ÿþ <HTML><HEAD><TITLE>Algebra II Questionbook, Fall 2004</TITLE></HEAD> <body background="//www.mathnstuff.com/gif/grabkg.jpg" leftmargin=30 rightmargin=20><A NAME="top"></A> <A HREF="//www.mathnstuff.com/math/algebra/qb/a2qb04a.htm"> <IMG SRC="//www.mathnstuff.com/math/algebra/qb/gif/a2qb.gif" ALT="QB, graded assignments" align="left"></A> <A HREF="//www.mathnstuff.com/math/algebra/algebra.htm"> <IMG SRC="//www.mathnstuff.com/math/algebra/qb/gif/algnote.gif" align=left alt="Notes Sorted by Topic"></A> <A HREF="//www.mathnstuff.com/math/algebra/qb/algqb00.htm"> <IMG SRC="//www.mathnstuff.com/math/algebra/qb/gif/algqb.gif" ALT="QB, graded assignments" align="left"></A> <A HREF="//www.mathnstuff.com/math/math.htm"> <img src="//www.mathnstuff.com/gif/semestr.gif" width="45" alt="math home" align="left"></A> <dl><dt><h3>Algebra II QUESTIONBOOK QUESTIONS<br><dd>&copy; 1986, 1987, 1988, 1989, 2004, <a href="mailto:algebra@mathnstuff.com">A. Azzolino</a></h3></dl> <a href="//www.mathnstuff.com/inc.htm">www.mathnstuff.com</a> /<A HREF="//www.mathnstuff.com/math/math.htm">math</A>/algebra/<A HREF="a2qb04a.htm">qb</a>/a2qb04r.htm &nbsp; &nbsp; <a href="a2qb04r.htm">Cover Sheet</a> <!-- ------------------ --> <br><hr color="black"><br> <DL><DT><a href="a2letr.htm">a2letr</a>. <dt>Read the prof's <a href="//www.mathnstuff.com/math/letr.htm">letter</a> and reply. <Dt> Write a letter to introduced yourself to your prof. </dl> <ul> <li>Who are you? What are your non-math-class-worlds? <li>Discuss how your roles in these worlds (family, home, work) might effect your performance in this class. <li>Write about your math background. Tell me of your strengths, weaknesses, fears, and goals. <li>Discuss how mathematics might play a role in your future. <li>Tell me what I can do to help you achieve your goals for this class. <li>Perhaps state where you sit in class and the color and length of your hair. <li>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. </uL> <DL><DT>a2grch. <Dt>Read the "Grading & Cheating Policy" linked through the home page for your course. <dd>Include IN YOUR LETTER to me a statement that you "have read and understood the Grading Policy & Cheating Policy." </DL> <DL><DT>a2emal. <DD>Include IN YOUR LETTER your email address (one that is checked on a regular basis).</DL> <br><hr color="black"><br> <DL><DT><a href="a2plan.htm">a2plan</a>. <Dt>Create a plan to achieve whatever goal you have for THIS COURSE. <dt>The prof's letter states: "2nd:</dl> <ul> <li> Create a plan to achieve the task. <li>Create a well-thought, organized, detailed, complete design, a vision of your task, and <li>meditate upon it. <li>If you wish, speak your plan aloud, share it on the phone with a friend, <li>write <a name="plan"><font color="red">the plan on paper and hand it in as a questionbook question</font color="red"></a> . <li>Create and refine your vision. <li>Write and submit your plan to achieve your goal for the course and also to achieve questionbook credit. </uL> <!-- ------------------ --> <br><hr color="black"><br> <DL><DT><a href="a2birth.htm">a2birth</a>. <dt>Using the digits of your birth year, write expressions equivalent to the first 10 natural numbers -- 1, 2, 3, ..., 10. <dd>For example: If you were born in 1949, 0 might be (9 - 9)(1)<sup>4</sup> </DL> <!-- ------------------ --> <br><hr color="black"><br> <DL><DT><a href="a2signd.htm">a2signd</a>. <dt>Summarize in word and with examples: <dd>1st: how to add signed numbers; <dd>2nd: how to subtract signed numbers; <dd>3rd: how to multiply or divide signed numbers. <d>&nbsp; <dt>Use may use info at: "<a href="//www.mathnstuff.com/math/spoken/here/2class/130/c13how2.htm">ABSOLUTELY NOT!