CC1

a_n = a+(n-1)d

finding the nth term in arithmetic progression

s = n/2(2a₁+(n-1)d)

sum of all terms in arithmetic progression if the d is given

s = n/2(a+a_n)

sum of all terms in arithmetic progression if the d is unknown

a_n = a₁r^n-1

finding the nth term in geometric progression

s = a₁(1-rⁿ) / (1-r)

sum of all terms in geometric progression is r>1

s = a₁ / (1-r)

sum of all terms in geometric progression if r<1

complementary angles

sum of angles if 90^o

supplementary angles

sum of angles if 180^o

conjugate or explementary

sum of angles if 360^o

sin0 / cos0

tan0 in quotient identities

cos0 / sin0

cot0 or reciprocal of tan0 in quotient identities

1 / tan0

reciprocal identity of cot0

1 / sin0

reciprocal identity of csc0

1 / cos0

reciprocal identity of sec0

sin²0+cos²0=1

tan²0+1=sec²0

1+cot²0=csc²0

pythagorean identities

sin(a+b)=sina cosb + cosa sinb

cos(a+b)=cosa cosb - sina sinb

tan(a+b)=tana + tanb / 1 - tana tanb

sum identities addition formulas

sin(a-b)=sina cosb + cosa sinb

cos(a-b)=cosa cosb + sina sinb

tan(a-b)=tana - tanb / 1 + tana tanb

difference identities substraction formulas

S = 180(n-2)

sum of interior angles

S = n(180) - (sum of interior)

sum of exterior angles

N_d = n/2*(n-3)

formula for finding the no. of diagonals

A = 1/4na²L

area of regular polygon

A = (1/2)nr²sin(360/n)

polygon inscribed in a circle

A = nr²tan(180/n)

polygon circumscribing a circle

L = a/2tan(180/n)

length of apothem

A = 1/2bh

area of triangle if base and height is given

A = 1/2absin0

area of triangle if side-angle-side is given

centroid

intersection of lines in median

orthocenter

intersection of lines in altitude

incenter

intersection of lines in angle bisector

circumcenter

intersection of lines in perpendicular bisector

V = A_b(∑H/no. of heights)

volume of truncated prism with similar cross section

V = h/6(A₁+4A_m+A₂)

volume of prismatoid with similar cross section

V = 1/3(A_b*h)

volume of pyramid with similar cross section

V = h/3(A₁+A₂+√A₁A₂)

volume of frustum with similar cross section

A = 4πr²

area of a sphere

V = 4/3πr³

volume of a sphere

A = 4πr²(0/360)

area of spherical lune

V = 4/3πr³(0/360)

volume of spherical wedge

A = 2πrh

area of spherical zone

a² = b²+c²-2bc*cosA

b² = a²+c²-2ac*cosB

c² = a²+b²-2ab*cosC

cosine law

A_T =√s(s-a)(s-b)(s-c)

heron’s formula or area of triangle if all sides are given

A = √(s-a)(s-b)(s-c)(s-d)-abcdcos²0

area of general quadrilateral

m_a = √(2b²+2c²-a²)/4

median of a triangle

median

line drawn from a vertex towards the midpoint of the opposite side

angle bisector

line drawn from the vertex towards the opposite side such that the angle at the vertex is halved

altitude

line drawn perpendicular from a side towards the opposite vertex

perpendicular bisector

line drawn perpendicular from the midpoint of side

d₁d₂ = ac + bd

ptolemy’s theorem

A = 1/2d₁d₂sin0

area of a quadrilateral if diagonals are given