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2. 1
ˈ F ʽ F F
FF F F F F
F F F F F
F F F F F ˈ F ʽ F
1.1 ʽ F F
ʽ F F F
F ʽ F ˈ F
F F F F F F F ˈ F
F
F F F F F F
F F F F F
F F F F F
ʽ F ˈ F F F
1.2 F SI
F 7 F F F (m), (kg), (s), F (A), (K),
(mol) (cd)
F F F F F F (N) = kg.m/s2, (J) = N.m = kg.m2/s2
1.3 F F (Prefix)
F F F F F F F F
F F 1 F F 1000 ˈ F F
F F 1000 103 F F F F F F F
(1012), (10-12), (109), (10-9), (106), (10-6)
(103), (10-3), (102), (10-2), (101), (10-1)
F F F F F ˈ F ˈ F F , ,
, , , F F F
– F ˆ F www.schoolDD.com 1

3. F F F F 103 F F 103 F 106 109 1012 F F F 101 F
102 101 F F ˈ F F ... F ˈ ....
1012 10-12
109 10-9
106 10-6
103 10-3
102 10-2
101 10-1
F 1
F
. 4,700,000,000 F ˈ
F F F 1 = 106 F ˈ (10-6 x 106) F
F 1 F F F ...
∴ 4,700,000,000 x (10-6 x 106) = 4,700 x 106
= 4,700 Mm Ans
. F F F F 0.0004 F
1 = 10-3
∴ 0.0004 x (103 x 10-3) = 0.4 x 10-3
= 0.4 mm Ans
. 0.5
1 = 103
∴ 0.5 = 0.5 x 10-3
= 0.5 x 10-3 x (10-3 x 103)
= 0.5 x 10-6 x 103
= 0.5 x 10-6 kg Ans
. 1 ,
1 = 10-2
∴ (1 )2 = (10-2 )2
= 10-4 2
1 = 10-4 Ans
– F ˆ F www.schoolDD.com 2

4. 1 F F 101
(1 )2 = (101 )2
= 102 2
1 = 102 Ans
F F F Hard Disk F, F F
?
1.4 F
1.
F FF F F F F F F F
ଵ
s = ut + ଶ at2
୫ ୫
F F m = ୱ x s + ୱమ x s 2
F m = m +m
2.
F F F ˈ F F F F
F F
୴ି୳
F a= ୲
ౣ ౣ
୫ ି
౩ ౩
F F ୱమ
= ୱ
୫ ୫
F ୱమ
= ୱమ
ℓ
F F F F T = 2πට୥
୫
F F s = ට ౣ = √sଶ
మ ౩
F s=s
1.5 F F
(error) F F
F F
F A ˈ F F A ˈ F + A
ˈ A+ A
F F F F F 70 + 0.2 F F
ˈ F F F 69.8 70.2
– F ˆ F www.schoolDD.com 3

5. - F
F R = A +/- B
R = A+ B
F = ( A +/- B ) + ( A + B )
F R = A +/- 2B
R = A+2 B
F = ( A +/- 2B ) + ( A + 2 B )
- F F (%) F F F (%)
F
F R = A x/ൊ B
୅ ୆
R = ( x100 + x100 ) %
୅ ୆
୅ ୆
F = ( A x/ൊ B ) + ( ୅
x100 +
୆
x100 ) %
F R = A x/ൊ B2
୅ ଶ ୆
R= ( x100 + x100 ) %
୅ ୆
୅ ଶ ୆
F = ( A x/ൊ B2 ) + ( ୅
x100 +
୆
x100 ) %
F R = A x/ൊ √B
୅ ୆
R= ( x100 + x100 ) %
୅ ଶ୆
୅ ୆
F = (A x/ൊ √B ) + ( ୅
x100 +
ଶ୆
x100 ) %
F 2
F 12.44 + 0.01 . F ˈ 2 F F 4.52 + 0.02 F
F
F F R = A B
F F R = (A B) + ( A + B)
– F ˆ F www.schoolDD.com 4

