upcat math

Repeating numbers

0.2727272727… = 3/11

Terminating numbers

0.375 = 3/8 ; 0.8 = 4/5

Closure Property

A property of relational operators where any real numbers a and b, their sum and product are also real numbers.

Associative Property

A property of relational operators that indicates that (a+b)+c = a+(b+c) ; a(bc) = (ab)c

Commutative Property

A property of relational operators that indicates that a+b = b+a ; ab = ba

Distributive Property of Multiplication over Addition

A property of relational operators that indicates a(b+c) = ab + ac ; (b+c)a = ab + ac

Existence of an Identity Element Property

A property of relational operators that indicates that a + (

Additive Identity

a + 0 = a

Multiplicative Identity

a x 1 = a

Existence of an Inverse Element

A property of relational operators that indicates that a + (

Reflexive Property

A property of relational operators that indicates that a = a

Symmetric Property

A property of relational operators that indicates that a = b ; b = a

Transitive Property

A property of relational operators that indicates that a = b ; b = c ; a = c

(a+b)^2

a^2 + 2ab + b^2

(a

b)^2

(a+b)(a

b)

Greatest Common Factor

the greatest of the common factors of two or more numbers

Least Common Factor

the smallest number that two or more numbers will divide into evenly.

Penny

0.01 in american money

Nickel

0.05 in american money

Dime

0.10 in american money

Quarter

0.25 in american money

Vertical line test

A test used to determine whether a relation is a function by checking if a vertical line touches 2 or more points on the graph of a relation

Domain

The x value of a function

Range

The y value of a function

Linear function

y = ax + b

Quadratic function

y = ax^2 + bx + c

Cubic function

y = ax^3 + bx^2 + cx + d

Constant function

has a degree of 0

Identity function

y = f(x) = x ; Straight line and has a slope of one

Even and Odd functions

f(

Line bisector

line, ray or another line segment that passes through the midpoint of a line

Intersecting lines

lines that meet at only one point

Parallel lines

lie on the same plane but also do not intersect

Transversal

a line that intersects two or more lines

Perpendicular lines

Lines intersecting at or forming right angles

Complementary angles

Two angles whose sum is 90 degrees

Supplementary angles

Two angles whose sum is 180 degrees

Vertical angles

A pair of opposite congruent angles formed by intersecting lines

Linear pair

A pair of adjacent angles whose noncommon sides are opposite rays.

Equilateral triangle

A triangle with three congruent sides

Isosceles triangle

a triangle with at least two congruent sides

Scalene triangle

a triangle with no congruent sides

A = 1/2 (b1+b2)h

Area of a trapezoid

Parallelogram

A quadrilateral with two pairs of parallel sides

Rectangle

A parallelogram with four right angles

Rhombus

A parallelogram with four congruent sides

Square

A parallelogram with four congruent sides and four right angles.

S = (180)(n

2)

Cube

A prism with six square faces

Prism

A solid figure that has two congruent, parallel polygons as its bases. Its sides are parallelograms

SA = 6x^2

Surface Area of a Cube

SA = 2lh + 2wl + 2wh

Surface Area of a Prism

d = 2/ I^2 + h^2 + w^2

Distance of Sides of Prism

A = pieR^2(h)

Area of a Cylinder

2pieR ( r + h )

Surface Area of a Cylinder

V = 4/3(pie)r^3

Volume of a sphere

SA = 4(pie)R^2

Surface Area of a sphere

LA = (pie)RL

Lateral angle of Cone

V = 1/3(pie)R^2(h)

Volume of a cone

Chord

A segment whose endpoints lie on a circle

Diameter

A straight line passing from side to side through the center of a circle or sphere.

Radius

A straight line from the center to the circumference of a circle or sphere.

Secant

A line that intersects a circle in two points

Tangent

A line in the plane of a circle that intersects the circle in exactly one point.

Inscribed Angle

an angle whose vertex is on a circle and whose sides contain chords of the circle

Concentric Circles

circles that lie in the same plane and have the same center

(x

h)^2 + (y

S = (rad)R

Formula of arc length for Radius

2/ (x1

x2)^2 + (y1

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

Mid point formula

r = 2/ (x

h)^2 + (y

y

y1 = M (x

Parallel lines

have the same slope

Perpendicular line

negative reciprocal of the given slope

1 / cscx

sinx

1 / secx

cosx

1 / cotx

tanx

sinx / cosx

tanx

1 / sinx

cscx

1 / cosx

secx

1 / tanx

cotx

cosx / sinx

cotx

sin2x + cos2x = 1
1 + tan2x = sec2x
1 + cot2x = csc2x

Trigonometric identity equations

D = n(n

3) / 2

Mode

most occuring in the values

Median

middle value in the values, if there are two, divide it

Mean

sum of the values also called arithmetic average

Range

greatest in the value

Interest

amount paid or earned for the use of money

Principal

original or base amount borrowed or invested

Rate

Interest charged on a loan or paid on yearly basis or specified

Simple Interest

only principal bears the interest for the entire term

I = PRT

Formula for Simple Interest

Quartile

divide the data into four equal parts

Deciles

divide the data into ten equal parts ; often used in school awards or rankings

Percentiles

divide the data into groupings of 1% ; Standardized tests often use this and helps students compare their performance with their peers.