</a> - page 1, How to Add, Subtract, Multiply, Divide Signed Numbers - Writtten" as a resource. </DL> <!-- ------------------ --> <br><hr color="black"><br> <DL><DT><a href="a2solvf.htm">a2solvf</a>. <dt>Solve using the shortcut discussed in class <dd><img src="gif/a2solvf.gif"> </DL> <!-- ------------------ --> <br><hr color="black"><br> <DL><DT><a href="a2q5.htm">a2q5</a>. <dt>&nbsp; &nbsp; &nbsp; Sometimes when one solves a first-degree equation in one variabIe, one finds exactly one solution. This is not a surprise. <dt>&nbsp; &nbsp; &nbsp; 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. <dd>&nbsp; <dd>a.) How can an algebra student tell when the solution to an equation is "no solution?" <dd>&nbsp; <dd>b.) How can one tell when the solution is "all real numbers?" </DL> <!-- ------------------ --> <br><hr color="black"><br> <DL><DT><a href="a2q6.htm">a2q6</a>. <dt>Draw a graph of real numbers such that both statements are true: x > -3 and x < 4. <dd>&nbsp; <dd><img src="//www.mathnstuff.com/gif/line.gif"> <dd>&nbsp; <dt>Draw a second graph of the numbers such that both statements are true: x > -3 and x < - 4. <dd><img src="//www.mathnstuff.com/gif/line.gif"> <dd>&nbsp; <dt>Explain why the two graphs look so different. </DL> <!-- ------------------ --> <br><hr color="black"><br> <DL><DT><a href="a2q7.htm">a2q7</a>. <dt>1st: Graph & Describe in words the numbers x described by I x I < 3. <dd>&nbsp; <dd><img src="//www.mathnstuff.com/gif/line.gif"> <dd>&nbsp; <dt>2nd: Graph & Describe in words the numbers x described by |x | > 3. <dd><img src="//www.mathnstuff.com/gif/line.gif"> <dd>&nbsp; </DL> <br><hr color="black"><br> <DL><DT><a href="a2q8.htm">a2q8</a>. <dt>The graph of |x + 2| < 5 is different from the graph of |xl < 5. <dt>Graph each on a number line. <dd>&nbsp; <dd><img src="//www.mathnstuff.com/gif/line.gif"> <dd>&nbsp; <dd><img src="//www.mathnstuff.com/gif/line.gif"> <dd>&nbsp; <dt>Describe how they are different </DL> <br><hr color="black"><br> <DL><DT><a href="a2q9.htm">a2q9</a>. <dd>Write and solve a word problem similar to: <dt>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. </DL> <br><hr color="black"><br> <DL><DT><a href="a2q10.htm">a2q10</a>. <dt>Write in English a statement having the same meaning as: <dd>a<sup>m</sup> &divide; a<sup>n</sup> = a<sup>m - n</sup> </DL> <br><hr color="black"><br> <DL><DT><a href="a2q11.htm">a2q11</a>. <dt>In one sentence, explain how to raise x cubed to the fifth power. <dd>In other words, how do you simplify: (x<sup>3</sup>)<sup>5</sup> ? <DD> </DL> <br><hr color="black"><br> <DL><DT><a href="a2qlet2.htm">a2qlet2</a>. <dt>Write me a letter telling me how things are going in the course. </DL> <br><hr color="black"><br> <DL><DT><a href="a2q13.htm">a2q13</a>. <dt>Write the DECIMAL form of each starting with the smallest and finishing with the largest. <dd> 2<sup>-1</sup>, 2<sup>3</sup>, 3<sup>2</sup>, 2<sup>5</sup>, 5<sup>2</sup>, 2<sup>-1</sup>, 2<sup>-1</sup>, 3<sup>0</sup>, 2<sup>0</sup>, 3<sup>-2</sup>, 2<sup>-2</sup> 2<sup>-3</sup> </DL> <br><hr color="black"><br> <DL><DT><a href="a2q14.htm">a2q14</a>. <dt>&nbsp; &nbsp; &nbsp; The following are examples of expressions written in factored or in product form. <dt>&nbsp; &nbsp; &nbsp; Some of the products have special names. Complete the table. </dl> <CENTER><TABLE bgcolor=white><TR> <TD>Factored Form</TD><TD>Product</TD><TD>This