ACT FORMULA SHEET MATH
an = a1 + c(n – 1)
an = a1(c)n – 1
NUMBER AND QUANTITY
Sequences
Logarithms
Rates
Sequence with a constant of c:
arithmetic sequence:
geometric sequence:
distance = speed × time
variation: quantity = rate × time
logab = c — ac = b
STATISTICS AND PROBABILITY
Percents
Statistics
percent = part / whole × 100%
% symbol = divide by 100
a% of b = a/100 × b = a × b/100
percent change = change / original
average (mean) = sum of terms / number of terms
median = middle number (or average of 2 middle numbers)
mode = most common number
range = biggest – smallest
Probability and Counting Techniques
probability = number of desired terms / total number of terms
P(event happens) + P(event doesn’t happen) = 1
P(A and B) = P(A) × P(B)
GEOMETRY
ALGEBRA
Linear Graphs
slope-intercept formula: y = mx +b
m = slope = (y1 – y2) / (x1 – x2)
Quadratics
FOIL (First, Outer, Inner, Last): (a + b)(c + d) = ac + ad + bc + bd
discriminant: b² – 4ac
If . . .
b = y-intercept = (0,b)
distance formula: √[(y1 – y2)² + (x1 – x2)²]
midpoint formula: midpoint = [(x1 + x2)/2, (y1 + y2)/2]
quadratic formula: X= -b +√b2 - 4ac
2a
• discriminant > 0 2 real solutions
—
• discriminant = 0 1 real solution
—
• discriminant < 0 no real solutions
—
O
y
x
(x y
(x y
vertical angles are congruent
45 : 45 : 90 triangle ratio: x : x : x√2
30 : 60 : 90 triangle ratio: x : x√3 : 2x
angles of a triangle add to 180°
area of a triangle = ½ × base × height
Pythagorean theorem: a² + b² = c²
Triangles
supplementary angles add to 180°
complementary angles add to 90°
Lines and Angles
FUNCTIONS
Function Notation
fog(x) = f(g(x))
note: this is different from fg(x), which is f(x) × g(x)
Trigonometry on the Coordinate Plane
π radians = 180°
