7BOBO,<ôdHHHHHHÐ,;H,;”,<ì” "º ,<ø -ZÔÌÿÿ`“@xHHÚ(ÿáÿâùFG(üHHÚ(d'@ÿÿ,褆l.à/±ëF@ Xè,;H,;D<,:ü, ß ß(,;¸(â¸,:HFë,ü”7Ð t,;¨!ÿÿÿÿÿÿÿÿ(}ýDSETÚ%%(8 –6,;x,;€,;|Ôy,9ð-v+Ôy,9D!Î Ôy,9ì'> CÔy,9@x êÔy,9<œ–Ôy,;$°EÔy,;(01Ôy,:ä²rÔy,;-v/Ôy,:Ð'"mÔy,:Ä'"ŠÔy,:¨+Z"»Ôy,:¸-v(6Ôy,;(7Ôy,:¬ °ã丹£¤»¼½¾ !"#$%&'()*+,«¬­®¯ÉÊËÌö÷øMNOPQÀÁÂÃÄ    o q ½ ¾ ù ú 8 9 f g ¢ ¤ Ñ Ò Ó Ô î ï ð ñ    r s t u v å æ ç è é B C D y z { • – — ˜ Â Ã Ä      Œ Ž é ê ë$%&'ABCDnopÅÆÇÈÉ89:;<•–—¸ÐÒÓÔÕÖðñòótuvwxçèéêëDEF|}~„Ž”©²¾¿ÀÁÂÜÝÞß   `abcdÓÔÕÖ×012 JKL¡¢£¤¥qrsUV¥¦ !"#$%&'()*+,-./0š›œ°±ÈÊàáùúûüýþEFGœžŸ lmnoØÙ5678bcd¹º»¼½,-./0‰Š‹éêë  b © ý!&!'!(!)!*!F!G!H!I!J!K!L!f!g!h!i!“!”!•!ê!ë!ì!í!î"]"^"_"`"a"º"»"¼#Á#Â$©$ª%™%š%Å%Ç&&&Ä&Æ&Ç&È&â&ã&ä&å''''f'g'h'i'j'Ù'Ú'Û'Ü'Ý(6(7(8 ¯      o  í  î  õ  û  )  *  +  ,  4  :  [  \  c  d  e  —  ™  Ÿ     Å  Ç  Î  Ð  Ô  B  C  z  {  é  ê & ' • – Ð Ö D  0  q þ l  ‰ !L "º &È (6 nÀ,;tÀX,;pj,;l ‚,;h‚Á,;dCÔ,:ø,:Ô,:ؘ,:´!˜P,:ü$èQ,:¼À Unit 11 Study Activities 1. In the middle of this sheet of paper, draw a point and label ( or name) this point 0 ( zero) . This zero is in the middle of your number line. The zero point is also called the origin. Use your drawing kit and draw a straight horizontal line to the right of the zero point. To show that the number line goes on forever to the right of zero, draw an arrowhead at the right end of your line. Mark a point on the line a little to the right of the zero point (about as far as the width of your thumb). Label this point 1 (one) . The distance from 0 to 1 on the number line is called the unit for the number line. Your unit may not be exactly the same length as someone elseÕs. You can choose any convenient length for your unit. Now use your compass to mark additional units on the number line to the right of 1. To do this, place the metal point of your compass at 0. Then carefully open the Xcompass until the pencil just touches the point for 1. Keep this exact opening as you lift the compass and place the metal point on 1. Now use the pencil to make a mark to the right of 1 as Figure 11-2 page 6 describes. The distance from 0 to 1 in the same as the distance from 1 to 2. Each distance is exactly one unit. Keeping the width between the compass legs fixed, placed the metal point on 2 and make a mark for 3. Continue to do this for as many points as will fit on your paper. You have drawn a diagram that represents the number 0 and the numbers 1,2,3, and so forth. 2. Now finish drawing your number line. To do this, draw a straight horizontal line to the left of the zero point. To show that the number line goes on forever to the left of zero, draw an arrow at the left end of your line. j As you did before, mark off units on the number line, this time moving left. What label goes on the mark that is one unit to the left of zero? What are you looking for? What do you need to answer the questions? Estimate what your answer(s) might be ( think of both numbers and terms to be used)? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure you are close to your estimate and the units are correct):  3. The positive values are to the ______?_________ (right or left) of zero. The negative values are to the _______?__________ (right or left) of zero. Which temperature is farther to the right: 20 o or 30 o ? Which temperature is farther to the right : 20 o or - 30 o ? Which temperature is higher : 20 o or -30o? Which temperature is farther to the right : -20o or -30o? Which temperature is higher: -20 o or -30o? What are you looking for? What do you need to answer the questions? Estimate what your answer(s) might be ( think of both numbers and terms to be used)? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure you are close to your estimate and the units are correct):  4. Use your calculator to add -328.76 and -4.9785. What are you looking for? What do you need to answer the questions? Estimate what your answer(s) might be ( think of both numbers and terms to be used)? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure you are close to your estimate and the units are correct):  5. Try this one with your calculator. 678.93- (-982.5) What are you looking for? What do you need to answer the questions? Estimate what yourÁ answer(s) might be ( think of both numbers and terms to be used)? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure you are close to your estimate and the units are correct):  6. Use your calculator to find: -89.304 - (-93.607)= ? What are you looking for? What do you need to answer the questions? Estimate what your answer(s) might be ( think of both numbers and terms to be used)? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure you are close to your estimate and the units are correct):  7. LetÕs take a look at all the possible combinations of adding and subtracting signed numbers. Copy those combinations shown below on you paper and write the answer for each one. first try doing them Ò in your headÓ. If you have trouble, or are notÔ sure of your answer, try solving them on a number line. 4+3 4+ (-3) 4-3 4-(-3) -4 + (-3) -4 - 3 -4 - (-3) What are you looking for? What do you need to answer the questions? Estimate what your answer(s) might be ( think of both numbers and terms to be used)? