Student Handbook. Prerequisite Skills Extra Practice Mixed Problem Solving Preparing for Standardized Tests...

Transcription

1 Student Handbook Built-In Workbooks Prerequisite Skills Etra Practice Mied Problem Solving Preparing for Standardized Tests Reference English-Spanish Glossar R Selected Answers R Photo Credits R0 Inde R0 Formulas and Smbols Inside Back Cover 7 Eclipse Studios

2 The Student Handbook is the additional skill and reference material found at the end of the tet. This handbook can help ou answer these questions. What if I Forget What I Learned Last Year? Use the Prerequisite Skills section to refresh our memor about things ou have learned in other math classes. Here s a list of the topics covered in our book.. The FIL Method. Factoring Polnomials. Congruent and Similar Figures. Pthagorean Theorem. Mean, Median, and Mode. Bar and Line Graphs 7. Frequenc Tables and Histograms. Stem-and-Leaf Plots 9. Bo-and-Whisker Plots What If I Need More Practice? You, or our teacher, ma decide that working through some additional problems would be helpful. The Etra Practice section provides these problems for each lesson so ou have ample opportunit to practice new skills. What If I Have Trouble with Word Problems? The Mied Problem Solving portion of the book provides additional word problems that use the skills presented in each lesson. These problems give ou real-world situations where math can be applied. What If I Need to Practice for a Standardized Test? You can review the tpes of problems commonl used for standardized tests in the Preparing for Standardized Tests section. This section includes eamples and practice with multiple-choice, griddable or grid-in, and etended-response test items. What If I Forget a Vocabular Word? The English-Spanish Glossar provides a list of important or difficult words used throughout the tetbook. It provides a definition in English and Spanish as well as the page number(s) where the word can be found. What If I Need to Check a Homework Answer? The answers to odd-numbered problems are included in Selected Answers. Check our answers to make sure ou understand how to solve all of the assigned problems. What If I Need to Find Something Quickl? The Inde alphabeticall lists the subjects covered throughout the entire tetbook and the pages on which each subject can be found. What if I Forget a Formula? Inside the back cover of our math book is a list of Formulas and Smbols that are used in the book. Student Handbook 7

3 Prerequisite Skills Prerequisite Skills The FIL Method The product of two binomials is the sum of the products of F the first terms, the outer terms, I the inner terms, and L the last terms. EXAMPLE Find ( + )( ). F L ( + ) ( )= + ( ) + + ( ) I First uter Inner Last = + = EXAMPLE Find ( + )( + ). ( + )( + ) = = = + + Eercises Find each product.. (a + )(a + ) a + a +. (v - 7)(v - ) v - v + 7. (h + )(h - ) h -. (d - )(d + ) d -. (b + )(b - ) b + b -. (s - 9)(s + ) s + s (r + )(r - ) r + r. (k - )(k + ) k + k (p + )(p + ) p + p + 0. ( - )( - ) (c + )(c - ) c - 9c -. (7n - )(n + ) 7 n + 9n -. (m + )(m - ) m - 7m - 0. (g + )(g + 9) 0 g + g + 9. (q - 7)(q + ) q - q -. (t - 7)(t - ) t - 9t + NUMBER For Eercises 7 and, use the following information. I m thinking of two integers. ne is 7 less than a number, and the other is greater than the same number. 7. Write epressions for the two numbers. n - 7, n +. Write a polnomial epression for the product of the numbers. n - n - FFICE SPACE For Eercises 9, use the following information. Monica s current office is square. Her office in the compan s new building will be feet wider and feet longer. 9. Write epressions for the dimensions of Monica s new office. +, + 0. Write a polnomial epression for the area of Monica s new office Suppose Monica s current office is 7 feet b 7 feet. How much larger will her new office be? 7 sq. ft 7 Prerequisite Skills

4 Factoring Polnomials Some polnomials can be factored using the Distributive Propert. EXAMPLE Factor a + a. Find the GCF of a and a. a = a a a = a GCF: a or a a + a = a(a) + a() Rewrite each term using the GCF. = a(a + ) Distributive Propert Prerequisite Skills To factor quadratic trinomials of the form + b + c, find two integers m and n with a product of c and with a sum of b. Then write + b + c using the pattern ( + m)( + n). EXAMPLE Factor each polnomial. a. + + Both b and c are positive. In this trinomial, b is and c is. Find two numbers with a product of and a sum of. Factors of Sum of Factors, 7, The correct factors are and. + + = ( + m)( + n) Write the pattern. = ( + )( + ) m = and n = CHECK Multipl the binomials to check the factorization. ( + )( + ) = () FIL = + + b. - + b is negative and c is positive. In this trinomial, b = - and c =. This means that m + n is negative and mn is positive. So m and n must both be negative. Factors of Sum of Factors -, - - -, - - The correct factors are - and = ( + m)( + n) Write the pattern. = [ + (-)][ + (-)] m = - and n = - = ( - )( - ) Simplif. c. + - b is positive and c is negative. In this trinomial, b = and c = -. This means that m + n is positive and mn is negative. So either m or n must be negative, but not both. Factors of Sum of Factors, - - -, The correct factors are - and. + - = ( + m)( + n) Write the pattern. = [ + (-)]( + ) m = - and n = = ( - )( + ) Simplif. Prerequisite Skills 77

5 Prerequisite Skills To factor quadratic trinomials of the form a + b + c, find two integers m and n whose product is equal to ac and whose sum is equal to b. Write a + b + c using the pattern a + m + n + c. Then factor b grouping. EXAMPLE Factor In this trinomial, a =, b = 7 and c = -. Find two numbers with a product of (-) or - and a sum of 7. Factors of - Sum of Factors, , 7, , 9 7 The correct factors are - and = + m + n - Write the pattern. = + (-) m = - and n = 9 = ( ) + (9 - ) Group terms with common factors. = ( - ) + ( - ) Factor the GCF from each group. = ( + )( - ) Distributive Propert Here are some special products. Perfect Square Trinomials Difference of Squares ( a + b) = (a + b)(a + b) (a - b) = (a - b)(a - b) a - b = (a + b)(a - b) = a + ab + b = a - ab + b EXAMPLE Factor each polnomial. a The first and last terms are perfect squares. The middle term is equal to ()(). This is a perfect square trinomial of the form (a + b) = () + ()() + Write as a + ab + b. = ( + ) Factor using the pattern. b. - This is a difference of squares. - = - () Write in the form a - b. = ( + )( - ) Factor the difference of squares. Eercises Factor the following polnomials ab - ab a - 0ab + b a + ab + 9b c a - 9 b 7 Prerequisite Skills