is called a</TD> </TR><TR> <TD>(x + y)<sup>2</sup></TD><TD>____________</TD><TD>________________________</TD> </TR><TR> <TD>(x - y)<sup>2</sup></TD><TD>____________ </TD><TD>________________________</TD> </TR><TR> <TD>(x - y)(x<sup>2</sup> + xy + y<sup>2</sup>)</TD><TD>_________________</TD><TD>_________________________</TD> </TR><TR> <TD>(x + y)(x<sup>2</sup> - xy + y<sup>2</sup>)</TD><TD>_________________</TD><TD>_________________________</TD> </TR><TR> <TD>_________________</TD><TD>x<sup>2</sup> - y<sup>2</sup></TD><TD>__________________________</TD> </TR><TR> <TD>(x - y<i>i</>)(x + y<i>i</i>)</TD><TD>x<sup>2</sup> + y<sup>2</sup></TD><TD>_________________________</TD> </TR><TR> <TD>_________________</TD> <TD>x<sup>3</sup> + 3x<sup>2</sup>y + 3xy<sup>2</sup> + y<sup>3</sup></TD><TD>_________________________</TD> </TR><TR> <TD>_________________</TD> <TD>x<sup>3</sup> - 3x<sup>2</sup>y + 3xy<sup>2</sup> - y<sup>3</sup></TD><TD>_________________________</TD> </TR><TR> <TD>_________________</TD> <TD>x<sup>4</sup> + 4x<sup>3</sup>y + 6x<sup>2</sup>y<sup>2</sup> + 4xy<sup>3</sup> + y<sup>4</sup></TD><TD>_________________________</TD> </TR><TR> <TD>_________________</TD> <TD>x<sup>4</sup> - 4x<sup>3</sup>y + 6x<sup>2</sup>y<sup>2</sup> - 4xy<sup>3</sup> + y<sup>4</sup></TD><TD>_________________________</TD> </TR></TABLE></CENTER> <br><hr color="black"><br> <DL><DT><a href="a2q15.htm">a2q15</a>. <dt>Describe the method of factoring each of the following. Factor over the reals. <dd>a. 4yx<sup>2</sup> - 8y <dd>b. x<sup>2</sup> - 64 <dd>c. x<sup>2</sup> - 5x + 6 </DL> <br><hr color="black"><br> <DL><DT><a href="a2q16.htm">a2q16</a>. <dt>The expression 6x<sup>2</sup>- 7x - 10 is more difficult to factor than is the expression x<sup>2</sup>-7x +10. <dt>Explain how to factor 6x<sup>2</sup> - 7x - 10. </DL> <br><hr color="black"><br> <DL><DT><a href="a2q17.htm">a2q17</a>. <dt>Discuss and give examples of methods of solving quadratic equations by factoring. <dd>Let one example be just factoring. <dd>&nbsp; <dd>Let one example be factoring after terms have been regrouped from different sides of the equation.</DL> <br><hr color="black"><br> <DL><DT><a href="a2q18.htm">a2q18</a>. <dt>&nbsp; &nbsp; &nbsp; When solving equations with rational expressions it is important to include one step which is optional when solving other equations. <dd>Give an example. <dd>Discuss this additional step and why it is required. </DL> <br><hr color="black"><br> <DL><DT><a href="a2q19.htm">a2q19</a>. Write and solve your own proportion problem. </DL> <br><hr color="black"><br> <DL><DT><a href="a2q20.htm">a2q20</a>. Write and solve your own "work problem." </DL> <br><hr color="black"><br> <DL><DT><a href="a2q21.htm">a2q21</a>. Write the DECIMAL form of each of the following: <dd> 4<sup>-2</sup>, 4<sup>-1</sup>, (2/5)<sup>-1</sup>, (1/3)<sup>-1</sup>, (1/9)<sup>-1</sup> </DL> <br><hr color="black"><br> <DL><DT><a href="a2q22.htm">a2q22</a>. Complete: <dd>Any number to the zero power, other than zero, is _____________. <dd>Any number to the first power is ______________________________. </DL> <br><hr color="black"><br> <DL><DT><a href="a2q23.htm">a2q23</a>. Some text states a "Law of Radicals." <dt>In equation form it is stated as: <dd><img src="gif/a2qb2.gif"> <dt>In your own words, without symbols, explain this statement. </DL> <br><hr color="black"><br> <DL><DT><a href="a2q24.htm">a2q24</a>. The radical expression <img src="gif/a2qb3.gif"> may be simplified but the radical expression <img src="gif/a2qb4.gif"> can