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure you are close to your estimate and the units are correct):  8. Copy the table in Figure 11-7 onto your paper (pg 17). (DonÕt copy the question marks). Complete the table as you read through this section. To complete the table, multiply any number in the left-hand column by any number along the top row. The answer is written where the row and column containing the two numbers intersect. For example, 3 (left column, first row) times 3 (top row, seventh column) gives the answer 9, in the first row, seventh column. What are you looking for? What do you need to answer the questions? Estimate what your answer(s) might be ( think of both numbers and terms to be used)? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure you are close to your estimate and the units are correct):  9. Now study your completed table. Complete these statements about multiplying signed numbers. Write the completed statements on your paper. When two positive numbers are multiplied, the answer is always ______________. When two negative numbers are multiplied, the answer is always _____________. When a negative number and a positive number are multiplied, the answer is always ____________________. 10. Use the rule to help you write the answers to these division problems. Do NOT use your calculator. 12 divided by 4= 12 divided by (-4)= -12 divided by 4 = -12 divided by (-4)= What are you looking for? What do you need to answer the questions? Estimate what your answer(s) might be ( think of both numbers and terms to be used)? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure you are close to your estimate and the units are correct):  11. On a piece of graph paper, make a scale drawing for these vectors, with one square representing 10 miles per hour. Label your beginning point - the tail of the vector - as point A. Draw a line segment 10 squares long heading directly east from point A. Label the end point - the head of this vector - as point B. the arrow head is located at point B. From point B - and little below vector AB, so the lines donÕt overlap - draw another line segment 3 squares long, heading due west. Label the head of this vector as point C. The result of adding these two vectors is the vector from point A to point C. How long is the vector from A to C? What is its direction? What are you looking for? What do you need to answer the questions? Estimate what your answer(s) might be ( think of both numbers and terms to be used)? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure you are close to your estimate and the units are correct):  12. Use figure 11-15 to help you write the answers to the following questions on your paper. What is the scale for the vectors AB and BC? What is the direction of the vector AB? What is its size ( in miles)? What is the direction of the vector BC? What is its size ( in miles)? What is the direction of the vector AC? What is its approximate size ( in miles)? What is the ÒmeaningÓ of the vector AC? Place figure 11-15 here What are you looking for? What do you need to answer the questions? EstPimate what your answer(s) might be ( think of both numbers and terms to be used)? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure you are close to your estimate and the units are correct):  13. Now, try to construct a drawing similar to the bottom part of Figure 11-16. Use graph paper to make a scale drawing of the separate vectors so that you can measure what happens when two vectors are combined. Let each square represent 10 pounds of force. Label your starting point ( in middle of your graph paper) as point A. Draw a vector 5 squares long going directly to the left of point A. (Refer to Figure 11-16.) Label the head of this vector ( where the arrow is) as point B. From point B, draw another vector 3 squares long and going upQ at a 45- degree angle to your first vector. Label the head of this vector as point C. The result of adding these two vectors is the resultant vector from point A to point C. How long is the vector from point A to C? What general direction (angle )does it head from point A? The effect of combining these two forces is the same as the effect of one force of approximately ____________________ pounds pulling at about ____________________ degrees north of west. What are you looking for? What do you need to answer the questions? Estimate what your answer(s) might be ( think of both numbers and terms to be used)? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure you are close to your estimate and the units are correct):  DSET|ÿÿ(Hÿÿÿÿÿÿ,;`Ôˆ—N7 ˆÔ)6ÿÿ*—N7DSET¤ÿÿ(H4B ÿÿÿÿÿÿ,;\7ˆÔ—î7Ô6ÿÿ*— 7DSETR ,;P,;X,;TÔ,;    ,;LUnit 11 Study Activities