Q. 1.
(i) 2x = 4
2x = 22
x=2
(ii)
3x
= 27
3x
33
=
x=3
(iii)
5x
= 125
5x
53
=
x=3
(iv) 10x = 1,000
10x
=
103
x=3
(v)
4x
= 64
4x = 43
x=3
(vi)
3x
= 81
3x
34
=
x=4
(vii)
(i) 9x = 34
10x
= 10,000
10x
104
=
x=4
(viii) 6x = 216
6x = 63
x=3
(ix) 7x = 49
7x = 72
x=2
2x = 6
x=3
(iii) 5x = 252
5x = (52)2
5x = 54
x=4
(iv) 10x = 1003
10x = (102)3
10x = 106
x=6
(v) 11x = 1215
11x = (112)5
11x = 1110
x = 10
(vi) 2x = 165
2x = (24)5
2x = 220
x = 20
(vii) 42x = 83
(22)2x = (23)3
24x = 29
4x = 9
9
x = __
4
(viii) 33x = 272
33x = (33)2
3x = 6
x=2
(x) 3x = 729
3x = 36
x=6
Active Maths 2 (Strands 1–5): Ch 9 Solutions
9
2
1__
(ix) 45x = 85
(22)5x = (23)5
210x = 215
10x = 15
x=
(x)
a2x
a2x
(vii) 102x − 1 =
3
__
2
=
=
a6
102x − 1
__
101
1
2x = 1__
2
3
x = __
4
1
__
1
7__
2
2x = 2
__
1
x = 7__
2
27
(ii) 2x = __
4
27
__
x
2 = 2
2
x
2 = 25
x=5
125
__
(iii) 5x = ____
√5
53
5x = _____1
52
x
5 = 52.5
x = 2.5
(viii) 4x =
22x
2
=
=
25 . 22
______
2
24.5
2x = 4.5
1
x = 2__
4
49
__
(ix) 49x = ___
√7
72
72x = _____1
72
72x = 71.5
9__
___
2x = 1.5
√3
3
x = __
4
216
__
(x) 36x + 2 = ____
√6
1
1__
3 2
1
x + 1 = 1__
2
1
x = __
2
63
(62)x + 2 = _____1
62
___
√ 10
(v) 10x − 3 = ____
100
1
__
10x − 3 =
32√ 2
_____
1
__
22x
32
3x + 1 = _____1
32
=
102
____
1
2x − 1 = __
2
2x = 27 . 22
102
____
102
10x − 3 = 10−1.5
x = 1.5
10
10
1
__
(i) 2x = 27√ 2
3x + 1
3
102x − 1 = 102
x=3
(iv) 3x + 1 =
=
Active Maths 2 (Strands 1–5): Ch 9 Solutions
62x + 4 = 62.5
2x + 4 = 2.5
2x = −1.5
3
x = −__
4
1
__
( 10 )2
______
3
__
(a2)3
2x = 6
Q. 3.
(vi) 7x = 7 3
2
x = 1__
3
Q. 4.
(i) 24
Q. 6.
(ii) 23
3
__
(iii) 22
16
24
__ = ___
(iv) ___
√ 8 2__32
= 22.5
22x − 1
=
2+n=4
n=2
(√ )
16
___
__
3
8
Q. 7.
2x − 1 = 7.5
32
_____
31 − n
71 + x
71 + x
x = 4.25
31 − n
72 × 49x
________
72 × 72x
________
2x = 8.5
9
_____
= 625
5n + 1
53 × 52n
________
= 54
5n + 1
53 + 2n − n − 1 = 54
22x − 1 = (22.5)3
Q. 5.
125 × 52n
_________
= 343
= 73
72 + 2x − 1 − x = 73
x+1=3
= 81
x=4
= 34
31 + n = 34
n=3
Q. 8.
p − q = 96
p + q = 160
Q. 9.
2p
= 256
q = 160 − p
p
= 128
q = 32
2x = p
2y = q
2x = 128
2y = 32
2x = 27
2y = 25
x=7
y=5
Let 3x = m and 3y = n
5m − 2n = 387
– 5m + 4n = – 369
–
2n = 18
5m = 387 + 2(9)
5m = 405
m = 81
n=9
3y
=9
∴y=2
x = 4 and y = 2
Q. 10.
3x = 81
∴x=4
______
√ y − 5 = 5 ⇒ y = 30
2x = 8 ⇒ x = 3
x + y = 30 + 3
= 33
Active Maths 2 (Strands 1–5): Ch 9 Solutions
11
Q. 11.
67 + 45 = 280,960
Q. 12.
244 + √ 144 = √ 244 + 12 =
√____
____________
____
∴5−x=2
x=3
_________
( )( )
1
__
√ 256 = 16 = 24
Q. 13.
(3)(3) = 35 − x
3 75
5 25
5 5
1
32 = 35 − x
∴5−x=2
x=3
Q. 15.
75 = 3 × 52
.