6 Congruent and Similar Figures Congruent figures have the same size and the same shape. Two polgons are congruent if their corresponding sides are congruent and their corresponding angles are congruent. A B D C ABC EFD F E Congruent Angles A E B F C D Congruent Sides AB EF BC FD AC ED Prerequisite Skills The order of the vertices indicates the corresponding parts. Read the smbol as is congruent to. EXAMPLE The corresponding parts of two congruent triangles are marked on the figure. Write a congruence statement for the two triangles. D List the congruent angles and sides. A D AB DE B E AC DC B ACB DCE BC EC C E Match the vertices of the congruent angles. Therefore, ABC DEC. A Similar figures have the same shape, but not necessaril the same size. In similar figures, corresponding angles are congruent, and the measures of corresponding sides are proportional. (The have equivalent ratios.) A B EXAMPLE C ABC DEF Congruent Angles A D, B E, C F Proportional Sides _ AB DE = _ BC EF = _ AC DF Read the smbol as is similar to. Determine whether the polgons are similar. Justif our answer. a. Since _ = _ = _ = _, the measures of the sides of the polgons are proportional. However, the corresponding angles are not congruent. The polgons are not similar. b. Since 7_ 0. = _. = 7_ 0. = _, the measures. of the sides of the polgons are proportional. The corresponding angles are congruent. Therefore, the polgons are similar. D E F Prerequisite Skills 79

7 Prerequisite Skills EXAMPLE CIVIL ENGINEERING The cit of Mansfield plans to build a bridge across Pine Lake. Use the information in the diagram to find the distance across Pine Lake. ABC ADE _ AB AD = _ BC Definition of similar polgons DE _ 00 0 = _ AB = 00, AD = = 0, BC = DE 00DE = 0() Cross products 00DE =,00 Simplif. D E B 0 m m C 00 m A DE = Divide each side b 00. The distance across the lake is meters. Eercises Determine whether each pair of figures is similar, congruent, or neither Each pair of polgons is similar. Find the values of and SHADWS n a sunn da, Jason measures the length of his shadow and the length of a tree s shadow. Use the figures at the right to find the height of the tree.. m. m? m 7. m. PHTGRAPHY A photo that is inches wide b inches long must be reduced to fit in a space inches wide. How long will the reduced photo be?. SURVEYING Surveors use instruments to measure objects that are too large or too far awa to measure b hand. The can use the shadows that objects cast to find the height of the objects without measuring them. A surveor finds that a telephone pole that is feet tall is casting a shadow 0 feet long. A nearb building is casting a shadow feet long. What is the height of the building? 0 Prerequisite Skills

8 Pthagorean Theorem The Pthagorean Theorem states that in a right triangle, the square of the length of the hpotenuse c is equal to the sum of the squares of the lengths of the legs a and b. That is, in an right triangle, c = a + b. EXAMPLE Find the length of the hpotenuse of each right triangle. a c b Prerequisite Skills a. in. c in. b. c = a + b Pthagorean Theorem c = + Replace a with and b with. c = + Simplif. c = 9 Add. c = 9 Take the square root of each side. c = in. The length of the hpotenuse is inches. cm c cm c = a + b Pthagorean Theorem c = + 0 Replace a with and b with 0. c = + 00 Simplif. c = Add. c = Take the square root of each side. c.7 0 cm Use a calculator. To the nearest tenth, the length of the hpotenuse is.7 centimeters. EXAMPLE Find the length of the missing leg in each right triangle. a. 7 ft ft a ft c = a + b Pthagorean Theorem = a + 7 Replace c with and b with 7. = a + 9 Simplif. - 9 = a Subtract 9 from each side. 7 = a Simplif. 7 = a Take the square root of each side. = a The length of the leg is feet. Prerequisite Skills

9 Prerequisite Skills b. c = a + b Pthagorean Theorem b m m m = + b Replace c with and a with. = + b Simplif. = b Subtract from each side. = b Take the square root of each side.. b Use a calculator to find the square root of. Round to the nearest tenth. To the nearest tenth, the length of the leg is. meters. EXAMPLE The lengths of the three sides of a triangle are, 7, and 9 inches. Determine whether this triangle is a right triangle. Since the longest side is 9 inches, use 9 as c, the measure of the hpotenuse. c = a + b Pthagorean Theorem Replace c with 9, a with, and b with Evaluate 9,, and 7. 7 Simplif. Since c a + b, the triangle is not a right triangle. Eercises Find each missing measure. Round to the nearest tenth, if necessar ft km a km m in. c ft ft in. c in. 7. a =, b =, c =?. a =?, b =, c = 9. a =, b =?, c = 0 0. a =, b = 9, c =? 9.. a =, b =?, c =.. a =?, b = 7, c =. The lengths of three sides of a triangle are given. Determine whether each triangle is a right triangle.. in., 7 in., in. no. 9 m, m, m es. cm, 7 cm, cm no. ft, ft, ft no 7. 0 d, d, d es. km, 0 km, km es 9. FLAGPLES Mai-Lin wants to find the distance from her feet to the top of the flagpole. If the flagpole is 0 feet tall and Mai-Lin is standing a distance of feet from the flagpole, what is the distance from her feet to the top of the flagpole? about. ft b m 0. CNSTRUCTIN The walls of the Downtown Recreation Center are being covered with paneling. The doorwa into one room is ft 0.9 meter wide and. meters high. What is the width of the widest rectangular panel that can be taken through this doorwa? about. m 0 km m cm d b cm d? ft 0 cm c d 0 ft Prerequisite Skills

