Your
Algebra II
Playbook
Algebra II Playbook
A Webquest for MCHS Algebra II Students
Designed by
Jane Moore
jmoore@mariposa.k12.ca.us
uh-oh, finals are coming . . .
Last Adapted 11/30/2008
Your Algebra II Playbook, a WebQuest
A WebQuest is an inquiry-oriented activity that solves a problem by
evaluating information, being creativity, and using critical-thinking skills.
Task This is amazing. Two new twin students, Polly and Ben Nomial, are
going to transfer to MCHS and be in our class. They will still need to take
the Algebra II First Semester Final even though they are transferring from a
much inferior high school not having such a good teacher much less such
wonderful kids! You will need to help them if they have a chance of learning
everything for the final and do well on the final. The first semester final
covers any concepts or information in chapters one through five of our text.
The Nomial siblings should be able to:
 Find complete solutions to inequality and absolute value equations
and inequalities.
 Identify solutions of systems of inequalities from graphs.
 Graph, write, and solve quadratic functions given in various forms,
 Find the axis of symmetry, vertex, and the minimum or maximum
values.
 Solve quadratic equations with real and/or imaginary solutions
using a variety of methods such as by factoring, the square root
principle, and completing the square.
 Perform operations with square roots and complex numbers.
 Simplify rational expressions that have a complex number
denominator.
 Simplify powers of i.
 Graph polynomial functions using knowledge of the shape of the
graph, of end behavior, the degree, and the zeros.
 Perform polynomial operations including polynomial division and
synthetic division.
 Solve polynomial equations by finding all zeros.
Process You need to create an Algebra II Playbook to share with Polly and
Ben. Use the given resources, or ones you find on your own, and create a
way for our new students to study, advice how to study that is based on
research, and design a practice multiple choice test that helps them prepare
for questions on the final. The following must be included in your activity:
1. Describe, show, tell how to study for our final, especially how
to study for and answer multiple multiple-choice questions on
the final. This must be researched-based and as effective as
possible.
2. A concise, but detailed, inventory of skills. This should be a
how-to-do device. It can be power point, video, graphic
organizer, or a mini-Cliff Notes.
It needs to include
explanations and how to do every kind of problem that could
be asked on the final. It must be designed to help Polly and
Ben be successful on the final!
3. Write a sample multiple-choice test with problems designed
from the short-answer practice test given in the recourses. It
must have at least 2 questions from each starred standard.
You may write more questions if you fell they are important to
include.
Be sure to include enhanced multiple choice
questions that ask to ‘find the incorrect step’ and what a
coefficient means in a quadratic or polynomial form. Answers
to the test must be given on a separate sheet.
Resources
TEST-TAKING SKILLS
Test Taking Tips for Math
http://www.mathpower.com/tip4.htm
Coolmath! How to Study for a Math Exam
http://www.coolmath.com/studytip.htm
How to Study for a Math Test
http://www.wikihow.com/Study-for-a-Math-Exam
YouTube HOW DO YOU STUDY FOR A MATH TEST?
http://www.youtube.com/watch?v=pm-svWfQP0A
Study Guides and Strategies
http://www.studygs.net/tsttak6.htm
Math Test-Taking Skills
http://wc.pima.edu/~carem/MATHTEST.html
Math Study Skills – The Final Exam
Link to Time Management Skills
http://salsa.missioncollege.org/mss/stories/storyReader$28
Suggestions to Students for Improving Math Study Skills
http://academic.cuesta.edu/acasupp/as/702.htm
Math Study Skills Inventory
http://mtsu32.mtsu.edu:11064/skill.html
Improving Math Study and Test Taking Skills, 6 Types Test Taking
Errors
http://people.richland.edu/james/misc/testtake.html
Brochure: Success in Mathematics
http://mathcs.slu.edu/undergrad-math/SuccessinMath.pdf
How to Take a Math Test or Quiz
http://www.tc3.edu/instruct/sbrown/math/test.htm
PRACTICE TESTS INFORMATION & CONTENT HELP
Test Prep Review
http://www.testprepreview.com/
Algebra II Glossary from Cliff Notes
Tools & Resources: Algebra II Glossary - CliffsNotes
Algebra II Study Cheat Sheet from Cliff Notes
http://www.cliffsnotes.com/WileyCDA/Section/Algebra-II-CheatSheet.id-305499,articleId-29901.html
Test Prep Review – Free Online Practice Tests
http://www.testprepreview.com/
Algebra II Publisher Holt Homework Help and Videos Site
NICE Examples, Videos, and Practice Problems - May need to find
correct section.
