Identify a pattern and find the next three numbers in the pattern. 5. 5(2s 2 1) 2 3(s 1 2); s 5 4


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1 Chapter 1 Test Do ou know HOW? Identif a pattern and find the net three numbers in the pattern. 1. 5, 1, 3, 7, c. 6, 3, 16, 8, c Each term is more than the previous Each term is half of the previous term; 11, 15, 19 term;,, 1 3. What properties of real numbers are illustrated b each equation below? a (8) Commutative Propert of Addition b. 1 () 5 0 Inverse Propert of Addition c. (8 1 t) 5? 8 1? t Distributive Propert d. 7 8? Inverse Propert of Multiplication Evaluate the epression for the given value of the variable.. a (a 1 1); a (s 1) 3(s 1 ); s The epression models the dail cost in dollars of renting scuba gear from the water sports store. In the epression, represents the number of hours the scuba gear is used. What is the cost of renting scuba gear for a da when the gear is used for 3 hours? $30 Solve each equation. 7. r 1 5 3r (t 1 1) Solve each equation for. State an restrictions on the variables. 9. t a a 3 5 t ; t u
2 Chapter 1 Test (continued) Write an equation and solve the problem. 11. Two buses leave Columbus, Ohio at the same time and travel in opposite directions. One bus averages 55 mi/h and the other bus averages 8 mi/h. When will the be 618 mi apart? 6 h Solve each inequalit. Graph the solution. 1. n 1 1 $ 7 n L a 1 5, 6a 1 1 a S Solve each compound inequalit. Graph the solutions #6 or 1 1 $ 3 K or L 115. t 1, and t, 6 1 R t R Solve each equation. Check for etraneous solutions. 16. u u or u b 1 u 5 b b The weatherman announced that the temperature T over the net few weeks will be at least 68F and at most 788F. Write an absolute value inequalit for the temperature over the net few weeks.»t 71 K7 Do ou UNDERSTAND? 19. What is another name for the multiplicative inverse? reciprocal 0. Reasoning Eplain in words wh u u, has no solution. Answers ma var. Sample: Dividing both sides b gives R. The absolute value of an number must be nonnegative, so the inequalit has no solution. 1. OpenEnded What is the difference between simplifing an epression and evaluating an epression? Answers ma var. Sample: Simplifing an epression is rewriting it using the properties of real numbers and combining like terms, resulting in a simpler epression. Evaluating an epression is substituting values for the variables, resulting in a numerical value. 68
3 Chapter Test Do ou know HOW? Determine whether each relation is a function. 1. 5(0, ), (, 3), (5, 5), (, 7)6. 5(1, 0), (5, ), (0, ), (, 8)6 no es Evaluate each function for the given value of, and write the input and output f() as an ordered pair. 3. f () for 5 (, 9). f () for 5 8 (8, ) For each function, determine whether varies directl with. If so, find the constant of variation, and write the function rule. 5. es; k 5 ; no Graph each equation O Write in pointslope form an equation of the line through each pair of points. 9. (5, 8) and (0, ) 10. (1, 3) and (6, ) 8 5 ( 5) or 3 5( 1) or 1 5 ( 0) 1 5( 6) 87
4 Chapter Test (continued) Write the function rule g() for the given transformations applied to the graph of f () units down, 1. 7 units up, 1 unit left 3 units right g( ) 5 ( 1 1) g( ) 5 ( 3) 1 7 Graph each equation. Then describe the transformation from the parent function f () translation units right O reflection in the ais O Graph each absolutevalue inequalit. 15., u 3 u $ u 1 5 u O Do ou UNDERSTAND? 6 6 O 17. If varies directl with and 5 18 when 5 6, what is the constant of variation? Find the value of when k 5 3; OpenEnded Graph a line that has a slope that is undefined. Answers ma var. Sample: a graph of an vertical line 19. Suppose ou manufacture and sell tarps. The table at the right displas our current sizes and prices. a. Draw a scatter plot showing the relationship between the area of a tarp and its price. Use area as the independent variable. b. Draw a trend line and write the equation. c. Reasoning Is this an accurate model? Eplain. d. Using our model, predict the price of a 50 ft tarp. b. Equations should be close to c. Yes; all the points are ver close to the line, so the linear model is accurate. d. about $10.0 Size (ft ) Price $1.39 $1.99 $3.19 $.79 $7.69 $7.99 $
5 Chapter 3 Test Do ou know HOW? Solve each sstem b substitution or elimination. 1. e e 6 51 no solution (, 1) (, 6) e Graph the solution of each sstem.. e $ 1 3, 5. e 1 # # 6. e. 1 # You have 13 bills in our wallet in $1, $5, and $10 bills. There are twice as man $1 bills as $5 bills. The number of $10 bills is one more than the number of $5 bills. How man of each bill do ou have? How much mone do ou have? si $1 bills, three $5 bills, four $10 bills; $61 Graph the sstem of constraints. Identif all vertices. Find the values of and that maimize or minimize the objective function. Then find the maimum or minimum value. # # 1 8 C(, 3) B(0, ) $ 0, $ 0 Maimize for P A(0, 0) 6 D(7, 0) ma P at (7, 0)
