Rates, Ratios, and Percents

Question 1

algebraic expression.

Answer 1

A combination of variables, constants, and arithmetical operations

Question 2

term

Answer 2

a constant, a variable, or a product of simpler terms that are each a constant or a variable

Question 3

constant term

Answer 3

A term with no variables

Question 4

coefficient

Answer 4

A constant in a term with one or more variables

Question 5

polynomial

Answer 5

an algebraic expression that’s a sum of terms and has exactly one variable. Each term in a polynomial is a variable raised to some power and multiplied by some coefficient.

Question 6

first degree (or linear) polynomial

Answer 6

the highest power a variable is raised to is 1

Question 7

second degree (or quadratic) polynomial

Answer 7

the highest power a variable is raised to is 2

Question 8

linear equation

Answer 8

has a linear polynomial on one side of the equals sign and either a linear polynomial or a constant on the other side—or can be converted to that form

Question 9

Different possibilities when evaluating two linear equations

Answer 9

1. If they are equivalent, infinite solutions
2. If they are not equivalent, one solution
3. If they have a contradiction, there is no solution

Question 10

Two strategies for solving linear equations with two unknowns

Answer 10

1. Substitute the value of one equation into the other
2. Make the coefficients of one unknown the same in both equations (ignoring the sign), then either add the equations or subtract one from the other

Question 11

factoring

Answer 11

first add or subtract to bring all the expressions to one side of the equation, with 0 on the other side. Then try to express the nonzero side as a product of factors that are algebraic expressions

Question 12

quadratic equation

Answer 12

ax2 + bx + c = 0, where a, b, and c are real numbers and a ≠ 0

Question 13

How many roots can a quadratic equation have?

Answer 13

At most two, but can have just one or no root

Examples:

The equation x2 − 6x + 9 = 0 can be written as (x − 3)^2 = 0 or (x − 3)(x − 3) = 0. So, its only root is 3.

The equation x^2 + 4 = 0 has no real root. Since any real number squared is greater than or equal to zero, x^2 + 4 must be greater than zero if x is a real number.

Question 14

How to factor a^2 - b^2

Answer 14

(a − b)(a + b)

Question 15

Quadratic formula

Answer 15

Question 16

How to solve a linear inequality with one unknown

Answer 16

The same as a regular linear equation, except if you divide or multiply by a negative number you have to flip the sign

Question 17

Function Domain

Answer 17

The set of all allowed inputs for a function. This can be restricted by the function’s definition

Question 18

Function range

Answer 18

The set of a function’s outputs

Question 19

Linear equation to define a line

Answer 19

y = mx + b

Question 20

Slope

Answer 20

the coefficient m in the formula y = mx + b

Question 21

y-intercept

Answer 21

The constant b in the formula y = mx + b. Also the y-coordinate of the point where the line intersects the y-axis

Question 22

Slope is 0

Answer 22

Line is horizontal, and has the equation y = b

Question 23

Find x-intercept

Answer 23

Set the variable “y” to zero and solve for x

Question 24

Given two points (x_1, y_1) and (x_2, y_2) with x_1 <> x_2, how to find slope?

Answer 24

ratio of the difference in their y-coordinates to the difference in their x-coordinates
m = (y_2 - y_1) / (x_2 - x_1)

Question 25

How to find the equation for a line given a single known point (x_1, y_1) and slope m

Answer 25

m = (y - y_1) / (x - x_1), or (y - y_1) = m(x - x_1)

Question 26

Three cases for two linear equations

Answer 26

1. Unique solution - graphs are two lines intersecting at the point that is the solution
2. Equations are equivalent - they both stand for the same line and have infinitely many solutions
3. No solution - parallel lines that don’t intersect

Question 27

Graphing a function f(x)

Answer 27

You can equate f(x) with y, as in y = f(x)
x-intercepts are solutions of the equation f(x) = 0
y-intercept is value f(0)