Name: ___________________________________ Block: _____
CCA Ch 1: MATH NOTES for FUNCTIONS
TERM
Absolute
Value
DEFINITION
Absolute value is the distance from zero on a number line.
5 
5
Use your graphing calculator to complete the functions’ tables and graphs.
Linear Functions:
Families of
Functions
Exponential Functions:
Quadratic Functions:
y  2x  5
y  2x
y  2x  4
2
x
x
x
y
y
y
y
y
x
x
Describe a Graph Completely:
y
x
(This graph should have arrows on the ends.)
Shape: _________________________
y
Symmetry: ______________________
Vertex: _________________________
Minimum: _______________________
Quadratics
Maximum: ______________________
x-intercept(s): ___________________
x
y-intercept(s): ___________________
Domain: _______________________
Range: ________________________
32  _____
9  _____
2 3  _____
3
8  _____
Roots
Use your calculator to estimate:
38  _______
3
38  _______
Function = A relationship in which each input (x) has only one output (y).
Example of a Function:
Example of a Non-Function:
y
y
Functions
x
x
Using the function f (x)  5  x to evaluate the following:
2
f (2)  _______
Evaluating
Functions
f (2)  _______
f (3.7)  _______
Use the same function to find two values of x so that f ( x)  4 .
x  _______
and
x  _______
Domain =
The set of input (x) values for a function.
y
Range =
The set of output (y) values for a function.
Domain
& Range
D: ___________________________
R: ___________________________
x
CCA Ch 2: MATH NOTES for LINEAR RELATIONSHIPS
TERM
DEFINITION
SLOPE =
rate of change = steepness of a line = m = ________ = ____________
Examples of Calculating Slope from…
A Graph:
m=
Change in x and y:
x  4 and y  2
m=
A Table:
Slope
4, 7 
Two Points:
m=
x
2
5
8
11
y
-5
-3
-1
1
2,21
and
m=
Sketch a line for each of the following slopes:
Positive Slope:
Negative Slope:
y
y
x
Zero Slope:
Undefined Slope:
y
x
y
x
x
Equations of Lines can be written in different forms.
Linear
Equations
Example of a line in Standard Form: _________________________
Example of a line in Slope-Intercept Form: _________________________
Slope-Intercept Form is y  mx  b .
In this equation, x and y are variables; they change throughout a situation
and m and b are constants; they stay the same throughout a situation.
SlopeIntercept
Form of
a Line
Using a Graph…
What is m?
What is b?
Using a Table…
What is m?
What is b?
Using a Tile Pattern…
What is m?
What is b?
Given Slope and Y-Intercept:
slope = 4 and y-intercept = 2
Equation:
Given a Graph:
How do you get a value for m?
How do you get a value for b?
Writing
Linear
Equations
Equation:
Given Two Points:
5,8 
and
How do you get a value for m?
Equation:
2,1
How do you get a value for b?
Where is the x-intercept of a line?
Use the equation 2x  3y  12 to
calculate the x-intercept. (Show
work.)
What is the y-coordinate of the xintercept? _______
x-intercept: ( _______ , _______ )
Where is the y-intercept of a line?
x- intercepts
and
y-intercepts
Use the equation 2x  3y  12 to
calculate the y-intercept.
Show work.
What is the x-coordinate of the yintercept? _______
y-intercept: ( _______ , _______ )
y
Use ONLY the x- and y-intercepts
to graph the line:
x
CCA Ch 3: MATH NOTES for SIMPLIFYING AND SOLVING
TERM
Laws of
Exponents
DEFINITION
Examples
Rules
x2  x5 
x a  xb 
x10 y 8
x 4 y10
xa
xb


3x y  
x  
xyz 0 
x0 
x 3 y2 
x a 
5
3 2
a b
1
x a

Example of a trinomial: ___________________________
Example of a binomial: ___________________________
Example of a monomial: __________________________
Polynomials
What is a term?
What operations separate terms from one another?
Complete the rectangle:
Area as a Product:
_____________________________
Generic
Rectangles
Area as a Sum:
_____________________________
(Monomial) x (Monomial)
4x 2x  
Multiplying
Polynomials
(Monomial) x (Binomial)
4x 2x  5 
_______________
___________________
What is this property called?