http://go.hrw.com/hrw.nd/gohrw_rls1/pKeywordResults?keyword=MB7+H
WHelp
Chapter 1 Foundations for Functions
Chapter 2 Linear Functions
Chapter 3 Linear Systems
Chapter 4 Matrices
Chapter 5 Quadratic Functions
Chapter 6 Polynomial Functions
Mathematics Content Standards - Algebra II Semester I Chapters 1 5
This discipline complements and expands the mathematical content and concepts of
algebra I and geometry. Students who master algebra II will gain experience with
algebraic solutions of problems in various content areas, including the solution of
systems of quadratic equations, logarithmic and exponential functions, the binomial
theorem, and the complex number system.
*1.0 Students solve equations and inequalities involving absolute value.
*2.0 Students solve systems of linear equations and inequalities (in two or three variables)
by substitution, with graphs, or with matrices.
*3.0 Students are adept at operations on polynomials, including long division.
*4.0 Students factor polynomials representing the difference of squares, perfect square
trinomials, and the sum and difference of two cubes.
*5.0 Students demonstrate knowledge of how real and complex numbers are related both
arithmetically and graphically. In particular, they can plot complex numbers as points in
the plane.
*6.0 Students add, subtract, multiply, and divide complex numbers.
*8.0 Students solve and graph quadratic equations by factoring, completing the square, or
using the quadratic formula. Students apply these techniques in solving word problems.
They also solve quadratic equations in the complex number system.
*9.0 Students demonstrate and explain the effect that changing a coefficient has on the
graph of quadratic functions; that is, students can determine how the graph of a parabola
2
changes as a, b, and c vary in the equation y = a(x-b) + c.
*10.0 Students graph quadratic functions and determine the maxima, minima, and zeros of
the function.
11.0 Students prove simple laws of logarithms.
*11.2 Students judge the validity of an argument according to whether the properties
of real numbers, exponents, and logarithms have been applied correctly at each step.
12.0 Students know the laws of fractional exponents, understand exponential functions,
and use these functions in problems involving exponential growth and decay.
24.0 Students solve problems involving functional concepts, such as composition,
defining the inverse function and performing arithmetic operations on functions.
25.0 Students use properties from number systems to justify steps in combining and
simplifying functions.
Algebra 1st Semester Practice Problems Chapters 1 - 5
Identify the property shown.
1. 50 + 0 = 50
Evaluate the expression.
2. –4x2 + 6xy when x = 2 and y = 5
Simplify the expression.
3. 4y + 6x
3(x
2y)
Solve the equation.
4. 4x + 21 = 7(x + 9)
3
9. Boiling Lake is a small lake on the island of
Dominica. The water temperature of the
lake is between 180 F and 197 F. Write a
compound inequality for this temperature
range. Graph the inequality.
Graph the equation.
10. 3x
2y
2=0
Write an equation of the line that passes
through the given point and has the given
slope. Write the equation in slope-intercept
form.
5.
11. (-5, 6), m = 3
Solve the equation for y.
6. 2xy + x = 12
12. Write an equation of the line that passes
through (–3, 4) and is perpendicular to the
line y = 2x 5.
Solve the inequality. Then graph your solution.