10 Mean, Median, and Mode Mean, median, and mode are measures of central tendenc that are often used to represent a set of data. To find the mean, find the sum of the data and divide b the number of items in the data set. (The mean is often called the average.) To find the median, arrange the data in numerical order. The median is the middle number. If there is an even number of data, the median is the mean of the two middle numbers. The mode is the number (or numbers) that appears most often in a set of data. If no item appears most often, the set has no mode. Prerequisite Skills EXAMPLE Michelle is saving to bu a car. She saved $00 in June, $00 in Jul, $00 in August, and $0 in September. What was her mean (or average) monthl savings? mean = sum of monthl savings/number of months $00 + $00 + $00 + $0 = = _ $00 or $.0 Michelle s mean monthl savings was $.0. EXAMPLE Find the median of the data. To find the median, order the numbers from least to greatest. The median is in the middle. The two middle numbers are.7 and =.9 There is an even number of data. Find the mean of the middle two. Peter s Best Running Times Week Minutes to Run a Mile EXAMPLE GLF Four plaers tied for first in the 00 PGA Tour Championship. The scores for each plaer for each round are shown in the table below. What is the mode score? Plaer Round Round Round Round Mike Weir David Toms 7 7 Sergio Garcia 9 7 Ernie Els 9 Source: ESPN The mode is the score that occurred most often. Since the score of occurred times, it is the mode of these data. Prerequisite Skills

11 Prerequisite Skills The range of a set of data is the difference between the greatest and the least values of the set. It describes how a set of data varies. EXAMPLE Find the range of the data. {,,,, 9,,, } The greatest value is and the least value is. So, the range is - or. Eercises Find the mean, median, mode, and range for each set of data. Round to the nearest tenth if necessar.. 0.; 0.; 0 and 0;. {,,,, } 0; ; no mode;. {, 7, 7,,, } ; 7; 7;. {7, 9,, 9, 00, } 9.; ; no mode;. {99, 00,, 9, 9, 99} 9., 97., 99,. {9.9, 9.9, 0, 9.9,., 9., 9.} 9.; 9.9; 9.9;.. {0, 0, 0, 0, 0, 0, 0, 0} 7. {7, 9,,,, 7, 9} ; ; no mode;. {,,,,,,, }.; 0; no mode; 9. {0., 0.0, 0.9,., 0.} 0.; 0.; no mode; 0. _ {, _ 7, _, _, } ; _ ; no mode; _ 7.0. CHARITY The table shows the amounts. SCHL The table shows Pilar s grades collected b classes at Jackson High in chemistr class for the semester. Find School. Find the mean, median, mode, her mean, median, and mode scores, and and range of the data. the range of her scores. 9.; 9; 9; Amounts Collected for Charit Class Amount Class Amount A $0 E $0 B $00 F $ C $ G $00 D $0 H $00 $0; $77.0; no mode; $90 Chemistr Grades Assignment Grade (out of 00) Homework 00 Electron Project 9 Test I 7 Atomic Mass Project 9 Test II Phase Change Project 90 Test III 9. WEATHER The table shows the precipitation for the month of Jul in Cape Hatteras, North Carolina, in various ears. Find the mean, median, mode, and range of the data..0;.; no mode; 9.77 Jul Precipitation in Cape Hatteras, North Carolina Year Inches Source: National Climatic Data Center. SCHL Kaitln s scores on her first five algebra tests are, 90, 9, 9, and 9. What test score must Kaitln earn on the sith test so that her mean score will be at least 90? at least 90. GLF Colin s average for three rounds of golf is 9. What is the highest score he can receive for the fourth round to have an average (mean) of 9?. SCHL Mika has a mean score of on his first four Spanish quizzes. If each quiz is worth points, what is the highest possible mean score he can have after the fifth quiz?. 7. SCHL To earn a grade of B in math, Latisha must have an average (mean) score of at least on five math tests. Her scores on the first three tests are, 9, and. What is the lowest total score that Latisha must have on the last two tests to earn a B test average? Prerequisite Skills

12 Bar and Line Graphs A bar graph compares different categories of data b showing each as a bar whose length is related to the frequenc. A double bar graph compares two sets of data. Another wa to represent data is b using a line graph. A line graph usuall shows how data changes over a period of time. EXAMPLE MARRIAGE The table shows the average age at which Americans marr for the first time. Make a double bar graph to displa the data. Step Draw a horizontal and a vertical ais and label them as shown. Step Draw side-b-side bars to represent each categor. Average Age to Marr Year Men 7 Women Source: U.S. Census Bureau Prerequisite Skills Average Age to Marr The legend indicates that the blue bars refer to men and the red bars refer to women. Age Men Women Year The side-b-side bars compare the age of men and women for each ear. EXAMPLE HEALTH The table shows Mark s height at -ear intervals. Make a line graph to displa the data. Age 0 Height (feet) Step Draw a horizontal and a vertical ais. Label them as shown. Step Plot the points. Step Draw a line connecting each pair of consecutive points. Height (feet) 7 0 Mark s Height 0 Age (ears) Eercises -. See Student Handbook Answer Appendi.. HEALTH The table below shows the life epectanc for Americans born in each ear listed. Make a double-bar graph to displa the data. Life Epectanc Year of Birth Male Female MNEY The amount of mone in Beck s savings account from August through March is shown in the table below. Make a line graph to displa the data. Month Amount Month Amount August $00 December $70 September $00 Januar $00 ctober $700 Februar $90 November $70 March $900 Prerequisite Skills

13 Prerequisite Skills 7 Frequenc Tables and Histograms A frequenc table shows how often an item appears in a set of data. A tall mark is used to record each response. The total number of marks for a given response is the frequenc of that response. Frequencies can be shown in a bar graph called a histogram. A histogram differs from other bar graphs in that no space is between the bars and the bars usuall represent numbers grouped b intervals. EXAMPLE TELEVISIN Use the frequenc table of Brad s data. a. How man more chose sports programs than news? b. Which two programs together have the same frequenc as adventures? a. Seven people chose sports. Five people chose news. 7 =, so more people chose sports than news. b. As man people chose adventures as the following pairs of programs. sports and music videos msteries and news msteries and soap operas comedies and music videos Favorite Television Shows Program Tall Frequenc Sports IIII II 7 Msteries IIII Soap operas IIII News IIII Quiz shows IIII I Music videos II Adventure IIII IIII 9 Comedies IIII II 7 EXAMPLE FITNESS A gm teacher tested the number of sit-ups students in two classes could do in minute. The results are shown. a. Make a histogram of the data. Title the histogram. b. How man students were able to do 9 sit-ups in minute? c. How man students were unable to do 0 sit-ups in minute? d. Between which two consecutive intervals does the greatest increase in frequenc occur? What is the increase? Number of Sit-Ups Frequenc a. Use the same intervals as those in the frequenc table on the horizontal ais. Label the vertical ais with a scale that includes the frequenc numbers from the table. b. Ten students were able to do 9 sit-ups in minute. c. Add the students who did 0 sit-ups and 9 sit-ups. So +, or 0, students were unable to do 0 sit-ups in minute. d. The greatest increase is between intervals 9 and 0. These frequencies are and. So the increase is =. Prerequisite Skills

