Hearne ISD
Mathematics
Course: Algebra II
Unit: Polynomial, Exponential and Logarithmic Functions
TEKS
Assessment
Guiding Questions/
Specificity
Designated Six Weeks: 4th
Days to teach: 27 days
Vocabulary
Instructional
Strategies
Resources/
Web-links
2A.2 Foundations for functions. The student understands the importance of the skills required to manipulate symbols in order to solve problems and
uses the necessary algebraic skills required to simplify algebraic expressions and solve equations and inequalities in problem situation.
2A.2(A)The student
Perform basic polynomial
Simplify the following
End Behavior
Link to ELPS Instructional Holt Algebra 2
6.1
uses tools including
operations with functions.
expression:
Leading Coefficient
Strategies:
4x(2x2 – 3x + 5 ) –
http://ritter.tea.state.tx.us/rule 6.2
factoring, and
Local Maximum
( 3x+5)(4x – 1 )
6.3
s/tac/chapter074/ch074a.html
properties of
Factor polynomials
Local Minimum
1E, 2D, 3D
6.4
exponents to simplify functions.
Monomial
Answer:
6.5
expressions and to
Multiplicity
8x3 – 24x2 + 3x + 5
6.6
transform and solve
Solve polynomial
Polynomial
 Use square roots and
A rectangle has a length
functions by factoring.
equations.
Polynomial Function
quadratic formula
3
of (x – 5x + 2) units
Synthetic Division
Supporting
 Add and subtract
and a width of (5x – 3)
Turning Point
Standard
polynomial functions.
units. Which expression

Multiply polynomial
represents its area?
College Readiness
functions- apply to area
A. 5x4 – 3x3 – 25x2 +
Standard:
 Factoring:
25x – 6
http://www.thecb.state.t
 GCF
x.us/collegereadiness/cr
B. 5x3 + 22x2 – 5x – 6
 Binomials – square and
3
2
s.pdf
C. 5x – 28x + 25x – 6
cubes
4
3
2
D. 5x – 3x + 25x –
Numeric B.1.b

Trinomials – no lead
5x – 6
Algebraic B.1.a
coefficient and lead
Answer: A
Functions C.1.c
coefficient
Find an expression that
 Polynomials by grouping
represents the width of
 Solve polynomials after
a rectangle with length
factoring:
x + 5 and area
x3 + 12x2 + 47x + 60.
A. x2 + 7x + 12
B. x 17x 132  720
2
C.
x 5
50
x 2 17x 38 
x 5
D. x3 + 7x2 + 12x
Answer: A
7/3/2014
Page 1
Hearne ISD
Mathematics
Course: Algebra II
Unit: Polynomial, Exponential and Logarithmic Functions
TEKS
Assessment
Guiding Questions/
Specificity
Designated Six Weeks: 4th
Days to teach: 27 days
Vocabulary
Instructional
Strategies
Resources/
Web-links
2A.11 Exponential and logarithmic functions. The student formulates equations and inequalities based on exponential and logarithmic functions, uses a
variety of methods to solve them, and analyzes the solutions in terms of the situation.
2A.11(A) develop
the definition of
logarithms by
exploring and
describing the
relationship between
exponential functions
and their inverses;
Readiness Standard
College Readiness
Standard:
http://www.thecb.state.t
x.us/collegereadiness/cr
s.pdf
Functions B.2.g
Functions C.1.c
Develop the definition of
logarithms by looking at
an exponential function
and its inverse.
Develop the rule to convert
exponential form to
logarithmic form and vice
versa.
What is the inverse of
1
h(x)  log (x) ?
3
2
(2 x)
A. h (x) 3
1
B.
C.
h1 (x) 2(3)( x)
h1 (x) 2(log 3)
x
D.
h1 (x) log (2x)
3
Correct answer: A
Released EOC 2013
Q# 21
Inverse Function
Inverse Relation
Natural Logarithm
Natural Logarithmic
Function
Properties of
Logarithms
Link to ELPS Instructional
Strategies:
http://ritter.tea.state.tx.us/rule
s/tac/chapter074/ch074a.html
4F, 2D
Holt Algebra 2
7.2
7.4
7.6
Graph an exponential
function ( y = 2x ) and then
graph its inverse.
Show how the inverse of an
exponential is a logarithmic
function.
Convert between the two
forms of the problem: y = 2x
and y = log2 x.
Show students 490B- Holt
Example 505. Make sure
students understand the
properties of Exponents and
Logarithm Page 490 B – Holt
algebra II has a nice chart .
