ACT - Math USE

real number

All numbers on number line (ex: pos, zero, frac and more)

non-real number

The number not on the number line (ex: i, neg root )

rational number

decimal and fraction that is terminating or repeating

irrational number

determinable and repeating frac and deci (ex: π or sqrt{2} )

number line

spectrum of all real number extends infinitely both direction

absolute value

distance from one value to other (always positive)

integer

pos, 0, neg number that is not written in frac or deci

whole number

positive integer (no 0, or neg)

multiple

multiplying WN by other WN (ex: 7 x 1 or 7 x 2)

factor

WN that results from dividing other two WN (ex: 30=5*6)

prime number

WN with only two factors (ex: 7: 1,7)

composite number

WN that has more than 2 factors (ex: 12: 1,2,3,4,6,12)

prime factorization

factoring of composite number (30: 2x3x5)

percent of change

measuring in a denominator of 100 (ex: 2/5 → 40/100, 40%)

percent of group

putting sub group over entire group and finding percent

reciprocal

Inverse or the switching of the value (ex: 3/4 → 4/3)

ratio

compare quantity in reduced fraction (ex: 5/10→1/2→2:1)

exponent

base number multiplied by itself in number of times

imaginary number

i = √-1

i^2 = -1

i^3 = i

i^4 = 1

complex number

z = a + bi (on graph: a → change y axis, b → change slope)

distance formula

d = √(x2-x1)^2 + (y2-y1)^2

note: equation on right is under √

mid-point formula

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

conjugate

when binomial are same but with different operator

(ex: 2x + 1 and 2x - 1)

vector

arrow with both magnitude and direction

Pythagorean theorem

x^2 + y^2 = z^2

matrix

rectangular array that is used for data manipulation

algebra

equations of relationship between number and quantities

scientific notation

5000 → 5.0 x 10^3, or 0.005 → 5.0 x 10^-3

systems of equation

two or more equation in single instance (ex: x = 5)

inequality

relationship between two values or expressions (ex: x < 5)

coefficient

quantity of unknowns (ex: 3x, there is x, 3 times)

substitution

placing a given value of letter into the equation

linear equation

any equation with one or more unknowns, infinite solution

linear systems

find the values of the variables that satisfy all linear equation

y ≤ x+5, y ≥ x+3

area below the line, area above the line

quadratic equation

is x^2, and x can have two possible solution in one position

quadratic formula

equation to solve the function with no linear term

standard form

Ax + By = C

vertex form

y=a(x-h)²+k, vertex: (h, k) highest or lowest point on a parabola

factored form

f(x) = a(x-r1)(x-r2)

roots

value that, when multiplied by itself, gives the original number

logarithmic equations

inverse function of exponential equation

function

assigns a unique output value to each input value

series/sequence

terms that are added together following a pattern or rule

consecutive number

series of number follow each other in difference of 1

slope-intercept form

y=mx+b

slope formula

(y2-y1)/(x2-x1)

system of function

two or more function in a single instance

trigonometric function

graph of a continuous smooth periodic oscillation

period/phase

one complete cycle of trig function

frequency

number of cycle of trig function

amplitude

distance from the mean (x-axis)

geometry

interpretation of 2 and 3 dimensional shapes and spaces

origin

center of the coordinate plane (0, 0)

quadrant

an arc of 90°

line

composition of dot as thin layer, is starlight and continuous

segment

line that has an two endpoint

angle

measure of arc between two intersecting segment or line

complementary angle

sum of angle = 90°

supplementary angle

sum of angle = 180°

bisector

dividing the segment into two equal part from any angle

perpendicular bisector

diving segment into two part equally with 90°

vertical angles

4 angles formed by two intersecting line with sum of 360°

transversal

line intersecting two parallel line creating 8 angles

congruent

identical shape rotated in different angle

similar

shape that has different size but same angle, and side length ratio

polygon

complete shape having more than two sides

angle total

finding total angle of polygon: a = (n-2)180

perimeter

length of the outline of a shape

triangle

three sided shape, with the total 180°

Area of triangle

1/2 (base) (height)

Isosceles triangle

has two identical sides and angles

equilateral

three identical sides and angles

Area of equilateral

A = (s²√3)/4, s → side

right triangle

one angle is 90°

triangle ratio

side length 3:4:5

side length 5:12:13

30° -60° -90°, 1: 2: √3/2

45°-45°-90°, 1: 1: √2

quadrilateral

four sided shape, with the total of 360°

Area of quadrilateral

A = side^2

Area of rectangle

A = length * height

Area of parallelogram

A = base * height

Area of trapezoid

A= (b1 + b2)/2 * height, b → base

Area of rhombus

A = (d1 * d2)/2, d → distance

circle

shape where each point of the is same distance from center

radius of circle

distance from the center of the circle

diameter of circle

full length segment that goes through center point

tangent of circle

line that just touches the circle at one point

chord of circle

line in-between diameter and tangent

pi

ratio of circumference to diameter

circumference of circle

C = 2 * *pi ** r

Area of circle

A = pi * r^2

radius in coordinate plane

r^2 = (x - h)^2 + (y - h)^2

reflection

over x-axis: (2, 3) → (2, -3). over y-axis: (2, 3) → (-2, 3)

rotation

rotating the shape on coordinate plane

cylinder

volume = pi * radius^2 * height

volume of rectangular solid

volume = length * width * height

cube

volume = sides ^ 3

surface area of cube

volume = 6 * sides ^ 2

trigonometry

relationships between angles and ratios of lengths

sine

opposite / hypotenuse

cosine

adjacent / hypotenuse