14 Eercises ART For Eercises, use the following information. The prices in dollars of paintings sold at an art auction are shown Make a frequenc table of the data. See Student Handbook Answer Appendi.. What price was paid most often for the artwork? $00. What is the average price paid for artwork at this auction? $9.. How man works of art sold for at least $00 and no more than $00? Prerequisite Skills PETS For Eercises 9, use the following information. Number of Pets per Famil Use a frequenc table to make a histogram of the data. See Student Handbook Answer. How man families own two to three pets? Appendi. 7. How man families own more than three pets?. To the nearest percent, what percent of families own no pets? 9% 9. Name the median, mode, and range of the data. median =, mode =, range = TREES For Eercises 0, use the histogram shown. 0. Which interval contains the most evergreen seedlings? 0 9. Which intervals contain an equal See Student number of trees? Handbook Answer Appendi.. Which intervals contain 9% of the data? See Student Handbook Answer Appendi.. Between which two consecutive intervals does the greatest increase in frequenc occur? What is the increase? See Student Handbook Answer Appendi.. MARKET RESEARCH A civil engineer is studing traffic patterns. She counts the number of cars that make it through one rush hour green light ccle. rganize her data into a frequenc table, and then make a histogram See Student Handbook Answer Appendi. Prerequisite Skills 7

15 Prerequisite Skills Stem-and-Leaf Plots In a stem-and-leaf plot, data are organized in two columns. The greatest place value of the data is used for the stems. The net greatest place value forms the leaves. Stem-and-leaf plots are useful for organizing long lists of numbers. EXAMPLE SCHL Isabella has collected data on the GPAs (grade point average) of the students in the art club. Displa the data in a stem-and-leaf plot. {.0,.9,.,.9,.,.7,.,.,.0,.9,.,.,.9,.,.,.} Step Find the least and the greatest number. Then identif the greatest place-value digit in each number. In this case, ones. least data:. greatest data:.0 The least number has The greatest number in the ones place. has in the ones place. Step Draw a vertical line and write the stems from to to the left of the line. Step Write the leaves to the right of the line, with the corresponding stem. For eample, write 0 to the right of for.0. Step Rearrange the leaves so the are ordered from least to greatest. Step Include a ke or an eplanation. Stem Stem Leaf Leaf =. Eercises GAMES For Eercises, use the following information. The stem-and-leaf plot at the right shows Charmaine s scores for her favorite computer game.. What are Charmaine s highest and lowest scores? 0; 90. Which score(s) occurred most frequentl? 90, 9. How man scores were above?. Has Charmaine ever scored? no. SCHL The class scores on a 0-item test are shown in the table at the right. Make a stem-and-leaf plot of the data.. See Student Handbook Answer Appendi.. GEGRAPHY The table shows the land area of each count in Woming. Round each area to the nearest hundred square miles and organize the data in a stem-and-leaf plot. Prerequisite Skills Stem Leaf = Test Scores Count Area (mi) Count Area (mi) Count Area (mi) Alban 7 Hot Springs 00 Sheridan Big Horn 7 Johnson Sublette Campbell 797 Laramie Sweetwater 0, Carbon 79 Lincoln 09 Teton 00 Converse Natrona 0 Unita 0 Crook 9 Niobrara Washakie 0 Fremont 9 Park 9 Weston 9 Goshen Platte 0 Source: The World Almanac

16 9 Bo-and-Whisker Plots In a set of data, quartiles are values that divide the data into four equal parts. median lower half upper half } } The median of the lower half of a set The median of the upper half of a set of data is the lower quartile, or LQ. of data is the upper quartile, or UQ. Prerequisite Skills To make a bo-and-whisker plot, draw a bo around the quartile values, and lines or whiskers to represent the values in the lower fourth of the data and the upper fourth of the data EXAMPLE MNEY The amount spent in the cafeteria b 0 students is shown. Displa the data in a bo-and-whisker plot. Step Find the least and greatest number. Then draw a number line that covers the range of the data. In this case, the least value is and the greatest value is.. Amount Spent $.00 $.00 $.00 $.00 $.00 $.0 $.0 $.00 $.0 $.00 $.00 $.0 $.0 $.00 $.00 $.0 $.00 $.00 $.0 $.0 Step Find the median, the etreme values, and the upper and lower quartiles. Mark these points above the number line.,,,.,,,,,.,.,.,.,.,,.,,,,,. LQ = _ + or M = least value: $ $ $ $ $ $ $ lower quartile: $ median: $ $ $ $ $ $ $ Step Draw a bo and the whiskers. upper quartile: $.7 or. UQ =. + or.7 greatest value: $.0 $ $ $ $ $ $ The interquartile range (IQR) is the range of the middle half of the data and contains 0% of the data in the set. Interquartile range = UQ - LQ The interquartile range of the data in Eample is.7 - or.7. An outlier is an element of a set that is at least. interquartile ranges less than the lower quartile or greater than the upper quartile. The whisker representing the data is drawn from the bo to the least or greatest value that is not an outlier. Prerequisite Skills 9