Example 1 pg. 505
7/3/2014
Page 2
Hearne ISD
Course: Algebra II
Unit: Polynomial, Exponential and Logarithmic Functions
TEKS
Assessment
Guiding Questions/
Specificity
Mathematics
Designated Six Weeks: 4th
Days to teach: 27 days
Vocabulary
Instructional
Strategies
Resources/
Web-links
2A.11 Exponential and logarithmic functions. The student formulates equations and inequalities based on exponential and logarithmic functions, uses a
variety of methods to solve them, and analyzes the solutions in terms of the situation.
Which type of
2A.11(B) use the
Recognize the parent
Asymptote
Link to ELPS Instructional Holt Algebra 2
transformation can be
7.1
parent functions to
function for exponential
Asymptotic behavior
Strategies:
used to obtain the graph Base
http://ritter.tea.state.tx.us/rule 7.7
investigate, describe,
and logarithmic functions.
s/tac/chapter074/ch074a.html
and predict the
Exponential Decay
of g(x) = 4(2x) from the
graph of f(x) = 2"?
3D
effects of parameter
Predict the changes in
Exponential Function
changes on the
domain and range when the F Vertical shrink
Exponential Growth
G Vertical shift down
Look at the effects of
graphs of exponential horizontal and vertical
H Vertical shift up
changing a, h, and k has on
and logarithmic
asymptotes are changed.
the parent functions of
3 Vertical stretch
functions, describe
exponential and logarithmic
limitations on the
Demonstrate that in y =abx, hQuestion 46
functions.
domains and ranges,
a represents the yand examine
intercept.
Compare and contrast the
asymptotic behavior;
graphs of y = 2x, y = -2x and
Supporting
y = 2(2)x and y = 2x +1 and
Standard
y = 2x+1 .
College Readiness
Discuss movement of
Standard:
http://www.thecb.state.t
asymptotes and new domain
x.us/collegereadiness/cr
and range.
s.pdf
Functions B.2.c,d
7/3/2014
Page 3
Hearne ISD
Mathematics
Course: Algebra II
Unit: Polynomial, Exponential and Logarithmic Functions
TEKS
Assessment
Guiding Questions/
Specificity
Designated Six Weeks: 4th
Days to teach: 27 days
Vocabulary
Instructional
Strategies
Resources/
Web-links
2A.11 Exponential and logarithmic functions. The student formulates equations and inequalities based on exponential and logarithmic functions, uses a
variety of methods to solve them, and analyzes the solutions in terms of the situation. The student is expected to:
What is the domain of
2A.11(C) determine
Discuss why the range of
Common Logarithm
Link to ELPS Instructional Holt Algebra 2
the function y = 3x-5
7.1
the reasonable
the exponential parent
Exponential Equation
Strategies:
http://ritter.tea.state.tx.us/rule 7.3
domain and range
function and the domain of
Logarithm
A. -5 < x < 5
7.5
s/tac/chapter074/ch074a.html
values of exponential the parent logarithmic
Logarithmic Equation
7.6
B. x > -5
3H, 3D
and logarithmic
function will not include
Logarithmic Function
C. x > 5
functions, as well as
negatives.
Natural Logarithmic
D. all real numbers
Show the relationship
interpret and
Function
between an exponential and
determine the
Look at graphs of
Answer: D
logarithmic function.
reasonableness of
exponential and
solutions to
logarithmic functions and
Look at the restrictions of
exponential and
how the asymptotes effect
What is the domain of
each graph in the domain and
logarithmic equations the domain and range.
the function:
range.
and inequalities;
F(x) = log8 ( x + 2 )
Supporting
Interpret and explain
Standard
A. x > 8
graphical representations.
B. x > 2
College Readiness
C. x > -2
Interpret and explain
Standard:
http://www.thecb.state.t
D. x > 0
equation representations.
x.us/collegereadiness/cr
s.pdf
Answer: C
Functions B.1.b,c
Functions C.1.c
7/3/2014
Page 4
Hearne ISD
Mathematics
Course: Algebra II
Unit: Polynomial, Exponential and Logarithmic Functions
TEKS
Assessment
Guiding Questions/
Specificity
Designated Six Weeks: 4th
Days to teach: 27 days
Vocabulary
Instructional
Strategies
Resources/
Web-links
2A.11 Exponential and logarithmic functions. The student formulates equations and inequalities based on exponential and logarithmic functions, uses a
variety of methods to solve them, and analyzes the solutions in terms of the situation. The student is expected to:
3
x
2A.11(D) determine
Solve exponential and
Exponential Equation
Link to ELPS Instructional Holt Algebra 2
4
Solve: 32 1653x
7.1
solutions of
logarithmic equations
Logarithmic Equation
Strategies:
http://ritter.tea.state.tx.us/rule 7.5
exponential and
using a variety of methods. A. 65
28
s/tac/chapter074/ch074a.html
logarithmic equations
37
4F
using graphs, tables,
Introduce change of base
B. 4
and algebraic
formula.
