Maths Formula Sheet by Gaurav Suthar

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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