17 Prerequisite Skills EXAMPLE SCHL The number of hours José studied each da for the last month is shown in the bo-and-whisker plot below. 0 a. What percent of the data lies between. and.? The value. is the lower quartile and. is the upper quartile. The values between the lower and upper quartiles represent 0% of the data. b. What was the greatest amount of time José studied in a da? The greatest value in the plot is, so the greatest amount of time José studied in a da was hours. c. What is the interquartile range of this bo-and-whisker plot? The interquartile range is UQ - LQ. For this plot, the interquartile range is. -. or.7 hours. d. Identif an outliers in the data. An outlier is at least.(.7) less than the lower quartile or more than the upper quartile. Since. + (.)(.7) =.7, and >.7, the value is an outlier, and was not included in the whisker. Eercises DRIVING For Eercises, use the following information. Tler surveed 0 randoml chosen students at his school about how man miles the drive in an average da. The results are shown in the bo-and-whisker plot What percent of the students drive more than 0 miles in a da? %. What is the interquartile range of the bo-and-whisker plot? 7 mi. Does a student at Tler s school have a better chance to meet someone who drives the same mileage the do if the drive 0 miles in a da or miles in a da? Wh?. See Student Handbook Answer Appendi.. SFT DRINKS Carlos surveed his friends to find the number of cans of soft drink the drink in an average week. Make a bo-and-whisker plot of the data. {0, 0, 0,,,,,,,,,,, 7, 0, 0, 0,, }. BASEBALL The table shows the number of sacrifice hits made b teams in the National Baseball League in one season. Make a bo-andwhisker plot of the data.. ANIMALS The average life span of some animals commonl found in a zoo are as follows: {, 7, 7, 0,,,,,, 0, 0, 0,, 0, 00}. Make a bo-and-whisker plot of the data. Team Home Runs Team Home Runs Arizona 7 Milwaukee Atlanta Montreal Chicago 7 New York Cincinnati Philadelphia 7 Colorado Pittsburgh 0 Florida 0 San Diego 9 Houston 7 San Francisco 7 Los Angeles 7 St. Louis Source: ESPN 90 Prerequisite Skills

18 Etra Practice Lesson - (pages 0) _ Evaluate each epression if q =, r =., s = -, and t =.. qr - st. qr st. qrst. qr + st. _ q s. _ qr t 7. r(s - ) t Evaluate each epression if a = -0., b =, c =, and d = -.. q s + t - 9. b + d 0. ab + c. bc + d a. 7ab - d. ad + b - c. a + c b. ab - d a. a + ad bc Lesson - (pages 7) Name the sets of numbers to which each number belongs. (Use N, W, Z, Q, I, and R.) _ Name the propert illustrated b each equation. 7. ( + 9a)b = b( + 9a). _ ( = ) 9. a( - ) = a - a 0. (-b) + b = 0. jk + 0 = jk. (a)b = (ab) Etra Practice Simplif each epression.. 7s + 9t + s - 7t. (a + b) + (a - b). ( - ) - ( + ). 0.(m - ) + 0.( - m) 7. _ (7p + q) + _ (p - q). _ (v - w) - _ (7v - w) Lesson - (pages ) Write an algebraic epression to represent each verbal epression.. twelve decreased b the square of. twice the sum of a number and a number negative nine. the product of the square of a number. the square of the sum of a number and and Name the propert illustrated b each statement.. If a + =, then (a + ) = ().. If + ( + ) =, then + 9 =. 7. If 7 =, then 7 - = -.. If + = and =, then + =. Solve each equation. Check our solution. 9. t + = = -. _ = _ +. s - = (s + ). (k - ) = k +. 0.z + 0 = z +. q - _ q =. - _ 7 r + _ 7 = 7. d - = _ (d - ) Solve each equation or formula for the specified variable.. C = πr; for r 9. I = Prt, for t 0. m = _ n - n, for n Etra Practice 9

19 Lesson - (pages 7 ) Evaluate each epression if = -, =, and z = z. - + z z Etra Practice Solve each equation. Check our solutions. 9. d + = 7 0. a - = 0. - =. t =. p =. g - =. + =. b - 0 = b = 0. c + - = m - = 0. + z + = 0. d =. t = 0. d - = d = 7 +. b + - = b +. t + = t + Lesson - (pages 9) Solve each inequalit. Then graph the solution set on a number line.. z + 7. r - > b <. - >. (f + ). - > g ( - ) -9. 7a + > a (b - ) b ( - ) < ( - ). (c - ) > c +. (d + ) - (d + ). - t < ( - t). - _ +. _ a + _ 7 + a 7. - < _ + 7. ( - ) - ( - ). s - (s + 7) > - s Define a variable and write an inequalit for each problem. Then solve. 9. The product of 7 and a number is greater than. 0. The difference of twice a number and is at most.. The product of -0 and a number is greater than or equal to 0.. Thirt increased b a number is less than twice the number plus three. Lesson - (pages ) Write an absolute value inequalit for each of the following. Then graph the solution set on a number line.. all numbers less than -9 and greater than 9. all numbers between -. and.. all numbers greater than or equal to - and less than or equal to Solve each inequalit. Graph the solution set on a number line.. m - < 7 or m + >. < n + < 7. - s - 7. t + -7 or t < or - > p. 7d -. a + <. t - >. - <. d <. v + > 9. r + < 0. w - 9. z q < 0. h + < 0. n - 9 Etra Practice

20 Lesson - (pages ) State the domain and range of each relation. Then determine whether each relation is a function. Write es or no.. Year Population 970,0 90, 990,0 000,0.. Graph each relation or equation and find the domain and range. Then determine whether the relation or equation is a function and state whether discrete or continuous.. {(, ), (, ), (, ), (, )}. {(0, ), (0, ), (0, ), (0, 0)}. = - 7. = -. = 9. = - Find each value if f() = + 7 and g() = ( + ). 0. f(). f(-). f(a + ). g(). g(-). f(0.). g(b - ) 7. g(c) Etra Practice Lesson - (pages 70) State whether each equation or function is linear. Write es or no. If no, eplain our reasoning.. _ - = 7. = +. g() = _. f() = 7 - Write each equation in standard form. Identif A, B, and C =. = - 7. = 7 +. = _ = = - Find the -intercept and the -intercept of the graph of each equation. Then graph the equation.. + =. - = -. = -. =. _ - =. = - Lesson - (pages 7 77) Find the slope of the line that passes through each pair of points.. (0, ), (, 0). (, ), (, 7). (, ), (, -). (., -), (,.). _ (-, _, _ ) ( 0, - _. (-, c), (, c) ) Graph the line passing through the given point with the given slope. 7. (0, );. (, ); 0 9. (-, ); - _ Graph the line that satisfies each set of conditions. 0. passes through (0, ), parallel to a line with a slope of -. passes through (, -), perpendicular to the graph of - + = Etra Practice 9