6 Chapter 3 Test (continued) What is the solution of the sstem represented b the matri? C 3 1 0S (, 1, 3) (1,, 3) (3,, 1) (1, 3, ) C Do ou UNDERSTAND? 10. Writing Eplain how ou determine whether a sstem of linear equations is independent, dependent, or inconsistent without graphing the lines. Rewrite both equations in slopeintercept form. If the lines have the same slope and same intercept, then the are equations of the same line, and the sstem is dependent. If the lines have the same slope but different intercepts, the are parallel lines, and the sstem is inconsistent. If the lines have different slopes, then the sstem is independent. 11. Mechanic A charges $5 for car repairs and $80 for each hour spent on our car. Mechanic B charges $60 for repairs and $60 for each hour spent on our car. a. If our car takes 5 hours to repair, which mechanic charges the least mone? Mechanic B b. How much will it cost ou to have the work done b the less epensive mechanic? $ At a bookstore, ou spend $76 on 11 books and magazines. Books cost $8 each and magazines cost $5 each. Write a matri that represents this sstem. How man books and how man magazines did ou bu? B ` 11 R ; 7 books, magazines Reasoning The sum of three numbers is 15. The second number is twice the third number. Do ou have enough information to determine the three numbers? If so, what are the three numbers? If not, what information do ou still need? No; ou need a third equation that defines another relationship between two or three of the numbers. 68
7 Chapter Test Do ou know HOW? Identif the verte, the ais of smmetr, the maimum or minimum value, and the domain and the range of each function ( ) 1 6 verte 5 (, 6); ais of smmetr 5 ; minimum 5 6; domain 5 all real numbers; range 5 all real numbers L 6. 5( 1 ) 3 verte 5 (, 3); ais of smmetr 5; maimum 53; domain 5 all real numbers; range = all real numbers K 3] O 10 O 8 Factor each epression. 5. c 1 c g 9 (c 1 1) (g 1 7)(g 7) Use a graphing calculator to solve each equation. Give each answer to at most two decimal places and and 51.9 Complete the square j j 9 81 Evaluate the discriminant for each equation. Determine the number of real solutions ; 0 real solutions 8; real solutions Plot each comple number and find its absolute value i! i 8 8i imaginar ais i real ais 8 O i 7 i 8i imaginar ais i real ais 8 O i 8i 97 8i
8 Chapter Test (continued) Find all solutions to each quadratic equation i, 1 3 i Solve each sstem b graphing "11 3 i, 1 3 "11 3 i d d, 1. O O Do ou UNDERSTAND? 19. The parabolic path of a hit tennis ball can be modeled b the table at the right. The top of the net is at (, 10). a. Find a quadratic model for the data b. Will the ball go over the net? If not, will it hit the net on the wa up or the wa down? No; it will hit the net on the wa down Writing Eplain the relationship between the intercepts of quadratic function and the zeros of a quadratic function. The are the same thing because the intercepts are the coordinates where the quadratic function equals zero. 1. The period of a pendulum is the time the pendulum takes to swing back and forth. The function l t relates the length l in feet of a pendulum to the period t. a. If a pendulum is 30 ft long, what is the period of the pendulum in seconds? b. Reasoning Wh does onl one of the solutions work for this problem? The other solution is negative and ou cannot have negative time. t s 98
9 Chapter 5 Test Do ou know HOW? Write each polnomial in standard form. Then classif it b degree and b number of terms ; quintic trinomial ; cubic, terms Determine the end behavior of the graph of each polnomial function up and up down and up Find the zeros of each function. State the multiplicit of multiple zeros ( 1 )( 3) multiplicit 1; 3 multiplicit 0 multiplicit ; multiplicit 1 Find the real solutions of each equation using a graphing calculator. Where necessar, round to the nearest hundredth , 0.86 Divide using long division. Check our answers. 9. ( ) ( 1 ) 10. ( ) ( 1 1) 1, R , R 7 Write a polnomial function with rational coefficients so that P() = 0 has the given roots ,, 6 1. i,! P() P() 5 Find all the zeros of each function , i, i 3, 3, "5, "5 97
10 Chapter 5 Test (continued) Epand each binomial. 15. ( 1 ) ( 1 3) Find a cubic function to model the data in the table. Let represent ears after N Births in the United States Determine the cubic function that is obtained from the parent function = 3 after each sequence of transformations. 18. a vertical stretch b a factor of 3; a reflection across the ais; and a horizontal translation units right 53( ) 3 Year SOURCE: Births (millions) a reflection across the ais; a horizontal translation units left; and a vertical translation 6 units down 5( 1 ) 3 6 Do ou UNDERSTAND? 0. The product of three integers is 56. The second number is twice the first number. The third number is five more than the first number. What are the three numbers?,, 7 1. What is P() given that P() ? Use snthetic division and the Remainder Theorem. P() OpenEnded Write a polnomial function of degree 3 with rational coefficients and eactl one real zero. List all of the zeros of the function. Answers will var. Sample: ; zeros: 3, i "5, i"5 1. A cubic bo is in. on each side. If each dimension is increased b in., what is the polnomial function modeling the new volume V? V in. 3 98
