Algebra 2
HS Mathematics
Unit: 06 Lesson: 01
A Screeching Halt KEY
When a car must make a sudden stop, it often leaves skid marks on the
pavement.
Is there any way to tell from the skid mark how fast a car was going before it put on the
brakes?
The equati
Algebra 2
HS Mathematics
Unit: 03 Lesson: 02
Exploring Equations KEY
Equations with a variable on both sides can be solved using a graphing calculator.
Sample:
Enter the left side of the
equation into Y1, and the
right side into Y2.
2 x - 1 =x +4
Graph th
Algebra 2
HS Mathematics
Unit: 08 Lesson: 01
Evaluating Exponents KEY
Tables. Match the tables to the correct exponential function.
3.
1.
x
x
1
B
A
f ( x ) 5 2
f ( x) 5 2
2.
C
f ( x ) 2 5 x
A
X
0
1
2
3
4.
D
B
f(x)
5
2.5
1.25
0.625
x
0
1
2
3
f ( x ) 2 x 5
Algebra 2
HS Mathematics
Unit: 03 Lesson: 02
Exploring Inequalities KEY
Graphing calculators can also be used to solve inequalities, such as
3x - 7
You can enter the left side of the inequality in Y 1
and the right side into Y2, then graph.
Finding the p
Algebra 2
HS Mathematics
Unit: 03 Lesson: 02
Equations and Inequalities KEY
Solve the equations and restrict solutions to the given domains.
2)
1)
1
4
4 - 2(1- x ) = - 38 - 4 x
4x x = 3x +
10
5
Solution
real numbers
A) Solution
B) Solution
x=
cfw_
20
3
20
Algebra 2
HS Mathematics
Unit: 04 Lesson: 01
Electrical Problems KEY
While doing some
renovations to their home,
a family needs to hire an
electrician.
Electrical Services
After looking through the
phone directory, they find
advertisements for two
differe
Algebra 2
HS Mathematics
Unit: 01 Lesson: 01
Data Collection Analysis Summary KEY
Data Relationship
Diagram of Procedure
Data Table
Sample Graphs
Parent Function
(Name and Symbolic)
Linear
function
The number of uniformsized spherical pieces
needed to fil
Algebra 2
HS Mathematics
Unit: 11 Lesson: 01
Completing the Square KEY
General Equation:
x2 6x y 2 7
Calculator graph:
Transformations for
entering into calculator:
y 7 x 2 6x
Recall that we have explored many
representations of the conic sections. For
ex
Algebra 2
HS Mathematics
Unit: 12 Lesson: 01
Data with Diamonds KEY
Many things can affect the price of a diamond. Often, when determining the value
of such a stone, jewelers look for the four Cscut, color, and clarity, and
especially caratage. Caratage r
Algebra 2
HS Mathematics
Unit: 11 Lesson: 01
Cooling Tower KEY
Power plants use water in cooling
towers to transfer heat generated in
energy production. The Didcot Power
Station in Oxfordshire, England has six
such cooling towers, each 100 m tall.
While t
Algebra 2
HS Mathematics
Unit: 02 Lesson: 02
Combined Transformations KEY
Consider the parent functions below. Use the tables to sketch their graphs.
y = x2
y = x
x
y
x
y
-2
2
-2
4
-1
1
-1
1
0
0
0
0
1
1
1
1
2
2
2
4
We know how to transform these parent fu
Algebra 2
HS Mathematics
Unit: 09 Lesson: 01
Combine and Solve KEY
In each equation, combine the terms correctly to make a logarithm of a single expression. Rewrite as
an exponential expression. Then solve for the variable.
Sample A:
Sample B:
log x 5 log
Algebra 2
HS Mathematics
Unit: 09 Lesson: 01
Constructing Radio Dials KEY
On a radio dial the distance from 50 kilohertz to 53 kilohertz is not
much different than the distance from 140 kilohertz and 160 kilohertz. It
appears that the markings on the dial
Algebra 2
HS Mathematics
Unit: 11 Lesson: 01
Conic Characteristics (Student Page) KEY
Ellipse
Hyperbola
Parabola
Any line through
the center
Both vertical and
horizontal through
the center
Both vertical and
horizontal through
the center
Either
vertical th
Algebra 2
HS Mathematics
Unit: 12 Lesson: 01
At the Bike Shop KEY
Jane Gallagher opens a bike shop in which she will sell childrens bicycles as well
as adult mountain bikes. She is trying to determine the initial cost to stock her store
with these two typ
Algebra 2
HS Mathematics
Unit: 02 Lesson: 02
Distorted Points of View KEY
Transformations are an important tool for studying functions. In this activity, you will investigate
transformations on the graph of a function.