21 Lesson - (pages 79 ) Write an equation in slope-intercept form for each graph... (, ) (, ) (,) Etra Practice Write an equation in slope-intercept form for the line that satisfies each set of conditions.. slope -, passes through (7, ). slope _, passes through the origin. passes through (, -) and (-, ). -intercept -, -intercept 7. passes through (, ), parallel to the graph of + =. passes through (0, 0), perpendicular to the graph of + = Lesson - (pages 9) Complete parts a c for each set of data in Eercises. a. Draw a scatter plot and describe the correlation. b. Use two ordered pairs to write a prediction equation. c. Use our prediction equation to predict the missing value.. Telephone Costs. Washington. Federal Minimum Minutes Cost ($) Year Population Wage ,, Year Wage ,, 9 $ ,, 990 $ ,,9 99 $ ,9, 99 $.7? 00? 997 $. 0? Source: The World Almanac Source: The World Almanac Lesson - (pages 9 0) Identif each function as S for step, C for constant, A for absolute value, or P for piecewise... Graph each function. Identif the domain and range.. f() = +. g() = -. f() = -. h() = - 7. h() = -. g() = + 9. h() = { if < - 0. f() = if - { - if - if > 9 Etra Practice

22 Lesson -7 (pages 0 0) Graph each inequalit.. -. < > < - 7. > _ _ _ -. - < > < < _ - Lesson - (pages ) Solve each sstem of equations b graphing or b completing a table.. + =. - =. + = - + = 7 - = 0 _ + =. + = 0. - = 7. = _ + + = _ - _ = - = + Graph each sstem of equations and describe it as consistent and independent, consistent and dependent, or inconsistent =. - = 9. = = - = - = = 7. _ - = 0. _ = _. -. =. _ + _ = - = 0 Etra Practice Lesson - (pages 9) Solve each sstem of equations b using substitution.. + = 0. = = -7 + = + = - + = -7 Solve each sstem of equations b using elimination = 9. r + s = -7. p + q = 0 - = r - s = - p - q = - Solve each sstem of equations b using either substitution or elimination = 7. a + b = - 9. c + d = - + = a - b = c - d = =. m + n =. = - = - 9 m - n = - - =.. +. = -. _ + _ =. _ 7 c - _ d = = _ - = -7 _ 7 c + _ d = - Etra Practice 9

23 Lesson - (pages 0 ) Solve each sstem of inequalities... <. + <. + < < < _ > + 9. > Etra Practice Find the coordinates of the vertices of the figure formed b each sstem of inequalities _ + _ 7 -_ _ + _ Lesson - (pages ) A feasible region has vertices at (-, ), (, ), (, ), and (, -). Find the maimum and minimum values of each function.. f(, ) = -. f(, ) = +. f(, ) = -. f(, ) = - +. f(, ) = -. f(, ) = - Graph each sstem of inequalities. Name the coordinates of the vertices of the feasible region. Find the maimum and minimum values of the given function for this region f(, ) = + f(, ) = + f(, ) = f(, ) = f(, ) = + f(, ) = + Lesson - (pages ) For each sstem of equations, an ordered triple is given. Determine whether or not it is a solution of the sstem z = -. u + v + w =. + = z = - u - v + w = -9 + z = z = ; u - v - w = -; + z = ; (-,, ) (,, -) (-, -, ) Solve each sstem of equations.. a =. s + t =. u - v = b - c = 7r - s + t = 0 v + w = - a + 7c = - t = u - w = 7. a + b - c =. + - z = z = 7 a + b - c = z = z = a - b + c = + + z = - + z = 9 Etra Practice

24 Lesson - (pages 7) Solve each matri equation.. [ -z] = [ -z ]. + - =. - w + - z = z. = 0-0 z. - = z = = - +. = 0 z - - Lesson - (pages 9 7) Perform the indicated matri operations. If the matri does not eist, write impossible [0 - ] [- 9] - [ -7 ] Etra Practice Use matrices A, B, C, D, and E to find the following. A = A + B. C + D 9. A - B 0. B. D - C. E + A. D - B. A + E - D Lesson - (pages 77 ) Find each product, if possible.. [- ] Etra Practice 97

25 Lesson - (pages 9) For Eercises, use the following information. The vertices of quadrilateral ABCD are A(, ), B(-, ), C(-, -), and D(, -). The quadrilateral is dilated so that its perimeter is times the original perimeter.. Write the coordinates for ABCD in a verte matri.. Find the coordinates of the image A'B'C'D'.. Graph ABCD and A'B'C'D'. Etra Practice For Eercises 0, use the following information. The vertices of MQN are M(, ), Q(, -), and N(, -).. Write the coordinates of MQN in a verte matri.. Write the reflection matri for reflecting over the line =.. Find the coordinates of M'Q'N' after the reflection. 7. Graph MQN and M'Q'N'.. Write a rotation matri for rotating MQN 90 counterclockwise about the origin. 9. Find the coordinates of M'Q'N' after the rotation. 0. Graph MQN and M'Q'N'. Lesson - (pages 9 00) Evaluate each determinant using epansion b minors Evaluate each determinant using diagonals Lesson - (pages 0 07) Use Cramer s Rule to solve each sstem of equations.. - = 9. p - q =. - + = 7 + = p + q = 0 + =. _ - _ = -. _ c + _ d =. 0.a +.b = 0. _ + _ = - _ c - _ d = - 0.a +.b = z =. a + b - c = - 9. r + s - t = z = - a - b + c = -r + s + t = + - z = - -a - b + c = r - s + t = -9 9 Etra Practice

26 Lesson -7 (pages 0 ) Determine whether each pair of matrices are inverses.. A = -7. X = 0-7, B = -7 0, Y = C = -. N = 0 -, D = - - 0, M = - - Find the inverse of each matri, if it eists Lesson - (pages ) Write a matri equation for each sstem of equations.. a + b =. + = -. m + n = a - b = 9 - = m - n = c - d = z =. a - b - c = c - d = z = a + b + c = + + z = a - b - c = - Etra Practice Solve each matri equation or sstem of equations = = = = 7. m + n =. c + d = 7. a - b = + = m + n = c - 0d = - a + b =. r - 7s =. + = -. m - n = 7. + = -r + s = = -m + 9n = - - = - Lesson - (pages ) For Eercises, complete parts a c for each quadratic function. a. Find the -intercept, the equation of the ais of smmetr, and the -coordinate of the verte. b. Make a table of values that includes the verte. c. Use this information to graph the function.. f() =. f() = -. f() = +. f() = - -. f() = +. f() = f() = + -. f() = f() = f() = + -. f() = f() = Determine whether each function has a maimum or a minimum value and find the maimum or minimum value. Then state the domain and range of the function.. f() = 9. f() = 9 -. f() = - +. f() = f() = - 9. f() = f() = f() = - + _. f() = - + _ + _ Etra Practice 99

