Chapter 2 Square Square Roots Cubes & Cubes Roots
Transcript of Chapter 2 Square Square Roots Cubes & Cubes Roots
Module PMR
CHAPTER 2 SQUARES,SQUARE ROOTS.CUBES AND CUBE ROOTS
A. SQUARES
- a number multiply by itself- a2 = a × a- examples :
a). 22 = 2 × 2 = 4
b). ( - 4 )2 = ( -4 ) × ( -4 ) = 16
c). ( 2 = ( ) × ( ) =
d). ( 0.3 )2 = 0.3 × 0.3 = 0.09
- the square of any number is greater than zero and is always positive.
B. SQUARE ROOTS
- the square roots of any number is the number when multiplied by itself, equals to the given number.(inverse operation of squaring that number)
- If = a2, then - examples :
a).
b).
c).
- some fractions are required to reduce to the lowest terms in order to find the square roots.
- examples:
a).
- to find the square roots of a mixed number, change the mixed number into an improper fraction.
- example :
a).
- The square root of negative numbers do not exist
SQUARES SQUARE ROOTS
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12 = 1 = 1
22 = 4 = 2
32 = 9 = 3
42 = 16 = 4
52 = 25 = 5
62 = 36 = 6
72 = 49 = 7
82 = 64 = 8
92 = 81 = 9
102 = 100 = 10
112 = 121 = 11
122 = 144 = 12
132 = 169 = 13
142 = 196 = 14
152 = 225 = 15
162 = 256 = 16
172 = 289 = 17
182 = 324 = 18
192 = 361 = 19
202 = 400 = 20
C. CUBES
- a number multiply by itself twice- a3 = a x a x a - examples :
a). 33 = 3 x 3 x 3 = 27
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b). ( )3 =
c). ( 0.2 )3 = 0.2 x 0.2 x 0.2 = 0.008
d). ( - 5 )3 = ( - 5 ) x ( - 5 ) x ( - 5 ) = - 125
- The cube of a positive number is positive- The cube of a negative number is negative.
D. CUBE ROOTS
- a number when multiply by itself twice, equal to the given number.-- examples :
a).
b).
c).
d).
- The cube root of a positive number is positive, the cube root of a negative number is negative.
CUBES CUBE ROOTS
13 = 1 = 1
23 = 8 = 2
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33 = 27 = 3
43 = 64 = 4
53 = 125 = 5
63 = 216 = 6
73 = 343 = 7
83 = 512 = 8
93 = 729 = 9
103 = 1000 = 10
QUESTIONS :
A. Find the value of the following.
1). 32 = 2). 62 =
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3). 82 = 4). 92 =
5). 112 = 6). 122 =
7). ( - 2 )2 = 8). ( - 4 )2 =
9). ( - 5 )2 = 10). ( - 7 )2 =
11). ( - 9 )2 = 12). ( - 10 )2 =
13). = 14). 2
5
2
=
15). = 16). =
17). = 18). =
19). = 20). =
21). ( 0.4 )2 = 22). ( 1.2 )2 =
23). ( - 0.3 )2 = 24). ( - 0.05 )2 =
B. Find the value of the following.
1). = 2). =
3). = 4). =
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5). = 6). =
7). = 8). =
9). = 10). =
11). = 12). =
13). = 14). =
15). = 16). =
17). = 18). =
19. = 20. =
21. = 22. =
C. Find the values of the following:
1). 23 = 2). 43 =
3). 73 = 4). ( - 5 )3 =
5). ( - 3 )3 = 6). 103 =
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7). = 8). =
9). = 10). =
11). = 12). =
13). ( 0.1 )3 = 14). ( 0.6 )3 =
15). ( - 0.2 )3 = 16). ( - 0.03 )3 =
17). ( 1.2 )3 = 18). ( - 0.4 )3 =
D. Find the value of the following.
1). = 2). =
3). = 4). =
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5). = 6). =
7). =8). =
9). = 10). =
11). = 12). =
13). = 14). =
15). = 16). =
Common Errors.