(Binomial) x (Binomial)
4x  32x  5 
________________________
Solve for x:
3x  4   x
(Binomial) x (Trinomial)
4x  32x 2  x  5 
________________________
Solve for y:
2x  3y  12
Check:
Solve for x:
6x 1x  2  3x 2x 1 2
Solve for x:
2x 1  11
Solving
Equations
Check:
Check:
CCA Ch 4: MATH NOTES for SYSTEMS OF EQUATIONS
TERM
DEFINITION
Write a “LET” statement for each situation to define variables, then set up a
system of equations. (Do NOT solve these problems, just set up equations.)
1. The perimeter of a rectangle is 60 cm.
The length of the rectangle is 4 times the width.
LET…
Equations:
Writing
Equations
2. Mike bought red and blue candies and spent a total of $11.19. The red
candies cost $1.29 per pound and the blue candies cost $0.79 per
pound. The bag weighed a total of 11 pounds.
LET…
Equations:
The best time to use Equal Values Method is…
Example:
y  7x  6
y  2x 14
The Equal
Values Method
Solution = ( _____ , _____ )
The best time to use Substitution is…
Example:
y  4x  2
5x  2y  9
The
Substitution
Method
Solution = ( _____ , _____ )
The best time to use Elimination is…
Example:
5x  4y  2
2x  y  6
The
Elimination
Method
Solution = ( _____ , _____ )
If you solve a system of equations and get 5  3 , what does that mean?
What does that tell you about the graph?
If you solve a system of equations and get 0  0 , what does that mean?
Solutions of
Linear
Systems
What does that tell you about the graph?
If you solve a system and get x  3 and y  1 , what does that mean?
What does that tell you about the graph?
CCA Ch 5: MATH NOTES for SEQUENCES
TERM
DEFINITION
t(0)  ____________________________________
t(1)  ____________________________________
sequence
notation
t(n 1)  _________________________________
t(n)  ____________________________________
t(n 1)  _________________________________
General Sequence Information:
Types of
Sequences
Sequence
Generator
Explicit
Equation
Recursive
Equation
Shape of
the Graph
General Sequence Information:
Explicit Equation if starting amount is 10:
Increase by 8%:
Multipliers
for
% Increase
or
% Decrease
multiplier =
Explicit Equation if starting amount is 10:
Decrease by 8%:
multiplier =
3 , 7 , 11 , 15 , …
Examples
3 , 6 , 12 , 24 , …
n
n
t(n)
t(n)
Tables
Sequence
Generators
Term 0
Explicit
Equations
Recursive
Equations
Graphs
24
24
22
22
20
20
18
18
16
16
14
14
12
12
10
10
8
8
6
6
4
4
2
2
2
4
6
Should the graphs above be continuous or discrete?
Continuous
or Discrete
Explain:
2
4
6
CCA Ch 6: PREVIEW for SCATTERPLOTS AND REGRESSION LINES
1.
Wing Span
(cm)
Height
(cm)
162
160
155
157
173
172
192
193
185
185
178
177
a. If the provided graph is 15 spaces wide,
how should the scale be set? Label the axes.
b. If the provided graph is 25 spaces wide,
how should the scale be set? Label the axes.
c. Plot the data on the graph.
d. Use your graphing calculator to make a scatterplot.
Enter data:
[STAT]
Graph your data:
1:Edit…
[2nd]
[Y=]
Enter x-values into L1.
1:Plot1…
[ENTER]
On
Enter y-values into L2.
[ZOOM]
9:ZoomStat
e. Describe the scatterplot in terms of direction, strength, form and outliers:
f. Sketch a line of best fit onto your scatterplot, select two ordered pairs that best define
that line, then calculate the equation for the line of best fit. Show all work.
Equation: ___________________________
g. If a person’s wingspan is 169 cm, use your equation to predict that person’s height.
2.
Foot Length
(cm)
Height
(cm)
20
157
23
167
29
185
30
190
28
180
21
171
a. If the provided graph is 11 spaces wide,
how should the scale be set? Label the axes.
b. If the provided graph is 38 spaces wide,
how should the scale be set? Label the axes.
c. Plot the data on the graph.
d. Use your graphing calculator to make a scatterplot.
e. Describe the scatterplot in terms of direction, strength, form and outliers:
f. Sketch a line of best fit onto your scatterplot, select two ordered pairs that best define
that line, then calculate the equation for the line of best fit. Show all work.
Equation: ___________________________
g. If a person’s foot length is 19 cm, use your equation to predict that person’s height.