27 Lesson - (pages ) Use the related graph of each equation to determine its solutions = 0. - = = 0 f () f() f () f () f() f() Etra Practice Solve each equation b graphing. If eact roots cannot be found, state the consecutive integers between which the roots are located.. - = = = = = = = 0. + =. = = = = 0 Lesson - (pages ) Solve each equation b factoring = 0. = = 9. = - 0. = 0. - = =. = = 0. - = =. - = = =. + 7 =. - = Write a quadratic equation with the given roots. Write the equation in the form a + b + c = 0, where a, b, and c are integers. 7.,. -, 9. -, , _. -, _. - _, - _ Lesson - (pages 9 ) Simplif _. -b. t -_ 7s. (7i). (i)(-i)(i) 7. ( -)( -). -i 9. i 7 i i 0. ( - i) + (- + 9i). (7i) - ( + i). ( + i) - ( + i). (7 + i)(7 - i). ( - i)( + i). ( + i). 7. i. - 7i - i + i + i Solve each equation = 0. _ 9 + =. + =. - 9 = =. _ + = Etra Practice

28 Lesson - (pages 7) Find the value of c that makes each trinomial a perfect square. Then write the trinomial as a perfect square c c. - + c. - _ + c c. + _ + c 7. - _ + c. - + c Solve each equation b completing the square = = = = = = = = = = = = = = = = = = = = = 0 Etra Practice Lesson - (pages 7 ) For Eercises, complete parts a c for each quadratic equation. a. Find the value of the discriminant. b. Describe the number and tpe of roots. c. Find the eact solutions b using the Quadratic Formula = = = = = 0. = = = = =. 7 =. = = = = 0 Solve each equation b using the method of our choice. Find eact solutions = = 0. + = 9 9. = =. + + = = = 0. = 0 Lesson -7 (pages 9) Write each quadratic function in verte form, if not alread in that form. Then identif the verte, ais of smmetr, and direction of opening.. = ( + ) -. = ( - ) -. = -( + ) + 7. = -9( - 7) +. = = Graph each function. 7. = - +. = = = = _ = = + +. = = Etra Practice 90

29 Lesson - (pages 9 0) Graph each inequalit > > Etra Practice Use the graph of the related function of each inequalit to write its solutions < 0 Solve each inequalit algebraicall < > > Lesson - (pages ) Simplif. Assume that no variable equals m m m (-) (-). _ t t. -_ 7. _. _ p q 7 p q 9. -(m ) 0. ( ) (abc). ( ). (b ). (- ) ( ) -. (-) ( ). ( a7 b c). Evaluate. Epress the result in scientific notation. _ - _ 7. a + a -. ( )(. 0 7 ). (. 0 )( ) 7. (. 0 )( ) (. 0 ) Lesson - (pages 0 ) Simplif.. ( ) + ( ). ( - + ) + (7 + - ). ( ) + (- - + ). ( ) - (- - + ). 7_ uw ( u w - uw + _ 7u) w ( ) 7. ( - )( + 7). ( - )(- - ) 9. ( - )( - ) 0. ( + )( - ). ( - 7)( + 7). ( + w)( - w). (a + )(a - ). (- + 0)(- - 0). ( - ). ( + ) 7. (- + ). _ ( + + ) 9. - _ a (a - a + a) 90 Etra Practice

30 Lesson - (pages 0) Find p() and p(-) for each function.. p() = 7 -. p() = p() = + -. p() = - +. p() = -. p() = _ + 7. p() = p() = p() = - If p() = and q() = -, find each value. 0. q(n). p(b). q(z ). p(m ). q( + ). p( - ). q(a - ) 7. q(h - ). [p(c - )] 9. q(n - ) + q(n ) 0. -p(a) - p(a). [q(d + )] + q(d) Lesson - (pages ) For Eercises, complete each of the following. a. Graph each function b making a table of values. b. Determine the values of between which the real zeros are located. c. Estimate the -coordinates at which the relative maima and relative minima occur.. f() = + -. f() = f() = f() = f() = f() = f() = f() = f() = f() = f() = f() = f() = f() = f() = f() = Etra Practice Lesson - (pages 9 ) Factor completel. If the polnomial is not factorable, write prime.. a b c - a b c + 7a b c. 0a - - ab + b p - pq - q t a - b. a + a - a ac - bd - 7ad + bc. h - 0hj + h - j Simplif. Assume that no denominator is equal to Etra Practice 90

31 Etra Practice Lesson - (pages 9 ) Simplif.. r s + r s 9r s. v w - v w -v w (bh + ch) (b + c). (c d + 0c d - cd) cd. (f + 0f 9 - f ) f 7. (m + mn - m )(m) -. (g + 9g - g + 9) (g + ) 9. (p + p + p 7 - )(p 7 + ) - 0. (k - k + 9) (k - 7). (r + r - ) (r + ). (n + ) (n + ). ( ) ( - ). (q + q + q + 7) (q + ). (v + v - v + ) (v - ). ( ) ( + ) 7. (s + s - 7) (s + ). (t - t + t - t + ) (t - ) 9. (z - z - z - z - ) (z - ) 0. (r - r - r + r - ) (r + ). (b - b + b + 9) (b - ) Lesson -7 (pages ) Use snthetic substitution to find f() and f(-) for each function.. f() = - +. f() = + -. f() = f() = f() = f() = 0 + Given a polnomial and one of its factors, find the remaining factors of the polnomial. Some factors ma not be binomials. 7. ( ); ( + ). ( ); ( - ) 9. ( ); ( - ) 0. ( - ); ( - ). ( + + ); ( + ). ( ); ( + ). ( ); ( - 7). ( ); ( - ). ( ); ( + ). ( ); ( - ) 7. ( ); ( - 7). ( ); ( + ) Lesson - (pages ) Solve each equation. State the number and tpe of roots = = 0. - = - 0 State the number of positive real zeros, negative real zeros, and imaginar zeros for each function.. f() = f() = f() = f() = f() = f() = Find all of the zeros of the function. 0. f() = f() = f() = f() = f() = f() = Etra Practice

