Study Guide 1.1 to 1.3 (Order of Operations)
Period 11: Int. Algebra 1
1. Redo problems from the homework and the review sheet.
2. Expressions may not contain the equal sign (=) or any type of inequality.
3. An equation is a mathematical sen
Much of the history of mathematics is marked
by the discovery of special types of numbers
like counting numbers, zero, negative
numbers, pi, and imaginary numbers.
pi and i, e denotes a number.
Called The Euler Number after
Think about 2x = 6.
We cant calculate the exact value in our
heads, but we could give an interval for x.
l To find the exact value of x, we will use
Definition of a logarithm with
Let b and
8.5 Exponential Growth
What is exponential growth?
A quantity is growing exponentially if
it increases by the same percent in
each unit of time.
y = C(1 + r)t
C = the initial amount
t = the time period (how much time h
9.4 Solving Quadra2c
Equa2ons by Graphing
Solving Quadra2c Equa2ons Using
The solu2on of a quadra2c equa2on in one
variable x can be solved or checked graphically
with the following step
2x2 + 10 = 28
- 10 -10
2x2 = 18
x2 = 9
x = + 3 These are the solutions/roots of the equation.
We did not need the quadratic formula to
solve this quadratic equation because it was
in the form
ax2 + c = #
where b = 0.
is a formula used
The discriminant is the expression inside the
radical in the quadratic formula.
The discriminant can be used to find the
number of solutions of the quadratic
Consider the quadratic equation:
ax + bx + c = 0
10.4 Solving Polynomial
Equa5ons in Factored Form
Factored form: A polynomial is in factored
form if it is wriGen as the product of two or
more linear factors.
10.5 Factoring x + bx + c
To factor a [email protected] expression means to
write it as the product of two linear
You know from the FOIL method that
(x + p
Way Analysis of Variance
To compare several means.
Examples: Highway gas mileage for 1998
model vehicles (midsize, pickup, SUV)
Stemplots for Vehicle
the same form as
growth functions f(x) =
abx where a > 0 BUT:
0 < b < 1 (a fraction
between 0 and 1)
State whether f(x) is an exponential
growth or decay function
1. f(x) = 5(2/3)x
b=2/3, 0<b<1 it is a decay function.
2. f(x) = 8(3/2)x
8.1 - Exponential Growth
y = ab
b > 1
The graph passes through the point (0, a).
So, the y-intercept is a.
The x-axis is an asymptote of the graph
(y = 0 is an asymptote).
The domain is all real numbers.
7.4 Inverse Functions
Review from chapter 2
Relation a mapping of input values (x-values)
onto output values (y-values).
Here are 3 ways to show the same relation.
y = x2
Study Guide 2.2 to 2.7, Properties of Real Numbers
1. Addition, SAME sign: add the numbers keep the sign
8 + 6 = 14
-8 + (-6) = -14
2. Addition, DIFFERENT sign: take difference of the two numbers, keep sign of larger
-8 + 6 = -(8 6) =
Solving linear equations with variables on both sides
1. Write the original equation
ax +b = cx + d
3x + 5 = -2x + 15
2. Simplify the expression on the left side of the equal sign
a) Use order of operations (PEMDAS)
b) Distribute to remove parenthesis
Due Date: Friday, June 14th, 2013
(10 points off for entire group for each day late)
Create a game using at least 4 sections from our textbook (chapters 8 - 12)
Your project MUST include:
1. A new and different name for your game.
Intermediate Algebra 1
MP 4 Project
Due on Tuesday, 5/14
STAINED GLASS PARABOLAS
1. Make up 4 quadratic equations, labeling them 1, 2, 3 & 4.
2. Two of the graphs must open up and two must open down.
3. For each equation, find the vertex, the axis
Period 11: Algebra 1
Due: February 28, 2013
Modeling Real-Life Problems as Linear Equations
This project is to create a business and model it with a linear function. (50 points)
A. You are to come up with a business that you can start. Your projec
Pi Day Project (60 Points)
Due Pi Day (Thursday March 14, 2013)
Pi day is Thursday, 3/14! In honor of this special day, we will be creating projects. You have a
choice of projects. Projects must be neat, well organized, color
Planning a Sundae Party (40 people)
Number of each
Ice Cream and Serving Items
Icecream gallon top
Icecream 1 gallon top
Icecream 1 gallon
50 plastic bowls
24 plastic spoons
Algebra 1: Properties of Exponents
An expression like 46 is called a power.
The exponent 6 represents the number of times the base 4 is used as a factor.
Product of Powers: am an = am+n
example: 35 36 = 35+6 = 311
Power of a Pow
Solving Systems of Linear Equations
Solve by graphing
Write equations in slope intercept form: y = mx + b
Begin with b graph the y-intercept (0, b)
Move m the slope rise/run
o If positive move the rise units up and run units to the right
o If negative
10.1 Adding and Subtrac2ng
1. A polynomial is an expression which is the
sum of terms of the form axk where k is a
2. A polynomial is wriDe