Description
Maths Formula Sheet Chapter 1 : Real Numbers HCF x LCM = a x b Chapter 2 : Polynomials For zeroes of Quadratic polynomial, p(x) = ax2 + bx + c, a ≠ 0 1) Sum of zeroes = α + β = 2) Product of zeroes = αβ =
-b a c a
For zeroes of Cubic polynomial, p(x) = ax3 + bx2 + cx + d, a ≠ 0 1) Sum of zeroes = α + β + γ =
-b a
-d 2) Product of zeroes = αβγ = a 3) Sum of product of zeroes taken two at a time = αβ + βγ + αγ =
c
a
Algebraic Identities – 1)
(a + b)2 = a2 + b2 + 2ab
2)
(a - b)2 = a2 + b2 – 2ab
3)
a2 - b2 = (a + b) (a – b)
4)
(a + b)3 = a3 + b3 + 3a2b + 3ab2
5)
(a - b)3 = a3 - b3 - 3a2b + 3ab2
6)
(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)
7)
a3 - b3 = (a - b) (a2 + b2 + ab)
8)
a3 + b3 = (a + b) (a2 + b2 - ab)
9)
a3 + b3 + c3 - 3abc = (a + b + c) ( a2 + b2 + c2 – ab – bc - ca)
10) If a + b + c = 0 then a3 + b3 + c3 = 3abc Chapter 3 : Pair of Linear Equations in Two Variables 1)
a1 a2
2)
a1 b1 = a2 b2
3)
a1 a2
≠
=
b1 (Intersecting, Consistent, One solution) b2
b1 b2
≠ =
c1 (Parallel, Inconsistent, No solution) c2 c1 c2
(Coincide, Consistent, Infinite solution)
Chapter 4 : Quadratic Equations ax2 + bx + c = 0, where a ≠ 0 and a, b, c are real number. -b ±√b 2 -4ac 1) Quadratic Formula : x = 2a 2) Discriminant (D) = b2 - 4ac - If D > 0, then two distinct real roots - If D = 0, then two equal rots - If D < 0, then no real roots Chapter 5 : Arithmetic Progression General form of AP = a, a + d, a + 2d, a + 3d, ..... 1)
an = a + (n - 1)d
2)
Sn =
3)
Sn =
4)
an = Sn – S(n–1)
5)
If a, b, c are in AP then 2b = a + c
n 2 n 2
[2a + (n-1) d] (a + l)
Chapter 7 : Coordinate Geometry 1)
Distance Formula = √(𝑥2 − 𝑥1 )2 + (𝑦2 − y1 )2
2)
Distance of point (p, x) from origin = √p2 + 𝑥 2
3)
Section formula =
4)
Mid-point formula =
𝑚1 𝑥2 + 𝑚2 𝑥1 𝑚1 + 𝑚2 𝑥1 + 𝑥2 𝑦1 + 𝑦2 2
,
Chapter 8 : Trigonometry
Trigonometry Table
2
Ratios •
Sin θ =
•
Cos θ =
•
Tan θ =
Perpendicular Hypotenuse Base Hypotenuse
=
Perpendicular Base
=
P H
B H
=
P B
Conversions 1
•
Sin θ =
•
Cos θ =
•
1 Tan θ = Cotθ
•
Tan θ =
Cosecθ 1 Secθ
Sinθ Tanθ
Identities 1)
sin2θ + cos2θ = 1
2)
sec2θ = 1 + tan2θ
3)
Cosec2θ = 1 + cot2θ
1
•
Cosec θ =
•
Sec θ =
•
1 Cot θ = Tanθ
Sinθ
1 Cosθ
Chapter 12 : Area Related to Circles Figure
r
90°
r
r
r
θ
θ
r
Area
Perimeter
πr2
2πr
πr2 2
πr + 2r
πr2 2
πr + 2r 2
θ 360
r
θ 360
x πr2
1 2
πr2 - r2 sinθ
θ 360
θ 360
x 2πr
πr + 2r sin
θ 2
Chapter 13 : Surface Area and Volume Figure
Curved Surface Area
Total Surface Area
Volume
2h(l + b)
2(lb + bh + lh)
lxbxh
4l2
6l2
l3
2πrh
2πrh + 2πr2
πr2h
πrl
πrl + πr2
1 πr2h 3
4πr2
4πr2
2πr2
3πr2
4 3
2 3
πr3
πr3
Chapter 14 : Statistics 1) Mean Mean
Assumed Mean method
Direct Method
̅ = x
∑ fi xi ∑ fi
̅ = a̅ x b -b
2) Mode = l + (2b -1 b 0- b ) x h 0 2 1 3)
n - CF Median = l + ( 2 )xh
f
4) 3 Median = 2 mean + Mode
Chapter 15 : Probability
1) P(E) =
No. of favourable outcome No. of all possible outcome
̅) = 1 2) P(E) + P(E 3) Probability always lies between O ≤ P(E) < 1
∑ fi di ∑ fi
Tossing of Coins 1) Tossing 1 coin – H, T (Outcome – 2) 2) Tossing 2 coins - HH, HT, TH, TT (Outcome - 4) 3) Tossing 3 coins - HHH, HTH, THH, TTH, HHT, HIT, THT,TTT (Outcome - 8) Throwing of Die 1) Throwing 1 die - outcome 6 2) Throwing 2 die - outcome 36 Playing Cards •
Face Cards : King, Queen, Jack
•
Number Cards : Ace(1), 2, 3, 4, 5, 6, 7, 8, 9, 10
52 Cards
26 Red
26 Black
13 Spades
13 Clubs
13 Hearts
13 Diamonds
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