﻿ Algebra II Questionbook, Fall 2004

### Algebra II QUESTIONBOOK QUESTIONS© 1986, 1987, 1988, 1989, 2004, A. Azzolino

www.mathnstuff.com /math/algebra/qb/a2qb04r.htm     Cover Sheet

a2letr.
Write a letter to introduced yourself to your prof.
• Who are you? What are your non-math-class-worlds?
• Discuss how your roles in these worlds (family, home, work) might effect your performance in this class.
• Discuss how mathematics might play a role in your future.
• Perhaps state where you sit in class and the color and length of your hair.
• If your reply is not complete enough, the grade of "I ," for incomplete, will be assigned and you will have to resubmit your letter with additional information.
a2grch.
Include IN YOUR LETTER to me a statement that you "have read and understood the Grading Policy & Cheating Policy."
a2emal.

a2plan.
Create a plan to achieve whatever goal you have for THIS COURSE.
The prof's letter states: "2nd:
• Create a plan to achieve the task.
• Create a well-thought, organized, detailed, complete design, a vision of your task, and
• meditate upon it.
• If you wish, speak your plan aloud, share it on the phone with a friend,
• write the plan on paper and hand it in as a questionbook question .
• Create and refine your vision.
• Write and submit your plan to achieve your goal for the course and also to achieve questionbook credit.

a2birth.
Using the digits of your birth year, write expressions equivalent to the first 10 natural numbers -- 1, 2, 3, ..., 10.
For example: If you were born in 1949, 0 might be (9 - 9)(1)4

a2signd.
Summarize in word and with examples:
1st: how to add signed numbers;
2nd: how to subtract signed numbers;
3rd: how to multiply or divide signed numbers.
Use may use info at: "ABSOLUTELY NOT! - page 1, How to Add, Subtract, Multiply, Divide Signed Numbers - Writtten" as a resource.

a2solvf.
Solve using the shortcut discussed in class

a2q5.
Sometimes when one solves a first-degree equation in one variabIe, one finds exactly one solution. This is not a surprise.
Sometimes a first-degree linear equation has no solution or the equation has all real numbers as its solution. These situations often come as a surprise to the solver.

a.) How can an algebra student tell when the solution to an equation is "no solution?"

b.) How can one tell when the solution is "all real numbers?"

a2q6.
Draw a graph of real numbers such that both statements are true: x > -3 and x < 4.

Draw a second graph of the numbers such that both statements are true: x > -3 and x < - 4.

Explain why the two graphs look so different.

a2q7.
1st: Graph & Describe in words the numbers x described by I x I < 3.

2nd: Graph & Describe in words the numbers x described by |x | > 3.

a2q8.
The graph of |x + 2| < 5 is different from the graph of |xl < 5.
Graph each on a number line.

Describe how they are different

a2q9.
Write and solve a word problem similar to:
If a number is decreased by three, the result is the same as if the number were multiplied by five then increased by seven. Find the number.

a2q10.
Write in English a statement having the same meaning as:
am ÷ an = am - n

a2q11.
In one sentence, explain how to raise x cubed to the fifth power.
In other words, how do you simplify: (x3)5 ?

a2qlet2.
Write me a letter telling me how things are going in the course.

a2q13.
Write the DECIMAL form of each starting with the smallest and finishing with the largest.
2-1, 23, 32, 25, 52, 2-1, 2-1, 30, 20, 3-2, 2-2 2-3

a2q14.
The following are examples of expressions written in factored or in product form.
Some of the products have special names. Complete the table.
 Factored Form Product This is called a (x + y)2 ____________ ________________________ (x - y)2 ____________ ________________________ (x - y)(x2 + xy + y2) _________________ _________________________ (x + y)(x2 - xy + y2) _________________ _________________________ _________________ x2 - y2 __________________________ (x - yi)(x + yi) x2 + y2 _________________________ _________________ x3 + 3x2y + 3xy2 + y3 _________________________ _________________ x3 - 3x2y + 3xy2 - y3 _________________________ _________________ x4 + 4x3y + 6x2y2 + 4xy3 + y4 _________________________ _________________ x4 - 4x3y + 6x2y2 - 4xy3 + y4 _________________________

a2q15.
Describe the method of factoring each of the following. Factor over the reals.
a. 4yx2 - 8y
b. x2 - 64
c. x2 - 5x + 6

a2q16.
The expression 6x2- 7x - 10 is more difficult to factor than is the expression x2-7x +10.
Explain how to factor 6x2 - 7x - 10.

a2q17.
Discuss and give examples of methods of solving quadratic equations by factoring.
Let one example be just factoring.

