ACT Math Formulas

Formulas to know for ACT

Pythagorean theorem

a^2 + b^2 = c^2

Circumference of a circle

C= (3.14)(d)

Area of a circle

A=(3.14)(r^2)

distance formula

D=(r)(t)

arithmetic sequence formula (explicit)

an = a1 + (n - 1)d

Sum of arithmetic sequence

S = (n/2) (a1 +(a1+(n-1)d)) or S = (n/2) (a1 + an)

Geometric sequence formula

an=a1(r)^n-1

Geometric Series formula Finite

Sn = a1 (1-r^n) / (1-r)

Combination formula

nCr=n!/r!(n-r)

Permutation

nPr=n!/(n-r)!

parabola

y=a(x-h)^2+k

circle

(x-h)^2+(y-k)^2

ellipse

((x-h)^2/a^2) + ((y-k)^2/b^2)= 1

hyperbola

((x-h)^2/a^2) - ((y-k)^2/b^2)= 1

Inscribed angle

IA=central angle(or intercepted arc)/2

Property of Parallelogram

Opposite sides are parallel and congruent

opposite angles are congruent

consecutive angles are supplementary

diagonals bisect each other

Property of Rectangle

4 90 degree angles

Property of Rhombus

4 congruent sides

Property of Square

4 90 degree angles and sides

Property of Trapezoid

one set of parallel sides

isosceles trapezoid

one set of parallel sides and 2 congruent sides

trigonometry functions

a sin (b(x-c))+d

area of trapezoid

a= (b1+b2/2)(h)

volume of a pyramid

B(length x width) x H

volume of a cone

(1/3)(pi)(r^2)(h)

volume of a cylinder

(pi)(r^2)(h)

volume of sphere

4/3(pi)(r^3)

volume of rectangular prisim

b x w x h

sum of angles in polygon

n=(n-2)(180)

single interior angle

n= (n-2)(180)/n

Trig Ratios/SOHCAHTOA

s=o/h, c=a/h, t=o/a

Reciprocal Trig Ratios

Csc=h/o, sec=h/a, cot=a/o

Slope formula 2 points on a line

Slope formula: 

the slope of a line and a point on the line

Point-slope formula: y - y₁ = m(x - x₁)

the slope and y-intercept of a line

Slope-intercept formula: y = mx + b

Parallel lines have equal slopes

The slopes of perpendicular lines are opposite reciprocals