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Gravity
Terms in this set (121)
Vertical Angles
Formed by 2 intersecting lines or segments. Always congruent.
Supplementary Angles
Two angles that form a line and add up to 180°.
Right Angle
An angle that measures 90°.
Complimentary Angles
Two angles that add up to 90°.
Alternate Interior Angles (Parallel Lines)
Ex. 3 & 6 are congruent
Alternate Exterior Angles (Parallel Lines)
Ex. 1 & 8 are congruent
Corresponding Angles (Parallel Lines)
Ex. 1 & 5 are congruent
Same Side Interior Angles (Parallel Lines)
Ex. 3 & 5 add up to 180º
Area of a Triangle
A=½(Base)(Height)
A=½bh
Triangle Inequality Theorem
The sum of the 2 shortest sides of a triangle is always greater than the length of the third side.
Equilateral Triangle
A triangle in which all three sides are equal and all three interior angles are 60°.
Isosceles Triangle
A triangle with two equal sides. Base angles (angles across from the congruent sides) are also equal.
Proportionality in Triangles
In every triangle, the longest side is opposite the largest angle and the smallest side is opposite the smallest angle.
Pythagorean Theorem
Used to find the missing side of a right triangle.
"c" is always the length of the hypotenuse.
a²+b²=c²
Similar Triangles
Triangles that have the same angle measures but different side lengths. Solve by setting up a proportion.
45-45-90 Special Triangle
Always in the ratio 1:1:√2
Isosceles right triangle
30-60-90 Special Triangle
Always in the ratio 1:√3:2
Pythagorean Triple
Three integers that, as side lengths of a triangle, form a right triangle.
Ex. 3/4/5 or 5/12/13
Degree Measure of a Triangle
The inside angles of a triangle always add up to 180°.
Area of a Circle
A=πr²
Degree Measure of a Circle
The central angles of a circle add up to 360°.
Circumference of a Circle
C=2πr or C=πd
Area of a Sector (Circle)
(n/360)(πr²), where n is the central angle.
Arc Length of a Sector (Circle)
(n/360)(2πr), where n is the central angle.
Area of a Polygon
A=½aP, where a is the apothem and P is the perimeter.
Sum of Interior Angles of a Polygon
Sum=180(n-2), where n is the number of sides.
Interior Angle of a Polygon
Where n is the number of sides
Degree Measure of a Quadrilateral
The interior angles of a quadrilateral add up to 360º.
Area of a Square
A=(side)(side)
A=s²
Diagonal of a Square
Diagonal=side(√2)
D=s√2
Area of a Rectangle
A=(length)(width)
A=lw
Perimeter of a Rectangle
P=2(length)+2(width)
P=2l+2w
Area of a Parallelogram
A=(base)(height) or A=bh
Angles in a Parallelogram
Opposite angles are equal.
Area of a Trapezoid
A=½(h)(b₁+b₂)
Surface Area of a Sphere
SA=4πr²
Surface Area of a Cylinder
SA=2πr²+2πrh
Surface Area of a Prism
SA=2(lw+lh+wh)
SA=2B+Ph, where B is the area of the base, P is the perimeter of the base, and h is the height of the prism.
Volume of a Sphere
V=(4/3)πr³
Volume of a Cube
V=side³
V=s³
Volume of a Cylinder
V=πr²h
Diagonal of a Cube
Diagonal = side√3
D=s√3
Volume of a Prism
V=lwh
Distance Formula
(think Pythagorean theorem)
Midpoint Formula
Used to find the midpoint of a line
Slope
Rate of change of a line;
rise over run;
change in y /change in x
Parallel Lines
Same slope
Perpendicular Lines
Form 90 degree angles;
Slopes are negative reciprocals
Horizontal Lines
slope = 0;
Defined by x=a, where a is a constant
Vertical Lines
slope = undefined;
Defined by y=a, where a is a constant
Slope-Intercept Formula
Use if you know the slope and the y-intercept
Point-Slope Formula
Use if you know the slope and a point on the line
Collinear Points
A, B, and C are all collinear points
Average (Arithmetic Mean)
Average Speed
Weighted Average
Mode
Value(s) that occurs most frequently!