5x
52 + x
=
56
1
2__
2
22x − 1 = 2
3
1
7__
2
22x − 1 = 2
x=4
1
∴ 2x − 1 = 7__
2
1
2x = 8__
2
1
x = 4__
4
( )( )
1
__
(i) 83 42 = 25 − x
(2)(2) = 25 − x
22 = 25 − x
Q. 16.
3
( )
= 56
1
__
1
1__
2
24
22x − 1 = ______1
1
2 2
∴2+x=6
Q. 14.
__
16 = 24, 2√ 2 = 2
( )
56
= ______2
3
3×5
5x
__
52
1
__
(ii) 273 92 = 35 − x
22 − 2
23 − 22
24 − 23
25 − 24
26 − 25
27 − 26
2
22
23
24
25
26
2p + 1 − 2p = 2p
Q. 17.
212
___
24
2x
(vi) 2.0 × 10−2
= 2x
=
(vii) 1.5 × 10−3
28
(viii) 1.67 × 10−4
∴x=8
Q. 18.
216
___
23
(ix) 6.12 × 10−3
(x) 2.3 × 10−5
= 2y − 1
2y − 1 = 213
Q. 2.
∴ y − 1 = 13
y = 14
Exercise 9.4
Q. 1.
12
(i) 400,000
(ii) 16,000,000
(iii) 5,400
(iv) 8,200,000
(v) 940
(i) 5.3 × 103
(vi) 0.0019
(ii) 1.75 × 105
(vii) 0.000236
(iii) 2.4 × 104
(viii) 0.026
(iv) 2.35 × 108
(ix) 0.56
(v) 7.376 × 106
(x) 0.00000506
Active Maths 2 (Strands 1–5): Ch 9 Solutions
Q. 3.
(i) 6.2 × 103
(ii) 520 × 102 − 3.8 × 102 = 516.2 × 102
= 5.162 × 104
(iii) 14.688 × 108 = 1.4688 × 109
(iv) 1.344 × 1011
Q. 4.
(i) 3.6 × 10−5
(ii) 5.613 ×
Q. 6.
= (2.9 × 108)(480)
(iii) 3.45 × 10−2
= 1.392 × 1011 m
(iv) 6.3 × 10−4
= 1.392 × 108 km
(v) 7.8 × 10−3
(vi) 4.04 ×
Q. 5.
Distance = speed × time
10−4
Q. 7.
10−2
1010 angstroms = 1 m
1
1 angstrom = ____
m
1010
= 10−10 m
(i) 4
(ii) 5
1.6 angstroms = 1.6 × 10−10 m
(iii) 3
(i) 3.66 × 104 m
Q. 8.
(iv) 3
(ii) 3.68 × 107 m2
(v) 2
(vi) 3
Q. 9.
1.36 × 108
__________
32,000
= 4.25 × 103 images
Q. 10.
3.8 × 103 × 2.6 × 102 = 988,000 litres
Q. 11.
(i) 140 million = 1.4 × 108
1.4 × 108
(ii) _________ = 1.94 × 106
72
Q. 12.
(i) 5.6 × 108 + 7.4 × 108 = 13 × 108
109
Q. 13.
= 1.3 × 109
1.3 ×
(ii) _________9 × 100 = 19.4%
6.7 × 10
(i) Difference = 1.21 × 105 − 1.21 × 104
= 108,900 km
(ii) Equator (Venus) = 2p (1.21 × 104)
Equator (Saturn) = 2p (1.21 × 105)
Difference = 2p [1.21 × 105 − 1.21 × 104] ≈ 6.8 × 105
= 6 orders of magnitude
(iii) Yes, it is 2π times the difference in orders of magnitude between both radii.
1
Q. 14. Width of gold leaf = __________ = 1.0 × 10−8 m
10,000,000
Width of an atom of gold = 0.26 × 10−9 m
Active Maths 2 (Strands 1–5): Ch 9 Solutions
13
1.0 × 10−8
Number of atoms thick = ___________
0.26 × 10−9
≈ 38 atoms
Q. 15.
(i) 1.0 × 10−9 seconds
1
(ii) ____________
= 333,333,333 calculations
3(1.0 × 10−9)