not be written in a simpler form. Why not? </DL> <br><hr color="black"><br> <DL><DT><a href="a2q25.htm">a2q25</a>. State the procedure for rationalizing a denominator. <dd>&nbsp; <dt>Comment on simplifying fractions with cube roots in the demominator as well as those with square roots in the denominator. </DL> <br><hr color="black"><br> <DL><DT><a href="a2q26.htm">a2q26</a>. Compare the method of solving <img src="gif/a2qb5.gif"> to the method of solving <img src="gif/a2qb6.gif">. </DL> <br><hr color="black"><br> <DL><DT><a href="a2q27.htm">a2q27</a>. Examine the <a href="//www.mathnstuff.com/math/spoken/here/2class/0/c0comp.gif">list</a> of rules for computation with complex numbers. <dd>Copy the symbolic rules for addition, subtraction, multiplication, and division. <dd>Give an example of computation using each operation. </DL> <br><hr color="black"><br> <IMG SRC="//www.mathnstuff.com/gif/5x5plan.gif"> <DL><DT><a href="a2q28.htm">a2q28</a>. The line y = 5x - 4 may be graphed quickly by a method called slope-intercept. <dd>1. Graph the line using the slope-intercept method. <dd>&nbsp; <dd>2. In words, in 5 or fewer steps, state how this method is completed. <dd>(Hint: List the instructions you would give to someone who needed to know how to do this.) </DL> <br><hr color="black"><br> <IMG SRC="//www.mathnstuff.com/gif/5x5plan.gif"> <DL><DT><a href="a2q29.htm">a2q29</a>. The line 4x - 3y = 12 may be graphed quickly by a method called intercepts. <dd>1. Graph the line using the intercept method. <dd>&nbsp; <dd>2. In words, in 5 or fewer steps, state how this method is completed. <dd>(Hint: List the instructions you would give to someone who needed to know how to do this.) </DL> <br><hr color="black"><br> <IMG SRC="//www.mathnstuff.com/gif/5x5plan.gif"> <DL><DT><a href="a2q30.htm">a2q30</a>. <Dt>1. Graph a vertical line which goes <dd>through the point (-3,4).<dd>&nbsp; <Dt>2. Name this line with an equation.<dd>_________________<dd>&nbsp; <Dt>3. Graph a horizontal line which <dd>contains the point (2,3).<dd>&nbsp; <Dt>4. Name this line with an equation.<dd>_________________<dd>&nbsp; </DL> <br><hr color="black"><br> <DL><DT><a href="a2q31.htm">a2q31</a>. Write a letter to the prof relating how things are going. </DL> <br><hr color="black"><br> <IMG SRC="//www.mathnstuff.com/gif/5x5plan.gif"> <DL><DT><a href="a2q32.htm">a2q32</a>. <dt>1. State: <dd>a. a sloppy definition of slope. <dd>b. a clean definition of slope. <dt>2. Give an example of a vertical lines and show the computation of its slope. <dt>3. Give an example of a "tilted" or oblique line and show the computation of its slope. <dt>4. Give an example of a horizontal line and show the computation of its slope. </DL> <br><hr color="black"><br> <IMG SRC="//www.mathnstuff.com/gif/5x5plan.gif"> <DL><DT><a href="a2q33.htm">a2q33</a>. Draw each line and state the equation of a line: <dd>#1) parallel to y = -4x + 8; <dd>#2) intersecting y = -4x + 8; <dd>#3) coincident to y = -4x + 8. </DL> <br><hr color="black"><br> <DL><DT><a href="a2q34.htm">a2q34</a>. You have been given the points (3,-4) and (2, 6). <dd>List at least 3 things your instructor might ask you to do on the next test with this info. </DL> <br><hr color="black"><br> <IMG SRC="//www.mathnstuff.com/math/algebra/gif1/0208h.gif"> <DL><DT><a href="a2q35.htm">a2q35</a>. Use the graph of this square root function as an example in a discusion of <a href="//www.mathnstuff.com/math/spoken/here/1words/d/d39.htm">domain</a> and <a href="//www.mathnstuff.com/math/spoken/here/1words/r/r7.htm">range</a>. </DL> <br><hr