Questions Errors Correct Steps
1. a). Find the value 0f .
b).Calculate the value of
a). (-5) x (-5) x (-5) or 5 P 0
b).
a). – 5 1m
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2 . = K 0
=
= N 0
b).
= 1m
=
= 1m
2. a). Find the value of .
b).Calculate the value of
.
a). 0.006 P 0
b).
=
= K 0
= N 0
a). 0.6 1m
b).
= 3
4
4
4
5
= 1m
= 1m
3. a). Find the value of
.
b). Calculate the value of
a).
or
P 0
b). 8 x K 0
=
a). 1m
b).
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=
N 0
= 1m
= – 6 1m
Questions based on PMR format
1. a). Find the value of .
b). Calculate the value of .
2. a). Find the value of .b). Calculate the value of 16 – .
3. a). Find the value of .
b). Calculate the value of .
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4. a). Find the value of .
b). Calculate the value of .
5. a). Find the value of .b). Calculate the value of 15 – .
6. a). Find the value of .
b). Calculate the value of .
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7. a). Find the value of .
b). Calculate the value of .
8. a). Find the value of .
b). Calculate the value of .
9. a). Find the value of (- 0.4)2 .b). Calculate the value of .
10.a). Find the value of .
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b). Calculate the value of 52 x .
11.a). Find the value of .
b). Calculate the value of 102 – .
12.a). Find the value of .
b). Calculate the value of .
PMR Past Years Questions
2004
a). Find the value of .Squares, Square Roots,Cubes & Cube Roots 22
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b). Calculate the value of 42 x . ( 3 marks )
2005
a). Find the value of .
b). Calculate the value of . ( 3 marks )
2006
a). Find the value of .
b). Calculate the value of ( 3 marks )
2007
a). Find the value of .
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b). Calculate the value of . ( 3 marks )
2008
a). Find the value of .
b). Calculate the value of . ( 3 marks )
CHAPTER 2 : SQUARES ROOTS,CUBES,&CUBE ROOTSANSWERS
A.
1). 9 2). 36
3). 64 4). 81
5). 121 6). 144
7). 4 8). 16
9). 25 10). 49
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11). 81 12). 100
13). 14).
15). 16). =
17). 18). =
19). 20).
21). 0.16 22). 1.44
23). 0.09 24). 0.0025
B.
1). 2 2). 5
3). 8 4). 9
5). 10 6). 12
7). 15 8). 14
9). 10).
11). 12).
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13). 14).
15). 16).
17). 18).
19). 0.8 20). 0.05
21). 1.1 22). 1.5
C.
1). 8 2). 64
3). 343 4). – 125
5). – 27 6). 1000
7). 8).
9). 10).
11). 12).
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13). 0.001 14). 0.216
15). – 0.008 16). – 0.00027
17). 1.728 18). – 0.064
D.
1). 2 2). 3
3). 6 4). – 5
5). – 8 6). 7
7). – 108).
9). 10).
11). = 2 12).
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13). 0.7 14). 0.5
15). – 0.4 16). – 0.5
No. Marking Scheme Marks1.
a).
b). ( - 2 )3
- 8
1
1
1 = 3
2.a). 0.2
b). 16 + 3
19
1
1
1 = 3
3. a). – 0.6
b).
1
1
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1 = 3
4.a). 0.9
b). ( 1.5 )2
2.25
1
1
1 = 3
5. a). 7
b). 15 + 4
19
1
1
1 = 3
6. a).
b).
1
1
1 = 3
7.
a).
b).
15
1
1
1 = 3
8.a).
b). 152
225
1
1
1 = 3
9.a). 0.16
b). ( 1.1)2
1.21
1
1
1 = 3
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10. a).
b).
- 30
1
1
1 = 3
11. a).
b). 100 + 10
110
1
1
1 = 3
12.a). 0.6
b). ( 1.2 )2
1.44
1
1
1 = 3
2004a). 0.8
b).
- 24
1
1
1 = 3
2005a).
b). ( 1.4)2
1.96
1
1
1 = 3
2006a). 0.7
b).
1
1
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1 = 3
2007a). – 4
b). ( 3 )3
27
1
1
1 = 3
2008a).
b). 72
49
1
1
1 = 3
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