1. The following are some values for
Algebra 2
HS Mathematics
Unit: 07 Lesson: 02
Evaluation: Algebra of Rational Functions KEY
Solve the rational equations and check using the graphing calculator. Box your final answer.
1.
2.
3
2x
5
2
x2 x 4 x2
Answer: x = 4
12
8
2
x 1 x
Answer: x = 4 or
Algebra 2
HS Mathematics
Unit: 12 Lesson: 01
Evaluation: Function Applications KEY
1. A parent function (f(x), shown dotted) has been
transformed to make the graph of another function,
g(x).
a) What is the equation for the parent function used
here (f(x),
Algebra 2
HS Mathematics
Unit: 09 Lesson: 01
Exponential Equations: Plug and Solve KEY
Read about each situation. Decide whether each question requires you to evaluate or solve the given
function. In every case, show the steps that lead to your answer.
1.
Algebra 2
HS Mathematics
Unit: 08 Lesson: 01
Exponent Rules KEY
Know these rules regarding exponents.
Symbolic Rule
Numerical Examples
Verbal Description
3 4 35 39
x 7 x 9 x 16
a m n a m n
a
To multiply terms that have the
same bases, you can
ba b c b a c
Algebra 2
HS Mathematics
Unit: 08 Lesson: 01
Exponent Practice 3 KEY
Solve the following equations algebraically. Check solutions using the graphing calculator. Round
answers to the nearest hundredth, if necessary.
1.
2.
2
3
x 64
x = 512
3.
5
1
x 2
32
x=
Algebra 2
HS Mathematics
Unit: 08 Lesson: 01
Exponent Practice 2 KEY
Solve the following equations algebraically. Check solutions using the graphing calculator.
1.
2.
3 x 2 3 4 x
1
6 2 x 1
216
x=3
x = -1
3.
x=
5.
4.
23 x 1 64
x=
5
3
6.
82 x 16 x 3
x = -6
Algebra 2
HS Mathematics
Unit: 04 Lesson: 01
Evaluation Systems of Inequalities KEY
Multiple choice questions
D 1)
Which of the following ordered pairs would be included in the solution to the given system of
inequalities?
Point P (1,1)
System:
x +y <5
P
Algebra 2
HS Mathematics
Unit: 11 Lesson: 01
Evaluation of Conic Sections and their Applications KEY
In the following multiple choice items, tell whether the description refers to a circle, ellipse, hyperbola,
or a parabola.
_ 1)
P
The set of all points i
Algebra 2
HS Mathematics
Unit: 04 Lesson: 01
Evaluation Systems of Equations KEY
Multiple choice questions
_C_ 1.
x = 2y - 5
Which of the following describes the solution to the
given system of equations?
5x - 6y = 7
A
C
x = 11, y = 8
B
_B_ 2.
x = 1, y =
Algebra 2
HS Mathematics
Unit: 09 Lesson: 01
Evaluation: Exponential and Logarithmic Functions KEY
The graph shows the function
1. Graph its inverse,
f ( x ) 2 x
f 1 ( x ) log 2 ( x )
.
. State the domain and
range of each.
Domain:
y>0
Domain:
x>0
Range:
Algebra 2
HS Mathematics
Unit: 10 Lesson: 01
Evaluation: Combined Systems KEY
Solve the following equations using factoring or the quadratic formula.
1)
2)
3)
2
2
x 3 x 28 0
2x 2 2 x 10 x 2 11x 20
2x 7 x 4
Solutions:
x = 7 or x = -4
Solutions:
x = 0.5 or
Algebra 2
HS Mathematics
Unit: 02 Lesson: 01
Characteristics of Relations and Functions KEY
1.
Cartesian coordinate plane
On the graph provided:
A) Label each axis.
y
B) Label each quadrant.
Quadrant: II
Quadrant: I
( - ,+)
(+,+)
Quadrant: III
x
Calculato
Algebra 2
HS Mathematics
Unit: 06 Lesson: 01
Coke and Mentos KEY
Did you know that if you drop Mentos candy pieces into a fresh bottle of Coke, the
soda will immediately start to fizz and shoot out the top of the bottle in a fountain?
A
physics class hypo