37
Solve exponential equations
methods;
C. 20
using inverse properties.
Supporting
95
Standard
D.
Solve logarithmic equations
28
using inverse properties.
College Readiness
Standard:
Answer: A
http://www.thecb.state.t
Utilize 4 corner model to
x.us/collegereadiness/cr
show graphs, tables,
Solve the equation
s.pdf
algebraic methods and verbal
using the properties of
representations.
logarithms:
Functions B.1.b,c
Functions C.1.c
Use properties of logarithms
2 log x + log 4 = 2
and exponential functions to
solve equations.
Answer: x = 5
Use a table and graph
solve 32x = 6561
Create the change of base
formula.
A.
B.
C.
D.
Solve using the calculator to
analyze graphs and tables.
x=8
x=4
x = 19
x = 6.5
Answer: x = 4
7/3/2014
Page 5
Hearne ISD
Mathematics
Course: Algebra II
Unit: Polynomial, Exponential and Logarithmic Functions
TEKS
Assessment
Guiding Questions/
Specificity
Designated Six Weeks: 4th
Days to teach: 27 days
Vocabulary
Instructional
Strategies
Resources/
Web-links
2A.11 Exponential and logarithmic functions. The student formulates equations and inequalities based on exponential and logarithmic functions, uses a
variety of methods to solve them, and analyzes the solutions in terms of the situation. The student is expected to:
2A.11(E) determine
Solve exponential and
The graph of the
Exponential Equation
Link to ELPS Instructional Holt Algebra 2
7.5
solutions of
logarithmic inequalities by
exponential function f is Logarithmic Equation
Strategies:
http://ritter.tea.state.tx.us/rule
exponential and
looking at tables or graphs
shown on the grid
s/tac/chapter074/ch074a.html
logarithmic
on the calculator.
below.
4F
inequalities using
graphs and tables;
Use graphs to solve
and
logarithmic and exponential
Supporting
inequalities.
Standard
College Readiness
Standard:
http://www.thecb.state.t
x.us/collegereadiness/cr
s.pdf
Functions B.1.b,c
Functions C.1.c
7/3/2014
For what values of x is
f(x)>16?
F. x > -2
G. x > 0
H. -2 < x < 2
J. ∞ < x < -2
Correct answer: F
Released EOC 2013
Q#30
Write the solutions as
inequalities.
Understand solutions will be
infinite.
Page 6
Hearne ISD
Course: Algebra II
Unit: Polynomial, Exponential and Logarithmic Functions
TEKS
Assessment
Guiding Questions/
Specificity
Mathematics
Designated Six Weeks: 4th
Days to teach: 27 days
Vocabulary
Instructional
Strategies
Resources/
Web-links
2A.11 Exponential and logarithmic functions. The student formulates equations and inequalities based on exponential and logarithmic functions, uses a
variety of methods to solve them, and analyzes the solutions in terms of the situation. The student is expected to:
2A.11(F) analyze a
Create an exponential
There were 417 cell
Exponential Equation
Link to ELPS Instructional Holt Algebra 2
7.1
situation modeled by
function modeled by a
phones sold at an
Logarithmic Equation
Strategies:
http://ritter.tea.state.tx.us/rule 7.5
an exponential
situation.
electronics store in
Natural Logarithm
7.6
s/tac/chapter074/ch074a.html
function, formulate
January. Since then,
Natural Logarithmic
4F
an equation or
Use the function to solve
cell phone sales at this
Function
inequality, and solve
the given situation.
store have increased at
Use a four corners model to
the problem.
a rate of 3.75% per
represent exponential
month. At this rate of
Readiness Standard Talk about Chili 2010 8.8
functions using a table, a
quake, New Zealand 2011
growth, which function
graph, a function rule
8.9, and Japan 2011 9.0.
can be used to
College Readiness
(equation), and a verbal
Compare and Contrast.
determine the monthly
Standard:
http://www.thecb.state.t
description.
cell phone sales m
x.us/collegereadiness/cr
months after January?
s.pdf
Concentrate on the following
A. p(m) 417(0.0375)m
types of situations:
Functions B.1.b,c
B. p(m) 417(1.0375)m
Growth and Decay
Functions C.1.c
C. p(m) 417(0.9625)(m1)
Half-Life
D. p(m) 417(0.0375)(m1)
Compound Inequalities
Correct answer: B
Magnitude
Released EOC 2013
Decibel
Q#7
7/3/2014
Page 7