Let one example be factoring after terms have been regrouped from different sides of the equation.

a2q18.
When solving equations with rational expressions it is important to include one step which is optional when solving other equations.
Give an example.
Discuss this additional step and why it is required.

a2q19. Write and solve your own proportion problem.

a2q20. Write and solve your own "work problem."

a2q21. Write the DECIMAL form of each of the following:
4-2, 4-1, (2/5)-1, (1/3)-1, (1/9)-1

a2q22. Complete:
Any number to the zero power, other than zero, is _____________.
Any number to the first power is ______________________________.

a2q23. Some text states a "Law of Radicals."
In equation form it is stated as:
In your own words, without symbols, explain this statement.

a2q24. The radical expression may be simplified but the radical expression can not be written in a simpler form. Why not?

a2q25. State the procedure for rationalizing a denominator.

Comment on simplifying fractions with cube roots in the demominator as well as those with square roots in the denominator.

a2q26. Compare the method of solving to the method of solving .

a2q27. Examine the list of rules for computation with complex numbers.
Copy the symbolic rules for addition, subtraction, multiplication, and division.
Give an example of computation using each operation.

a2q28. The line y = 5x - 4 may be graphed quickly by a method called slope-intercept.
1. Graph the line using the slope-intercept method.

2. In words, in 5 or fewer steps, state how this method is completed.
(Hint: List the instructions you would give to someone who needed to know how to do this.)

a2q29. The line 4x - 3y = 12 may be graphed quickly by a method called intercepts.
1. Graph the line using the intercept method.

2. In words, in 5 or fewer steps, state how this method is completed.
(Hint: List the instructions you would give to someone who needed to know how to do this.)

a2q30.
1. Graph a vertical line which goes
through the point (-3,4).

2. Name this line with an equation.
_________________

3. Graph a horizontal line which
contains the point (2,3).

4. Name this line with an equation.
_________________

a2q31. Write a letter to the prof relating how things are going.

a2q32.
1. State:
a. a sloppy definition of slope.
b. a clean definition of slope.
2. Give an example of a vertical lines and show the computation of its slope.
3. Give an example of a "tilted" or oblique line and show the computation of its slope.
4. Give an example of a horizontal line and show the computation of its slope.

a2q33. Draw each line and state the equation of a line:
#1) parallel to y = -4x + 8;
#2) intersecting y = -4x + 8;
#3) coincident to y = -4x + 8.

a2q34. You have been given the points (3,-4) and (2, 6).
List at least 3 things your instructor might ask you to do on the next test with this info.

a2q35. Use the graph of this square root function as an example in a discusion of domain and range.

 a2q36. Graph each of the following and discuss what feature in the equation creates the change in the graph of y=x2. 1st: y = (x + 3)2 2nd: y = x2 + 3 3rd: y = - x2.

a2q37. A log is an exponent.
Why then is the log of 32 base 2 equal to 5,
why is log2(32) = 5?

a2q38. What's the "magic number" when converting
Give some computational examples.

a2q39. Write a "cheat sheet" for the final exam.
It should fit on one side of an 8-1/2" by 11" sheet of paper.

a2draw.(up to 4 points)     Designing A Picture
 Demonstrate your mastery of the linear, quadratic, absolute value, square root and other functions (including half circles) and things (half-planes) studied in Algebra II, their graphs, and their symbolic expressions. Do this by creating an original and mathematically correct picture and set of expressions (with restrictions if needed).     The picture must use graphs of functions as its component parts and must represent something recognizable to the instructor.     The set of expressions, with domain and/or range restrictions, must, when graphed, produce the picture.     It is suggested that once you have completed your design and generating expressions, you have another person review and correct your work.     Here is an example worth 2 or 3 of a 4 possilbe points.     The graph paper below may be CLICKED then PRINTED on a separate sheet of paper if desired. One may also RIGHT CLICK on it with the mouse then SAVE the picture as a file.

Quiz Questions
Quiz - Simplifying Expressions
Quiz - Factoring & Expanding Polynomials
Quiz - Point-plotting Graphs
Quiz - Linear Equations & Other Functions
Quiz - Equations
Quiz - Word Problems

a2proj. Project Questions
Pr1. Title/Topic.
Pr2.& Pr3. Draft
Pr4. Conference
Pr5. Final Notes
Pr6. Presentation
Pr7. Test Question
Pr8. Web Page

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