This document provides a concise summary of key scientific concepts and formulas in fewer than 3 sentences. It begins by defining common scientific units used to measure length, mass, time, electric current, temperature, amount of substance, and luminous intensity. It then explains the International System of Prefixes used to modify unit symbols and provides examples of their use. The document proceeds to demonstrate the application of scientific concepts and formulas to solve problems involving length, area, volume, speed, time period, percentage error, and other topics. Diagrams are included to illustrate geometric and trigonometric relationships. Key formulas from algebra, trigonometry, logarithms, and other areas are also summarized concisely.

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F F F
FF F F F F
F F F F F
F F F F F F F
1.1 F F
F F F
F F F
F F F F F F F F
F
F F F F F F
F F F F F
F F F F F
F 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 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 F F F , ,
, , , F F F
– F 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 F F ... F ....
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
F F F 1 = 106 F (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 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
s = ut + at2
F F m = x s + x s2
F m = m +m
2.
F F F F F F F
F F
F a=
F F =
F =
F F F F T=2
F F s= =
F s=s
1.5 F F
(error) F F
F F
F A F F A F + A
A+ A
F F F F F 70 + 0.2 F F
F F F 69.8 70.2
– F 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
R= ( x100 + x100 ) %
F = ( A x/ B2 ) + ( x100 + x100 ) %
F R = A x/
R= ( x100 + x100 ) %
F = (A x/ )+( x100 + x100 ) %
F 2
F 12.44 + 0.01 . F 2 F F 4.52 + 0.02 F
F
F F R = A B
F F R = (A B) + ( A + B)
– F 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 F F 1.20 + 0.01 F F
F F
V = WxLxH
F F V = (W x L x H ) + ( x100 + x100 + x100 ) %
= (1.20 x 1.20 x 1.20) + ( x100 x 3 )%
= 1.73 + 2.5 %
V = 1.73 + ( )
F V = 1.73 + 0.043 3
Ans
+ 0.043 2.5 % Ans
F 4
F F F (ℓ) 40.0 + 0.2 . F F F
T = 2π F F ( g = 10 m/s2 )
T = 2π
F F T = 2π +( x 100 ) %
= 2 x (22/7) x + ( x 100 ) %
= 1.256 + 0.25 %
T = 1.256 + ( )
F F T = 1.256 + 0.003 s Ans
– F F www.schoolDD.com 5

7. F 5
F F F 1.00 + 0.01 F F
F F
V = 4/3 x π x (d/2)3
F F V = 4/3 x π x (d/2)3 + ( x 100 ) %
= 4/3 x (22/7) x (1.00 /2 )3 + ( x 100 ) %
= 0.523 + 3 %
V = 0.523 + ( )
V = 0.523 + 0.02 m3 Ans
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 F F F 4.24 . 4.26 .
– F 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 F 12000 F 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 7.37 ( F 3 5
F F 5 )
5354 - 21.6 = 5332.4 5332
F F F
F F
2.34 x 100.9 = 236.106 236
7.3 ÷ 874 = 0.0083524 0.0084
537.13 x 4.5 = 2417.085 2.4 x 103
1.7 F
F F F F F
F F y = mx + c x y
y x F m = y/ x c y (y x
F y2 , y , 1/y
½
x2 , x , 1/x F )
½
F F F F F F F F
F F F F F F
y y
y = mx + c
xy = k y=
c
x x
F F
y = mx + c y= k F
– F F www.schoolDD.com 7

9. 1.8 F F
F F F F F F F F F
F F F F F F F F F
F
1.8.1 F F F F F F F
F
θ
θ
θ F 2 F F F F
θ
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 F www.schoolDD.com 8

10. c α c2 = a2+b2
a
θ c= a b
1
60
b
30
3
F sin , cos , tan
5
sin θ = sin α = 53
3
cos θ = cos α = 37
4
tan θ = tan α =
1
tan θ = 45
1
sin2 θ + cos2 θ = 1
1.8.2 F
y (x , y ) y 3 1>2>3
2
3=0
1 4
θ
(x1 , y1) (slope) = = tan θ
4 -
x x
y y y y
(+) (-)
x x x x
y y
y = mx + c F F = (k)xy
c
x y x
– F F www.schoolDD.com 9

11. 1.8.3 F
1. = a-x , ax.ay = a(x + y) , = 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
1. F ax2 + bx + c = 0 F x=
2. F x 2 a2 = 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 x
y=5 x or
3. 2x = 4x - (3x + x2)x
3 2
x F ?
4. y = 3x + 2 x y F ?
1.8.6 F F
1. F a b =
2. F a =
3. F A x B = C x D A<C F B>D
4. D =P F F FX F F F F ?
5. A = (N )X A = (6 - N) Y F N = 3 F X F Y?
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12. 1.8.7 F F F F
F F F F FF F F F
F F F F F F 44
F F F5 F F 2 F F F
F =A
F =B
=C
F 44 F
44+1+1+1 = 47
F A + B + C = 47 ----(1)
FF
F F F5
F F F B - A = 5 ----(2)
F F 2
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
F 13, 18 16 Ans
F F F F F F F F F F
! F F F F F F FF F F
F F
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