Q. 16.
(i) Jupiter
(ii) Saturn
(iii) 1.906 × 1027 kg
(iv) 1.894 × 1027 kg
(v) 5 – 4 = 1 order of magnitude
Revision Exercises
Q. 1.
Q. 2.
Q. 5.
__
(i) 711
(22)5 ___
210
(ii) ____
= 3
3
2
2
7
=2
32
3x = _____1
32
1
1__
2
3x = 3
(iv) 117
1
∴ x = 1__
2
(i) 5−4
1
__
Q. 6.
3
__
(iii) 175
(iv)
42
___
5
__
=
(ii) (811)2 = 822
(iii) (24)6 = 224
Q. 4.
=
435
Q. 7.
(iii)
1
−__
2
(i) 64
1
1
= ______1 = __
8
642
=
1
__
3
__
p2
16
___
(iv) (p16)5 = p 5
27
22x + 1 = _____1
22
1
6__
2
22x + 1 = 2
1
∴ 2x + 1 = 6__
2
1
__
2x = 5
2
11
x = ___
4
14
1
__
(ii) 128 = 27, √ 2 = 22
(ii) p20
p4
(3 × 2)2011 × 22011
__
(i) p9
6
__
2011
24024
= _____
24022
= 22
(i) (610)2 = 620
(iv)
2 2012
(2 )
×3
_________________
24024 × 32011
= ___________________
2011
3
× 22011 × 22011
1
– __
4 2
42
(45)7
1
__
(ii) 9 = 32, √ 3 = 32
(iii) 210
(ii) 126
Q. 3.
(i) 5
Active Maths 2 (Strands 1–5): Ch 9 Solutions
Q. 8.
x+y=0
∴ y = −x
x2012
_____
y2012
x2012
+ 100 = _______
+ 100
(−x)2012
x2012
= _____
+ 100
x2012
= 1 + 100
= 101
Q. 9.
5x + 4y = 5 × 4 × 10−5 + 4 × 6 × 10−7
= 20 × 10−5 + 24 × 10−7
= 2000 × 10−7 + 24 × 10−7
= 2024 × 10−7
= 2.024 × 10−4
Q. 10.
googol2 = (10100)2 = 10200
(i) 100 × googol = 100 × 10100 = 10102
3 × googol = 3 × 10100
googol = 10100
googol3 = (10100)3 = 10300
In order of increasing magnitude
googol, 3 × googol, 100 × googol, googol2, googol3
(ii) googol3
(iii) 100 orders of magnitude
(iv) googol2 and googol3
Q. 11.
n2 − 5n + 5 = 1
∴ n2 − 5n + 4 = 0
n2 + 2n − 24 = 0
n2 − 5n + 5 = −1
(n − 4)(n − 1) = 0
(n + 6)(n − 4) = 0
n2 − 5n + 6 = 0
n = 1 or n = 4
n = −6 or n = 4
(n − 3)(n − 2) = 0
n = 3 or n = −2
If n = 3, then
n2 + 2n − 24 is odd
Therefore, n = 3 is not a solution.
If n = −2
n2 + 2n − 24 is even
Therefore, n = −2 is a solution.
Solutions: n = −6 or n = −2 or n = 1 or n = 4
Active Maths 2 (Strands 1–5): Ch 9 Solutions
15
Q. 12.
(i) a4 + a4 + a4 + a4 = 4a4
24 + 24 + 24 + 24 = 4(24)
= 22 (24) = 26
1
__
1
__
1
__
1
__
( )
1
__
(ii) 24 + 24 + 24 + 24 = 4 24
( )
1
__
= 22 24
9
__
= 24
(iii) 3a5 + 6a5 = 9a5
3(35) + 6(35) = 9(35) = 32 (35) = 37
(iv) 27(38) = 33 (38) = 311
Q. 13.
3 × 104 + 5 × 104 = 8 × 104
Joe is correct.
Q. 14.
3
−__
4
1
1
1
1
= ______3 = _____3 = __3 = __
1
__
8
2
164
164
16
−
64
2
−__
3
( )
1
__
1
1
= ______1 = __
8
642
2
1
1
1
= _____2 = _____2 = __
1
__
4
83
83
8
2
__
−
∴8
Q. 15.
3
( )
is the odd one out.
Mach 3 = 3708 km/hr
= 61.8 km/min
In 5 minutes the plane would travel 61.8 × 5 = 309 km.
Q. 16.
(i) % through Dublin: 18.7/22.7 × 100 = 8.24 × 101 %
(ii) 15.6 × 18.7 million = 291,720,000 kg
(iii) 97% = 2,400,000
100% = 2.474 × 106
Q. 17.
3.9 × 1020 is 20 orders of magnitude
5.9 × 1012 is 13 orders of magnitude
Therefore, the radii differ by 7 orders of magnitude.
Q. 18.
Number of light years: 4.047 × 1013 ÷ 9.5 × 1012
= 4.26 light years
Q. 19.
16
803,000
___________
0.00000525
= 1.53 × 1011 bits/sec
Active Maths 2 (Strands 1–5): Ch 9 Solutions