ACT Math Formulas Flashcards
Algebra: Slope
(y2-y1) / (x2-x1)
Algebra: Slope-Intercept Form
y = mx + b
- m: slope, b: y-int
Algebra: Midpoint of a Line
((x1+x2)/2) , (y1+y2)/2)
Algebra: Distance between 2 Points
√(x2-x1)^2 + (y2-y1)^2
logbx asks
to what power does b have to be raised to result in x
Logarithms formulas
logbx = y → b^y = x
logbxy = logbx +logby
logb(x/y) = logbx - logby
Probability: Outcome happening
of desired outcomes / total # of possible outcomes
Probability: 2 Ind Outcomes both happening
probability of event A x probability of event B
Combination
- order doesn’t matter
possible combinations = # of element A x # of B x # of C…
Percent: find x % of given # n
n(x/100)
Percent: what % a # n is of another # m
(100n)/m
Percent: what # n is x % of
(100n)/x
Pythagorean Theorem
a^2 + b^2 = c^2
Special Right Triangles
30-60-90 degrees: side lengths are x, x√3, 2x
45-45-90 degrees: side lengths are x, x, x√2
Area of a Trapezoid
A = ((a+b)/2)h
- a & b are parallel sides
(bases)
Area of a circle
A = πr^2
Area of an arc
A = (πr^2)(deg measure of center of arc/360)
Circumference
C = 2πr or C = πd
Circumference of an arc
(2πr)(deg measure of center of arc/360)
Circle Equation (given center point & radius)
(x-h)^2 + (y-k)^2 = r^2
Volume of a Cylinder
V = πr^2h
Trig- SOH, CAH, TOA
sine = opp/hypotenuse
cosine = adj/hyp
tangent = opp/adj
Trig- Cosec, Sec, Cot
Cosecant- reciprocal of sin
Secant- recip of cos
Cotangent- recip of tan
Trig- sine & cosine
sin^2x + cos^2x = 1
sinx / cosx = tanx
Area of a parallelogram
A = bh
Arithmetic Sequence: Missing Term
an = a1 + (n-1)d
- a1: first term in seq
- an: missing term you need
- d: common difference
Arithmetic Sequence: Sum of terms
S = (n/2)(a1 + an)
Geometric Sequence: Missing Term
an = a1(r^n-1)
- r is raised to the n-1 power (r is multiplier)