32 Lesson -9 (pages 9 7) List all of the possible rational zeros for each function.. f() = f() = f() = 9-7 Find all of the rational zeros for each function.. f() = f() = f() = f() = f() = f() = Find all of the zeros of each function. 0. f() = f() = f() = Lesson 7- (pages 90) Find (f + g)(), (f - g)(), (f g)(), and ( f _ g ) () for each f() and g().. f() = +. f() =. f() = -. f() = + g() = - g() = g() = + g() = + Etra Practice For each set of ordered pairs, find f g and g f, if the eist.. f = {(-, ), (, -), (-, )}. f = {(0, ), (, -), (-9, )} g = {(, -), (-, ), (, -)} g = {(-, ), (, ), (, )} 7. f = {(, ), (, ), (-, ), (, 0)}. f = {(0, ), (-, ), (, ), (-, 0)} g = {(, ), (, ), (, -), (0, )} g = {(-, 0), (, -9), (-7, ), (-, -)} Find [g h]() and [h g](). 9. g() = - 0. g() = - 7. g() = + 7. g() = + h() = h() = + h() = _ - 7 h() = - If f() = +, g() =, and h() = -, find each value.. g[ f()]. [f h](). [h f ](). [g f ](-) 7. g[h(-0)]. f[h(-)] 9. g[ f(a)] 0. [f (g f)](c) Lesson 7- (pages 9 9) Find the inverse of each relation.. {(-, 7), (, 0), (, -)}. {(-, 9), (-, ), (, 9), (-, )} Find the inverse of each function. Then graph the function and its inverse.. f() = - 7. = +. g() = -. = = -. g() = - 9. h() = _ + 0. h() = - _. = _ -. = _ -. f() = +. g() = - Determine whether each pair of functions are inverse functions.. f() = -. f() = - 7. f() = -. f() = - 7 g() = - g() = _ + g() = - _ g() = _ + 7 Etra Practice 90

33 Lesson 7- (pages 97 0) Graph each function. State the domain and range of the function.. = -. = + 7. = - 0. = +. = + -. = -. = +. = + -. = _ +. = 9. = -. = - + Graph each inequalit.. >. < < - + Etra Practice Lesson 7- (pages 0 0) Use a calculator to approimate each value to three decimal places Simplif. 9. 9h _ ,000. -d 9. ). _ (- 9 a b. ± p q r s 0 ( - ). ± m n. - ( - ) (r + s). 9a + a ± a + a + a + Lesson 7- (pages 0 ) Simplif r ( - ). - ( - ). ( + )( + ). ( + )( - ). ( + ) 7. ( + )( - ). ( + ) 9. ( - 7 )( + 7 ) 0. ( - 7 ). _ m _.. _ a Etra Practice. _ r s t. _ _ 7 n

34 Lesson 7- (pages ) Write each epression in radical form.. 0 _. _. a _. (b ) _ Write each radical using rational eponents a. ab c Evaluate each epression _ 0. 7 _. (-) _. - _ 7) -. (-) - _. _ _. - _ _. ( Simplif each epression _ 9 7 _ 9. _ _ 9. ( k _ ) 0. _ _. m _ m _. ( p _ q 7_. 9. _ t 9_ 9a 0. _ ). a - _ ( 9_ c _ ). 7 r_ r 7_. v _ 7 - v _ 7 v _ _ + _ Etra Practice Lesson 7-7 (pages 7) Solve each equation or inequalit.. =. s - =.. z + = 7. m = 9 a + =. d + d - = 7. g + = g +. - = > 0. n -. w < c < -. + >. c > 0 7. n + -. z - - = (n - ) _ = 0 0. (7 - ) _ + =. (a - ) _ Lesson - (pages 9) Simplif each epression.. _. _ - _ _ _ 7 0. _ 9u v _ 7u v.. -a b ab. (-cd ) c d. _ - _ 0 7. _ u _ u. _ _ a a _ _ (ab) _ c. _ a b c Etra Practice 907

35 Lesson - (pages 0 ) Find the LCM of each set of polnomials.. a b, ab, 0a. - -, Etra Practice Simplif each epression.. _ 7d - _. _ + d -_ _ +. 7_ + _ 7. _ - + _ ( - ). _ - _ _. m + - m. _ - m _ -. a - - a. 7. c + a + c _ + + _ 9. - z - z + z _ - _ v + _ uv + _ u c + c _ _ - Lesson - (pages 7 ) Determine the equations of an vertical asmptotes and the values of for an holes in the graph of each rational function.. f() = _. f() = _ -. f() = + + ( + )( - ). f() = _. f() = -. f() = Graph each rational function. 7. f() = _. f() = _ 9. f() = f() = _. f() = - ( - ). f() = ( + )( - ). f() = + -. f() = _ + +. f() = Lesson - (pages 7) State whether each equation represents a direct, joint, or inverse variation. Then name the constant of variation.. = 0. _ 7 =. _ = -. = _. A = lw 7. _ b = - _. 0 = c. D = rt 9. If varies directl as and = when =, find when =. 0. If varies inversel as and = when = -, find when = -.. If m varies directl as w and m = - when w =., find m when w =... If varies jointl as and z and = 0 when z = and =, find when = and z =.. If varies inversel as and = _ when =, find when = _. 90 Etra Practice

36 Lesson - (pages 7 7) Identif the tpe of function represented b each graph.... Identif the function represented b each equation. Then graph the equation.. = 7. = -. = _ 0. = - +. = + -. = _. = =. = - Etra Practice Lesson - (pages 79 ) Solve each equation or inequalit. Check our solutions.. _ - = _. _ + _ = _. _ b - <. _ a + >. _ - = _ _ - n < n 7. _ d + _ d - = = 0 9. _ n + + _ n - = n - 0. p_ p + + _ + = 0. z + p - z - = _ -z - z + _. _ z = _ +. m - = m. + m _ - =. n + _ n + = _ n n - Lesson 9- (pages 9 0) Sketch the graph of each function. Then state the function s domain and range.. = (). = 0.(). = ( _ ). = (.) Determine whether each function represents eponential growth or deca.. = (). = 0-7. = ( _ ). = ( _ ) Write an eponential function for the graph that passes through the given points. 9. (0, ) and (, ) 0. (0, -) and (-, -). (0,.) and (, 0.) Solve each equation or inequalit. Check our solution = < +. + = > _ ( ) - =. + = 9. = - Etra Practice 909