Median
Middle point of an ordered list!
Fundamental Counting Principle
If an event can happen m ways and another, independent event can happen n ways, then both events can happen in m ∗ n ways.
Probability
Probability of two independent events happening
Ratios
Absolute Value
The distance from 0 (an absolute value takes any number and makes it positive)!
Multiplying Variables with Exponents
Dividing variables with exponents
Negative Exponents
Two Exponents, one base
Distributive Property
Base raised to the power of 0
Fractional Exponents
"FOIL"ing
Difference of Squares
Perfect Square Trinomials
Function Transformations: Amplitude increase of f(x) in which all values of y are multiplied by 3. A vertical stretch.
3(f(x))
Function Transformations: Amplitude decrease of f(x) in which all values of y are multiplied by 0.5. A horizontal Stretch.
0.5(f(x))
Horizontal Shift Right (ie: 3 units right)
y = f(x-3)
Horizontal Shift Left (ie: 3 units left)
y = f(x+3)
Vertical Shift up (ie: shift 2 units up)
y = f(x) + 2
Vertical Shift Down (ie: shift 2 units down)
y = f(x) - 2
Matrix Addition
Matrix Multiplication
Rewriting logarithms as exponentials
Logarithm Power Rule
Logarithm Product Property
Logarithm Quotient Property
Complex number i
Powers of i
SOH-CAH-TOA
Trigonometric Identities
Pythagorean Identities
Graph of y = sin(x)
Graph of y = cos(x)
Graph of y = tan(x)
Graphing Trigonometric Functions
y = Asin(Bx - C) + D
Integers
Any number that is not a decimal or a fraction. ie: -30, 1, 2, 50
Whole Number
Any number that is not a negative or a fraction. ie: 0, 2, 37, 455
Odd Integer
Any integer that cannot be divided by 2 without a remainder.
ie: −111, −57, −1, 1, 67!
Even Integer
Any integer that can be divided by 2 without a remainder (including zero!)
ie: 2, 20, -30
Consecutive Integers
Numbers that directly follow each other on a number line.
ie: −4,−3,−2,−1... or 3,4,5,6...
variable form: n, n+1, n+2, n+3
Consecutive Odd Integers
Odd numbers that follow each other on a number line.
ie: −5,−3,−1,1...
variable form: n, n+2, n+4
Consecutive Even Integers
Even numbers that follow each other on a number line.
ie: −6,−4,−2,0...
variable form: n, n+2, n+4, n+6
Real Number
Any number that can be found on a number line. Excludes infinity and imaginary numbers.
ie: All integers, rational numbers, and irrational numbers!
Rational Number
Any number that can be written as a fraction (ratio of integers).
ie: 0 ,4,12 ,−5,.20!
Irrational Number
Any number that cannot be written as a fraction.!
Prime Number
A positive number that can only be divided by 1 AND itself.
ie: 2, 3, 5, 7, 11, 13, 17, 19, 23, 279, 31, 37...!
(1 is NOT a prime number. 2 is the smallest prime number, and prime numbers cannot be negative or even)
Remainder
The amount left over when a quantity is divided by another number.
Factors
The numbers that divide evenly into a given number without a remainder.
The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30.
Multiples
The numbers that divide evenly by a given number without a remainder.
Multiples of 30 are 30, 60, 90, 120
Order of Operations
Parentheses!
Exponents!
Multiplication!
Division!
Addition!
Subtraction!
Percent
Means "divided by 100"
Percent Change
Arithmetic Sequence
Geometric Sequence
Sum of an arithmetic sequence
Sum of a finite geometric sequence
Sum of an infinite geometric sequence where r > 1
Translating word problems: Mathematical equivalent of the word "of"
Multiply (×)
Translating word problems: Mathematical equivalent of the word "per"
Divide (÷)
Translating word problems: Mathematical equivalent of the word "percent"
Divided by 100
Translating word problems: Mathematical equivalent of the word "is"
Equals (=)
Translating word problems: Mathematical equivalent of the word "a number"
V ariable (typically x or y)
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