# Algebra II and Trig

## 100 terms · BIDDIES ON MY MATH QUIZ

### what does the number system consist of?

real numbers and imaginary numbers

### what do real numbers consist of?

rational and irrational

### what do rational numbers consist of?

integers, whole numbers, and natural

π

### What is the order of operations?

PEMDAS (parenthesis, exponents, multiplication and division, addition and subtraction)

y = mx + b

Ax + By = C

### point-slope form

y - y(1) = m (x - x(1))

slope

### What are some ways to solve a system of equations?

substitution, elimination, and graphing

### What is the point of solving a system of equations?

to find the point of interception of two lines

### What happens if two lines have the same slope but different y-intercepts?

the lines will be parallel and there will be no solution

### What happens if two lines have the same slope and the same y-intercept?

the lines will be overlapping and the solution will be infinite (all real numbers).

### What happens if two line have opposite reciprocal slopes and different y-intercepts?

the lines will be perpendicular (forms 90˚ angle) and the lines will intersect at one point.

less than

greater than

### ≤

less than or equal to

### ≥

greater than or equal to

### On the number line, when do you use a closed circle?

if the point the circle is on is included (less than or equal to OR greater than or equal to)

### On the number line, when do you use an open circle?

if the point the circle is on is not included (less than OR greater than)

### When does the inequality flip?

when it is multiplied or divided by a negative

(0,0)

b^m+n

b^m-n

b^m*n

1/b^n

b^n

1

(3-√11)

### how do you check a rational expression?

plugging in any number for y in both the original problem and the simplified answer (they should be the same).

### difference of squares

a^2 -b^2 = (a+b)(a-b)

### what does a negative slope mean?

it means opposite direction

### What does a distance and time graph tell you?

the speed or velocity

acceleration

### why do you need to flip the inequality when dividing or multiplying by a negative?

for the statement to remain true

### what are the rows of a matrix?

(100) (010) (001)

h=at^2+bt+c

### what are four ways to solve a system of 3 equations?

substitution, elimination, matrices, and determinants

### what is the pythagorean theorem?

side^2 + side^2 = hypotenuse^2

it is always 1

csc

sec

cot

all

sin

tan

cos

### what is the first pythagorean identity?

sin^2Θ + cos^2 Θ = 1

### what is the second pythagorean identity?

1 + tan^2 Θ = sec^2 Θ

### what is the third pythagorean identity?

cot^2 Θ + 1 = csc^2 Θ

### What are the special right triangles?

30-60-90 triangles and 45-45-90

HALF

### what is the formula for a 30-60-90 triangle?

across from 30 is x, across from 60 is x√3, across from 90 is 2x

### what is the formula for a 45-45-90 triangle?

the sides are x and the side across from the hypotenuse is x√2.

0

1

0

-1

1

0

-1

0

0

undefined

0

undefined

### free falling objects formula

d = 1/2gt^2 (g=9.8)

### how do you verify identities?

you choose one side of the equation to manipulate, find a common denominator, factor, and use any of the pythagorean identities.

2sinΘcosΘ

cos^2Θ-sin^2Θ

2tanΘ/1-tan^2Θ

### sin, cos, and tan of 30˚

1/2, √3/2, and 1/√3

√2/2, √2/2, 1

√3/2, 1/2, √3

### what does the inverse help find?

the degree of an angle

the hypotenuse

### what does a^2 equal in law of cosines?

b^2 + c^2 - 2bc Cos A

### what does b^2 equal in law of cosines?

a^2 + c^2 - 2ac Cos B

### what does c^2 equal in law of cosines?

a^2 + b^2 - 2ab Cos C

ax^2 + bx + c

a(x-h)^2 + k

### how do you complete the square?

take half of the coefficient, square that quantity, balance the equation, factor, and simplify.

the vertex

√-1

-1

### what is the quadratic formula?

-b +or - √b^2 - 4ac / 2a

b^2-4ac

### how many solutions and what type do you get when the discriminant is equal to 0?

one solution; crosses the x axis once

### how many solutions and what type do you get when the discriminant is more than 0 (positive?

two solutions; crosses the x-axis twice

### how many solutions and what type do you get when the discriminant is less than 0 (negative)?

two complex solutions; does not cross the x axis at all

### how do you graph inequalities?

factoring or simplifying to find the x-intercept, plugging in 0 to find the y intercept, and then shading by checking the origin point.

set of x,y

### domain

set of all x values.

### range

set of all y values

### function

for every x-value in the domain, there is exactly one y-value for it in the range.

B^c = A

log(base b)A = C

yes