ACT Math formulas

These flashcards cover essential math formulas and properties relevant for exam preparation.

Area of a Circle

A = πr²

Volume of a Cylinder

V = πr²h

Circumference of a Circle

C = 2πr

Pythagorean Theorem

a² + b² = c²

Special Right Triangle (45-45-90)

leg length are equal and hypotenuse is rad two times the leg

Percent Increase Formula

(new - old)/old

Simple Interest Formula

A = P(1 + rt)

Slope Formula/rate of change formula

m = (Y₂ - Y₁) / (X₂ - X₁)

Standard Form of a Line

Ax + By = C

Area of a Triangle

A = 1/2 bh

Volume of a Sphere

V = (4/3)πr³

Sum of Interior Angles of a Polygon

180(n - 2), where n is the number of sides.

Properties of Parallelograms

Opposite sides are equal and parallel, diagonals bisect each other.

standard form of a parabola

f(x) = ax² + bx + c

factored form of a parabola

f(x) = a(x-m)(x-n) where m and n are x intercepts

x coordinate of vertex of a parabola using its factored form

m+n/2, insert into function to find y coord of vertex

vertex of a parabola using its standard form

-b/2a, f(-b/2a)

equation for finding x intercepts of parabola in standard form

-b +- sqrt b²-4ac/2a

vertex form of a parabola and its vertex

f(x) = a(x-h)² + k; vertex is h,k

difference of squares equation

a²-b² = (a+b)(a-b)

midpoint formula

(x1+x2/2, y1+y2/2)

Distance Formula

d = √((x₂ - x₁)² + (y₂ - y₁)²)

central angle is ______ the inscribed angle (write out full sentence)

central angle is double the inscribed angle

formula of a circle

(x-h)² + (y-k)² = r²

area of a trapezoid

1/2bh

sum of exterior angles of a polygon

360

consecutive angles of a parallelogram are _____ (write full sentence, consecutive means same side)

consecutive angles of a parallelogram are supplementary

shift up by k units

f(x)+k

shift down by k units

f(x)-k

shift left by h units

f(x+h)

shift right by h units

f(x-h)

reflect over the x axis (flip upside down)

-f(x)

stretch vertically by a factor of c (becomes skinnier)

cf(x)

shrink vertically by a factor of c (becomes fatter)

1/c * f(x)

discriminant solution rules (b²-4ac)

If its negative than no solution, if its 0 then 1 solution, and if its positive then 2 solutions

volume of a pyramid

1/3lwh

surface area of a cube

6s²

cosecant, secant, and cotangent are all _____ of sohcahtoa (finish the sentence)

cosecant, secant, and cotangent are all opposites of sohcahtoa

Interest compounded annually formula

A = P(1+r)^t

Interest compounded n times per year

A = P(1+r/n)^nt

general form of a conversion factor

ending units/starting units

distance formula (write out fully)

distance = rate * time

Final concentration of volume A and B

Concentration of A(Volume of A) + Concentration of B(Volume of B)

trig identity #1: the sine of a non right angle equals the ______ (write it out)

the sine of a non right angle equals the cosine of the other non right angle

trig identity: for any angle in a right triangle, the square of the sine plus the square of the cosine equals ___ (write it out)

for any angle in a right triangle, the square of the sine plus the square of the cosine equals one

sum of consecutive integers

n(n+1)/2

formula for the median count value

n+1/2 where n is the frequency sum

how to determine what goes on the bottom of a weighted average fraction

look for what tells you “how many of each”

for any arithmetic sequence of numbers, what is the relationship between the mean and median?

for any arithmetic sequence of numbers, mean = median

interest compounded annually

A=P(1+r)^t