6. = ( 12.44 - 4.52 ) + ( 0.01 + 0.02 )
R = 7.92 + 0.03
∴ F F = 7.92 + 0.03 . Ans
F 3
F ˈ F F 1.20 + 0.01 ˈ F F
ˈ F F
V = WxLxH
୛ ୐ ୌ
F F V = (W x L x H ) + (
୛
x100 +
୐
x100 +
ୌ
x100 ) %
଴.଴ଵ
= (1.20 x 1.20 x 1.20) + ( x100 x 3 )%
ଵ.ଶ଴
= 1.73 + 2.5 %
ଵ.଻ଷ ୶ ଶ.ହ
V = 1.73 + ( )
ଵ଴଴
F V = 1.73 + 0.043 3
Ans
+ 0.043 ˈ 2.5 % Ans
F 4
F F F (ℓ) ˈ 40.0 + 0.2 . F F F
ℓ
T = 2πට F F ( g = 10 m/s2 )
୥
ℓ
T = 2πට
୥
ℓ ℓ
F F T = 2πට + ( x 100 ) %
୥ ଶℓ
଴.ସ଴ ଴.ଶ
= 2 x (22/7) x ට + ( x 100 ) %
ଵ଴ ଶ୶ସ଴
= 1.256 + 0.25 %
ଵ.ଶହ଺ ୶ ଴.ଶହ
T = 1.256 + ( )
ଵ଴଴
F F T = 1.256 + 0.003 s Ans
– F ˆ F www.schoolDD.com 5

7. F 5
F F F 1.00 + 0.01 F F ˈ
F F
V = 4/3 x π x (d/2)3
ଷ ୢ
F F V = 4/3 x π x (d/2)3 + (
ୢ
x 100 ) %
ଷ ୶ ଴.଴ଵ
= 4/3 x (22/7) x (1.00 /2 )3 + ( x 100 ) %
ଵ.଴଴
= 0.523 + 3 %
଴.ହଶଷ ୶ ଷ
V = 0.523 + ( )
ଵ଴଴
V = 0.523 + 0.02 m3 Ans
ˈ 3 % Ans
1.6
F F 4.2 + F 0.05
= 4.25
1 2 3 4 5 6
F
. + .
F F F
F 6 F 4.25 + 0.01 .
F F 4.2
( ) 5
0.1 .
F 0.01 .
F ˈ F F F 4.24 . 4.26 .
– F ˆ F www.schoolDD.com 6

8. 1. FF F F F0 F F
F 0.671 , 4.03 , 0.043 , 20.00 , 0.40 , 0.0003 3, 3, 2, 4, 2
1
2. F F F F F F 0 F F 15 , 136 , 4245 , 70324 ,
2001 2, 3, 4, 5 4
3. F F F F 0 F A x 10n 1 ൑ A ൏ 10 10n
F ˈ F 12000 F ˈ 1.2 x 104 , 1.20 x 104, 1.200 x 104, 1.2000
x 104 2, 3, 4, 5
F F F
F F
3.21 + 4.156 = 7.366 ˈ 7.37 ( F 3 5
ˆ F F 5 ˆ )
5354 - 21.6 = 5332.4 ˈ 5332
F F F
F F
2.34 x 100.9 = 236.106 ˈ 236
7.3 ÷ 874 = 0.0083524 ˈ 0.0084
537.13 x 4.5 = 2417.085 ˈ 2.4 x 103
1.7 F
F F F F ˈ F
F F y = mx + c x ˈ y ˈ
ˈ y ˈ x F m = y/ x c ˈ y (y x
F y2 , y , 1/y
½
x2 , x , 1/x F )
½
F F F F F ˈ F F F
F F F F F F
y y
y = mx + c ୩
xy = k y=୶
c
x x
F F
௞
y = mx + c y=௫ k F
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9. 1.8 F ʽ F
ʽ F F F F F F ʽ F F F
F ˈ ˈ F F F ˆ F ʽ F F F F
ˈ ʽ F
1.8.1 F F F F F F F
F
α θ
θ α
α θ F 2 F ോോ F F F
θ α
θ
θ ∆ F 180°
θ
a a
90-θ
‫׵‬ θ ∆ F F = 180/3=60°
θ
a
F
c
a a/b = A/B
C θ
b A a/c = A/C
θ b/c = B/C
B
– F ˆ F www.schoolDD.com 8