11 Chapter 11 Test Do ou know HOW? 1. Your brother is ordering 5 pizzas for the famil. There are 18 different kinds of pizza. How man different was could he order 5 different kinds of pizzas? 8568 was A bo contains 8 blueberr muffins, 6 banana muffins, and pumpkin muffins. You pick one muffin from the bo at random. Find each theoretical probabilit.. P(banana) 1 3. P(not pumpkin) 7. P(banana or pumpkin) J and K are independent events. P(J) = 1 and P(K) = 3. Find P(J and K) A compan is testing a new sunscreen to see if it is more likel to cause skin irritation that the sunscreen it currentl sells. The results of the test are shown in the contingenc table. Used new sunscreen Used current sunscreen Totals Skin irritation No skin irritation Totals The compan decides to make and sell the new sunscreen. Based on the results of the test, did the compan make a good decision? Eplain. Answers ma var. Sample: Yes; about out of 0 people who use the new sunscreen have skin irritation, compared to about 3 out of 0 people who use the current sunscreen. Based on this stud, the new sunscreen is no more likel to cause skin irritation than the current sunscreen, so the compan made a good decision. For Eercises 7 and 8, use the following data set: Find the mean, variance, and standard deviation for the data set. 31; 18.8; Within how man standard deviations of the mean do all of the data values fall? All of the values fall within standard deviations of the mean. 107
12 Chapter 11 Test (continued) 9. A team of biologists is studing the foes in a state forest. The team captures foes, weighs them, and then releases them. Which tpe of stud method is described in this situation? Should the sample statistics be used to make a general conclusion about the population? observational stud; Answers ma var: Sample: The sample size ma be too small for the sample statistics to be reliable as a general conclusion. Find the probabilit of successes in n trials for the given probabilit of success p on each trial , n 5 9, p , n 5 1, p , n 5 7, p N 0.17 N 0.3 N A set of data has a normal distribution with a mean of 36 and a standard deviation of. What percent of the data are within the interval from 3 to 0? about 68% Do ou UNDERSTAND? 1. An alumni association compiled the following information about its recent graduates. 0% graduated with a B average or better 95% of those students who graduated with a B average or better were emploed within 6 months of graduation 50% of those that graduated with less than a B average were emploed within 6 months of graduation a. What is the probabilit that someone is emploed within 6 months of graduation, given that he had less than a B average? 0.50 or 50% b. What is the probabilit that someone is not emploed within 6 months of graduation, given that she had a B average or better? 0.05 or 5% 15. Make a boandwhisker plot for this set of values: Reasoning On a histor test, there were 1 As, 8 Bs, 6 Cs and 1 D. Are the numerical scores on the test likel to be normall distributed? Eplain. No; there are more As than an other test grade, so there are more high scores than low scores. The data are likel skewed rather than normall distributed. 108
13 Chapter 1 Test Do ou know HOW? Find each sum or difference c d 1 c1 1 5 d. c d c 1 6 d c 7 6 d 5 3 c 1 0 d Find the value of each variable.. c d 1 c1 z d 5 c z d 5. c d 5 c d 5 1; 5 3; z 5 5 3; 5 ; z 5 5 Find each product c 1 dc5 3 d 7. c dc 5 1 d 8. f1 3g c d 1 6 c d c d f10 19g Do ou UNDERSTAND? 9. Writing Describe the matri operations that ou must use to solve the following matri equation. Then find the value of X. c 1 d 1 X 5 c 3 d First, multipl b the scalar. Then, use the Subtraction Propert of Equalit to isolate the variable matri. Subtract corresponding elements. Finall, multipl each side b 1 7 and simplif; X 5 c 3 5 d 67
14 Chapter 1 Test (continued) Do ou know HOW? Determine whether the following matrices are multiplicative inverses. 10. c d, c1 d 11. c d, c d 1. c 1 d, no es es Use inverse matrices to find the solution of each matri equation c 3 8 d X 5 c5 X 5 c 10 d d 1. c3 1 5 X 5 c 7 1 d 17 3 d X 5 c5 d 15. c d X 5 c 1 11 d X 5 c 5 d Use matrices to solve the following sstems of equations e ; e ; z z z ; 5 3; z 5 7 Do ou UNDERSTAND? 19. Roger and Clarissa each sold boes of cookies for a fundraiser. The sold large and small boes for different prices. Roger sold 1 large boes and 8 small boes for a total of $ Clarissa sold 16 large boes and 11 small boes for a total of $ Use a sstem of two equations and matrices to find the price of a large bo and a small bo. large: $3.00; small: $.50 68
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