ACT Math Formulas

Arithmetic Sequence

an = a1 + (n-1)d

Geometric Sequence

an = a1 * (r^(n-1))

Quadratic Formula

x = (-b +- sqrt(b²-4ac))/2a

Determinent

b²-4ac
if positive: 2 real solutions
if 0: 1 real solution

if negative: no solutions

Point Slope

y - y1 = m(x-x1)

Inverse Trig

csc = hyp/opp
sec = hyp/adj

cot = adj/opp

Trig Match to Inverse

Sin = csc

Cos = sec
Tan = cot

Amplitude + Period

y = asin(bx)
Amp = a

Period = 2pi/b
IF TAN/COT, PERIOD = pi/b

Area of Trapezoid

1/2(b1 + b2)h

Probability

A and B = P(A) * P(B)
A or B = P(A) + P(B)

Sum of Internal angles of a Polygon

180(n-2)

Special Right Triangles

30-60-90: x, x*sqrt3, 2×
45-45-90: x, x, x*sqrt2

Law of Cosines

c² = a² + b²-2ab(cosC)

Law of Sines

sin A / a = sin B / b

Area of Triangle (Trig) (Uses two sides and the angle between it)

½ ab(sin C)

Determinant of Matrix

ad-bc

Volume of a Cylinder

pi*r²*h

Surface Area of a Cylinder

2pi*r²+2pi*rh

Reflection over X Axis

f(x) → -f(x)

Reflection over Y Axis

f(x) → f(-x)

Permutations

n!/(n-r)!

Combinations

n!/(r!*(n-r)!)

Set Theory: Intersection

elements present in both sets
A (upside U) B

Set Theory: Union

number of items present in both sets combined, without duplicates

A (U) B

Direct Proportion

y=kx (where k is a constant)

Indirect Proportion

y=k/x (where k is a constant)

Weighted Average

(avg 1)(weight 1) + (avg 2)(weight 2) / weight 1 + weight 2

Distance for two complex numbers A+bi and C+di

sqrt((a-c)²+(b-d)²)

Absolute value of A+bi

sqrt(a²+b²)

Binomial Theorem

(ax+by)^n = n+1 terms
sum of coefficients in the expansion of (ax+by)^n = (a+b)n

Arithmetic Sum

Sn = n/2 ( a1+an)

Geometric Sum

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