Show:
Expressions and Equations
Graphs and Lines
Functions
Exponents and Radicals
Factoring
100
1) What's the difference between and expression and an equation?

2) How do you know when an expression is simplified completely?
1) An expression does not have an equal sign and an equation does have an equal sign.

2) An expression is simplified completely when all like terms have been combined.
100
y = 4/5x-8

Use the equation to find the:
1) slope
2) y-intercept
of the graph of the equation.
1) Slope: 4/5
2) y intercept = (0,-8)
100
In order for something to be a function, what must be true?
In order for something to be a function, each input must have exactly one output.
100
How can you tell if an exponential expression is completely simplified? How can you tell if a radical expression is completely simplified?
An exponential expression is completely simplified when there are no negative exponents and none of the terms share the same base (i.e all like terms have been combined.)

A radical expression has been simplified when there are no radicals in the denominator and the number inside the radical has no perfect square factors.
100
What does it mean to factor an expression?
What is the difference between a polynomial and a monomial?
To factor an expression means to write it as a product of two or more expressions.
A monomial consists of one term while a polynomial is a combination of two or more monomials.
200
Combine like terms to simplify the following expression: 23y+5x-7y^2-7y-10x+z
-7*y^2-5x+16y+z
200
1) What is the equation for the vertical line that crosses through the point (7,9)?
2) What is the equation of the horizontal line that crosses through the point (-2, 3) ?
3) What is the intersection point of the two lines?
1) x = 7
2) y = 3
3) (7, 3)
200
The following is the input/output table for a function.

input output
0 2
1 4
2 6
3 8

Is the function linear? How can you tell?
Yes, the function is linear. The difference between consecutive outputs is always 2.
200
List the three basic laws of exponents:

1) a^b * a^c =
2) (a^b)/(a^c) =
3) (a^b)^c =

List the two additional rules:

4) (a*b)^m =
5) (a/b)^m =

Complete the definitions for the zero exponent and the negative exponent

6) a^0 =
7) a^-m =
Three basic laws:
1) a^b * a^c = a^(b+c)
2) (a^b)/(a^c) = a^(b-c)
3) (a^b)^c = a^(b*c)

Two additional rules:
4) (a*b)^m = a^m * b^m
5) (a/b)^m = (a^m)/b^m

Zero and Negative Exponent Definitions:
6) a^0 = 1
7) a^-m = 1/a^m
200
What are the two requirements needed in order to use the Zero Product Property to solve an equation?
The equation must be equal to zero, and it must be a product.
300
Solve the equation for the variable x:

3x-12-6x=12x+18
x=-2
300
For each pair of points, find the slope of the line that contains them.

1) (9, 7) and (-4,-5)
2) (0,-1) and (-3,4)
1) slope: 12/13
2) slope: -5/3
300
What is the difference between the closed form definition of a function and the recursive definition of a function?
The closed form definition of a function describes the relationship between the inputs and outputs of a function, while the recursive definition of a function describes the relationship between the consecutive outputs of the function.
300
Simplify each expression:
​​1) (x^2)^3*y*y^3

2) square root of 140
1) x^6*y^4

2) 2 * (square root of 35)
300
Find the greatest common factor of the terms below: 1) 16*y^3 and 24*x*y

2) 5*a^5*b^2*c^4 and 10*a^7*b*c^2*d and 55*a^2*b*c
1) 8y

2) 5*a^2*b*c
400
Solve for y.

4y+2x+36+y^2 = 8y-x-10+y^2
y = (3x+46)/4
400
Write down the equations of three different lines that will never intersect.
Any lines with the same slope will never intersect.
400
Find the domain of the function:
h(x)=3/(2x+1)
Domain: All real numbers except x = -1/2.
400
Simplify the expression below completely:

(x*x^2*z*(4y)^3*z^0) / 2*x^6*y*z^2*a
(32y^2)/x^3*z*a
400
Factor each expression completely:

1) (6x^3 * y^5) + (21*x^2*y^3)

2) (8*x^8*y^5*z^2) + (20*x^5*y^3*z^4) - (x^9*y^2*z)
1) (3*x^2*y^3)* (2*x*y^2 + 7)

2) (x^5*y^2*z) * (8*x^3*y^3*z + 20*y*z^3 -x^4)
500
A rectangle with a perimeter of 130 inches has width x and length x+3.

1) Write an equation for the perimeter of the rectangle in terms of x.
2) What is the area of the rectangle?
1) 2x + 2(x+3) = 130
2) Area = 1054 inches squared
500
Solve the following system of equations:

2x+5y=1
3x+6y=3

What does the solution represent?
x=3
y=-1
(3,-1)

This solution is the point where the two lines intersect.
500
The equations below define two functions:
f(x)= 1/2x-3

h(x)=4x+1

Use the functions to evaluate:
1) f(8)
2) h(f(x)) (Be sure to simplify the final answer)
3) h(f(4)).
1) f(8)=1
2) h(f(x)) = 2x-11
3) h(f(4)) = -3
500
Simplify each radical expression completely:

1) 5*(square root of 12)/(square root of 6)

2) 8*(square root of 25)/4 * (square root of 60)
1) 5*(square root of 2)

2) (square root of 15)/3
500
Find all solutions to each equation.
Hint: Use factoring and the Zero Product Property.

1) 16*x^4 - 4*x^3 = 0

2) 10*y^3 = 40*y
1) x = 0 and 1/4

2) y = 0, 2, and -2