10. c α c2 = a2+b2
a
θ c = √aଶ ൅ b ଶ 2
1
60
b
30
√3
F sin , cos , tan
ୟ ୠ 5
sin θ = ୡ sin α = ୡ 53
3
ୠ ୟ
cos θ = ୡ cos α = ୡ 37
ୟ ୠ 4
tan θ = ୠ tan α = ୟ
√2
1
ୱ୧୬ ஘
tan θ = ୡ୭ୱ ஘ 45
1
sin2 θ + cos2 θ = 1
1.8.2 F
y (x2 , y2) y 3 1>2>3
2
3=0
1 4
୷ ି୷
θ
(x1 , y1) (slope) = ୶మ ି୶భ = tan θ
మ భ 4 ˈ -
x x
y y y y
(+) (-)
x x x x
y y
y = mx + c F F = (k)xy
c
x y x
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11. 1.8.3 F
ଵ ୟ౮
1. ୟ౮
= a-x , ax.ay = a(x + y) , ୟ౯
= ax.a- y = a(x - y) , a0 = 1
2. F log a = x F a = 10x
F ln a = x F a = ex
log(a.b) = log a + log b
log(a/b) = log a - log b
1.8.4
ିୠേ√ୠమ ିସୟୡ
1. F ax2 + bx + c = 0 F x= ଶୟ
2 2
2. F x a =0 (x a)(x + a) = 0 F x = +a x = -a
3. F (x a)2 = 0 x2 2ax + a2 = 0 (x a)(x - a) = 0 F x = +a
4. F (x + a)2 = 0 x2 + 2ax + a2 = 0 (x + a)(x + a) = 0 F x = -a
5. F x2 - 4 x - 12 = 0 (x - 6)(x + 2) = 0 F x = 6 , -2
1.8.5 F
1. 5 = (3+t)2
5-3 = 2t or
2. y = 3x + 2√3 x
y = 5√3 x or
3. 2x = 4x - (3x + x2)x
3 2
x F ?
4. y = 3x + 2 x y F ?
1.8.6 F F
ୟభ ୠభ
1. F a ‫ן‬ b ୟమ
= ୠమ
ଵ ୟభ ୠమ
2. F a ‫ן‬ =
ୠ ୟమ ୠభ
3. F A x B = C x D A<C F B>D
ଡ଼
4. D =P F F FX F F F F ?
୐
ହ୆మ ଵ ଷ୆మ
5. A େିଵ = (N ଶ
)X A େିଵ = (6 - N) Y F N = 3 F X ˈ F Y?
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12. 1.8.7 F F F ˈ F
F ˆ F F F FF F F F ˆ
F F F F ˈ F ʾ F ˈ 44 ʾ
F F F5 ʾ F F 2 ʾ F ˆ F F
F ˆ =A ʾ
F =B ʾ
=C ʾ
ʾ F ˈ 44 ʾ F ˆ ˈ
44+1+1+1 = 47 ʾ
F A + B + C = 47 ----(1)
FF
F F F5 ʾ
F F F B - A = 5 ----(2)
F F 2 ʾ
F F F B - C = 2 ----(3)
F F F F F3 3 F F F F
F F 3 A C F B
(1) + (2) + (3) , (A+B+C) + (B-A) + (B-C) = 47 + 5 + 2
3B = 54
‫ ׵‬B = 18
F B (2) F A F B-A =5
18 - A = 5
18 - 5 = A
‫ ׵‬A = 13
F B (3) F C F B-C =2
18 - C = 2
18 - 2 = C
‫ ׵‬C = 16
‫ˆ ׵‬ F 13, 18 16 ʾ Ans
F F F F F F F ˇ F ʽ F F
! F F F F F F FF F F ˆ
ʽ F F
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