7.
8.
x+2
4
13. The variables x and y vary directly. When
. Write an equation that relates
the variables.
Graph the function.
14.
The table shows the number p (in thousands) of patents issued to United States residents where t is the
number of years since 1985. Draw a scatter plot of the data and describe the correlation shown. Then
approximate the best-fitting line for the data.
15. Source: Statistical Abstract of the United States
Graph the linear system and tell how many
solutions it has. If there is exactly one solution,
estimate the solution and check it algebraically.
Solve the matrix equation for x and y.
22.
16. y = 2x + 2
y = 2x 3
Evaluate the determinant of the matrix.
Solve the system using any algebraic method.
17. x y = 5
x + y = 11
23.
18. x + 3y z = 1
–4x 2y + 5z = 16
7x + 10y + 6z = 15
Graph the system of linear inequalities.
Use Cramer's rule to solve the linear system.
24. –4x + 5y = 10
5x 6y = 13
19. x + y 7
2x y 5
x
2
20. You are buying beads and string to make a
necklace. The string costs $1.50, a package
of 10 decorative beads costs $.50, and a
package of 25 plain beads costs $.75. You
can spend only $7.00 and you need 150
beads. How many packages of each type of
bead should you buy?
Perform the indicated operation(s).
Solve the matrix equation.
25.
Graph the quadratic function.
26. y =
(x + 1)(x
27. Write y = 4(x
5)
3)2
7 in standard form.
Solve the equation by factoring.
21.
28. 9x2 + 6x + 1 = 0
Write the expression as a complex number in
standard form.
38.
29. (8 + i)(6 + 2i)
Divide. Use synthetic division if possible.
Solve the equation by completing the square.
39.
30.
List all the possible rational zeros of f using the
rational zero theorem. Then find all the zeros
of the function.
Solve the quadratic equation using any
appropriate method.
31. 3(p
9)2 = 81
32. 6t2
2t + 2 = 4t2 + t
40.
Write a polynomial function of least degree
that has real coefficients, the given zeros, and a
leading coefficient of 1.
Graph the quadratic inequality.
33. y
x2 + 4x + 2
Solve the quadratic inequality.
34. 2x2
9 > 23
35. An insurance company charges a 35-yearold nonsmoker an annual premium of $118
for a $100,000 term life insurance policy.
The premiums for 45-year-old and 55-yearold nonsmokers are $218 and $563,
respectively. Write a quadratic model for
the premium p as a function of age a.
41. 1, 3, 4
42. Identify the x-intercepts, local maximum,
and local minimum of the graph of
f(x) = x3 + 2x2 13x + 10.
43. Show that
has nonzero
constant fourth-order differences.
Evaluate the expression without using a
calculator.
44.
Simplify the expression. Tell which properties
of exponents you used.
36.
Simplify the expression. Assume all variables
are positive.
45.
Describe the end behavior of the graph of the
polynomial function. Then evaluate the
function for x = 4, 3, 2, ... , 4. Then graph
the function.
Perform the indicated operation and state the
domain.
46.
37.
Perform the indicated operation.
47.
Find the inverse function.
48.
Graph the function. Then state the domain and
range.
49.
Solve the equation. Check for extraneous
solutions.
50.
Evaluation: The WebQuest ‘Your Algebra II Playbook’ counts as a TEST. Our
work must meet standards, must be complete, and submitted on time on the
due date. No late playbooks will be accepted.
+4 Exceeds Standards
+3 Meets Standards
All relevant material must be included and sited.
All work must be mathematically correct.
All Parts must be complete and turned in or emailed to me at my gaggle
address found on the MCHS Homepage.
1. How to study and take a test.
2. An inventory of skills that will be on the test.
3. A Practice Test.
WebQuest turned in on time.
Conclusion: Congratulations! You have not only helped the Polly and
Ben Nomial, but you have studied for your Algebra II first semester final!!