NYSTCE Part 2

sum of interior angles of a polygon

(n-2)180

midpoint formula

(x₁+x₂)/2, (y₁+y₂)/2

log 1

0

log of the base

1

3 ft= __ yd.

1 yd

1 liter= ? quarts

1.057 quarts

1 mile= ? kilometers

1.609 kilometers

Volume of a pyramid

1/3Bh

Volume of a cone

1/3πr²h

1 pound = ____ ounces

16 ounces

1 pint= ? cups

2 cups

1 quart= _____ pints

2 pints

If the discriminant is positive,

2 real solutions

1 ton= ? pounds

2,000 pounds

1 kilogram= ? pounds

2.2 pounds

Circumference of a circle

2πr

Surface Area of a Cylinder

2πr² + 2πrh

1 gallon= ? liters

3.785 liters

1 foot= ? centimeters

30.48 centimeters

full angle

360 degrees

1 galloon = _______ quarts

4 quarts

Volume of a sphere

4/3πr³

1 pound= ? grams

453.6 grams

Surface area of a sphere

4πr²

1 mile= ? feet

5280 feet

1 square mile= ______ acres

640 acres

Surface area of a cube formula

6s^2

Trapezoid

A quadrilateral with exactly one pair of parallel sides

area of a triangle

A=1/2bh

Area of a rhombus/ kite

A=1/2d1d2

Area of a trapezoid

A=1/2h(b1+b2)

Area of a parallelogram formula

A=bh

reflex angle

An angle that is greater than 180 degrees but less than 360 degrees

major arc

An arc of a circle whose measure is greater than 180 degrees.

FOIL

First, Outer, Inner, Last

Area of a cirlce formula

Pier^2

5 Congruent triangles

SSS SAS ASA AAS HL

Bisector

The line that divides something into two equal parts.

log of a product

The sum of the logs

concurrent lines

Three or more lines that intersect at a common point

similar triangles

Triangles in which corresponding angles are equal in measure and corresponding sides are in proportion (ratios equal)

supplementary angles

Two angles whose sum is 180 degrees

complementary angles

Two angles whose sum is 90 degrees

volume of a cube

V=s³

Volume of a cylinder

V=πr²h

how to tell if a graph is a function

Vertical line test - if a vertical line intersects more than once, it's not a function.

Trigonometric Functions

Wavy lines

Quadratic Formula

[-b ± √(b² - 4ac)] / (2a)

piecewise function

a function that is written using two or more expressions

one-to-one function

a function where each element of the range is paired with exactly one element of the domain test: horizontal line test

monotone function

a function whose graph either constantly increases or constantly decreases

step function

a function with a graph that is a series of horizontal line segments

Transversal Line

a line that intersects two or more lines

constant function

a linear function of the form f(x)=b slope of 0

Many-to-One Function

a member of the range may be paired with more than one member of the domain

Definition of a Kite

a quadrilateral with exactly two pairs of congruent consecutive sides, one line of symmetry

function

a relation in which each element of the domain is paired with exactly one element of the range

cos x

adjacent/hypotenuse

relation

any set of ordered pairs

Discriminant

b^2-4ac

distance between two points

d = √(x₁-x₂)² + (y₁-y₂)²

y variable

dependent variable

population equation

f (t)= ae^rt

(Fog) (x)

f(g(x))

identity function

f(x)=x slope= 1

square root function

f(x)=√xn always to the right of the 0 and above the x-axis

factor a quadratic expression

factors of ac that add up to B if none: use the quadratic equation

absolute value function

graph is a V

odd function

graph is symmetrical with respect to the origin; f(-x)=-f(x)

even function

graph is symmetrical with respect to the y-axis; f(x) = f(-x)

concave polygon

has at least one diagonal with points outside the polygon

convex polygon

has no diagonal with points outside the polygon

x variable

independent variable

If the discriminant is 0,

it only has one solution. -b/2a

minor arc

less than 180 degrees

log of a quotient

log (x/y) = log x - log y

inverse of exponential function

logarithmic function

Number of diagonals in a polygon

n(n-3)/2

exponential function graph

name the type of function shown f(x)=a^x for a>1 curved line

If the discriminant is negative,

no real solutions

sin

opposite over hypotenuse

tan x

opposite/adjacent

log of the base raised to a power

power

log of a value raised to a power

power times the log of the value

quadractic function

shaped like a U

slant height formula

square root of r^2+h^2

domain

x values

range

y values

slope equation

y2-y1/x2-x1

inverse function

y= k/x

Surface Area of a Cone

πrl+πr²