color="black"><br> <table><tr><td> <IMG SRC="//www.mathnstuff.com/gif/4by4.gif"></td><td> <IMG SRC="//www.mathnstuff.com/gif/4by4.gif"></td></tr> <tr><td> <IMG SRC="//www.mathnstuff.com/gif/4by4.gif"></td><td width="300"> <DL><DT><a href="a2q36.htm">a2q36</a>. Graph each of the following and discuss what feature in the equation creates the change in the graph of y=x<sup>2</sup>. <dd>1st: y = (x + 3)<sup>2</sup> <dd>2nd: y = x<sup>2</sup> + 3 <dd>3rd: y = - x<sup>2</sup>. </DL></td></tr> </table> <br><hr color="black"><br> <DL><DT><a href="a2q37.htm">a2q37</a>. A log is an exponent. <dd>Why then is the log of 32 base 2 equal to 5, <dd>why is log<sub>2</sub>(32) = 5? </DL> <br><hr color="black"><br> <DL><DT><a href="a2q38.htm">a2q38</a>. What's the "magic number" when converting <dd>degrees to radians? <dd>radians to degrees? <dt>Give some computational examples. </DL> <br><hr color="black"><br> <DL><DT><a href="a2q39.htm">a2q39</a>. Write a "cheat sheet" for the final exam. <dt>It should fit on one side of an 8-1/2" by 11" sheet of paper. </DL> <br><hr color="black"><br> <DL><DT><a href="a2draw.htm">a2draw</a>.(up to 4 points) &nbsp; &nbsp; Designing A Picture</dl> <TABLE width=600><TR><TD> <P>&nbsp; &nbsp; 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).</P> <P>&nbsp; &nbsp; The picture must use graphs of functions as its component parts and must represent something recognizable to the instructor.</P> <P>&nbsp; &nbsp; The set of expressions, with domain and/or range restrictions, must, when graphed, produce the picture.</P> <P>&nbsp; &nbsp; It is suggested that once you have completed your design and generating expressions, you have another person review and correct your work.</P> <P>&nbsp; &nbsp; Here is an <a href="gif/a2draw.jpg">example</a> worth 2 or 3 of a 4 possilbe points.</P> <P>&nbsp; &nbsp; 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.</P> </TD></TR></TABLE> <a href="//www.mathnstuff.com/gif/mciplane.gif"> <IMG SRC="//www.mathnstuff.com/gif/mciplane.gif" ALT="coord plane"></a> </DL> <br><hr color="black"><br> <DL><DT> Quiz Questions <dd>Quiz - Simplifying Expressions <dd>Quiz - Factoring & Expanding Polynomials <dd>Quiz - Point-plotting Graphs <dd>Quiz - Linear Equations & Other Functions <dd>Quiz - Equations <dd>Quiz - Word Problems </DL> <br><hr color="black"><br> <DL><DT><a href="a2proj.htm">a2proj</a>. Project Questions <DD>Pr1. Title/Topic. <DD>Pr2.& Pr3. Draft <DD>Pr4. Conference <DD>Pr5. Final Notes <DD>Pr6. Presentation <DD>Pr7. Test Question <DD>Pr8. Web Page </DL> <br><hr color="black"><br> </td></tr></table><!-- ------------------------------------- --> <!--------------><TABLE><TR><TD VALIGN="top"> <DL><dt><a href="algqb00.htm"> <A HREF="//www.mathnstuff.com/math/algebra/qb/a2qb04a.htm"> <IMG SRC="//www.mathnstuff.com/math/algebra/qb/gif/a2qb.gif" ALT="QB, graded assignments" align="left"></A> <A HREF="//www.mathnstuff.com/math/algebra/algebra.htm"> <IMG SRC="//www.mathnstuff.com/math/algebra/qb/gif/algnote.gif" align=left alt="Notes Sorted by Topic"></A> <A HREF="//www.mathnstuff.com/math/algebra/qb/algqb00.htm"> <IMG SRC="//www.mathnstuff.com/math/algebra/qb/gif/algqb.gif" ALT="QB, graded assignments" align="left"></A> <A HREF="//www.mathnstuff.com/math/math.htm"> <img src="//www.mathnstuff.com/gif/semestr.gif" width="40" alt="math home"></A> <dt> <A HREF="//www.mathnstuff.com/inc.htm"> <IMG SRC="//www.mathnstuff.com/math/spoken/here/1gif/mcihome.gif" ALT="[MC,i. 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