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Transcription

1 1. Many times, sales employees are paid a base salary plus a commission --- a percentage of the amount of merchandise value sold. Assume that a particular sales employee is paid $200 eer week, with a 20% comml sjo on the amqu t they sell. Which equation best represents the total salary (T) per week that an employee,is paid for selling any value of merchandise (m )?. T = m T=220m CQJ;) T = a,+o.2m,..::9=::d. T = m 2. A 1,SOO-gallon tank contains 200 gallons ofwa er Water begins to run into the tank at the rate of Q gallons per hour. After 2 hours, the rate increases to 80 gallons per hour. What is the total number of hours that the water can fl ow before the tank is fu ll, but not overfl owing? :tp"il 1 4hurt 37. o ('to c;. - alp Iole.. +a s-vvlc 16 hours, 22.5 minutes 0 2- If.- e- vj l. -h, J VASwr 17 hours, 20 minutes J /<.-t 3So. 18 hours, 45 minutes...:..4 '--"'" -+,,<).y,s +go 3. ibes the difference(s) between the graphs of:,i So 3x 10 and g(x) 6x - 5 SO The graph of[(x) is twice as steep as the graph of g(x) X:; Ie..{.31S, - "... The graph of [(x ) is half as steep hlgraph of g(x) '31S,A- The graph of.1.f:tj has ay-intercept of -5 while g(x ) has ay-intercept of ",l5.1? (, '" h our The graph of f (x) has a lower v-intercept than the graph of g(x) is S - -lse Solve the equation for x : 7-3(2x - 4) = 5x - 2 f -K +I?- -:=- 5x - "2 -i+ - 1'1 5)(. -L -I -G'J. S)(. -;2. -Sy. -5)(.. -II i ). 1 ::- -II Page 1 of 15

2 5. Solve for x: ra I:!-/ 4= 7 ()(-3) 31 (f;) x = 3 2'2 -t t..t ( )( - S') 7 ( -3) 47 X =- 7 '2..'L -t-l...x x= 3.,--- =-7)( X :::. IX -.:L x=- - 7)< 7x -I 7-3)( -3 -;:'-3 6. Mr. Shaw begins traveling east on the freeway with a full tank of gasoline. His car has an 18-gallon gas tank and gets 25 miles per gallon during highway trave. Let m = the number ofmiles Mr. Shindler has driven Let g =the number ofgallons ofgas remaining in his tank Select which equation describes the relationship between the number of miles Mr. Shaw has traveled and the number of gallons remaining in his gas t nk: g = 18-25m m = 25g -18 g =18-- m m = Justify your choice in the answer box below Support your answer using words, numbers, &/or diagrams. 9"" [t", s - G'--.o< sh O ("v '5::.,r is y'v'-: e 0 I, Jk o Ve."e.. ')s ).- C( "{j, s - I 50 1(., 2S,s ).S S l e-ttp.-r C s L-U:l ;..ov ov.l '. es lod IY sl(jr 7. Choose the correct solution to the equation Q';J 4X +3) 2 x=2 3x.-{ 9f< + (o 7 x =-- -)< -t'l -x -t, 0 X =-4 x = Page 2 of 15

3 8. Given the inequality: -S<2X+S Solve for x: - I'J. < 2)(..... >L 2 L - ' < 5 Represent the set of solutions on a number line: elk...",) S kc de5 < ' -vj()e'y'-' -, -<:, One worker at a gadget assembly factory can assemble 10 gadgets each hour. After working for 3 hours, the worker's supervisor starts to assemble gadgets also. The supervisor can assemble 12 gadgets each hour._ Together, they assemble 140 gadgets. ---v.jo S lo f< So J...o -to..h( e. How many hours did the worker assemble gadgets in order to have 140, total? Support your answer using words, numbers, and/or pictures. (S 0 "l -1 5 Co I 8 tl) () I'U w 3c) S1 --, (o II lid TID (,A.)(> y l. (" or-. L') '-.-7J W(}./lt?( ;-"2.-"1 St';CN" -;-2'1- How many hours will the worker assemble gadgets?... l+- b 10. Solve the system of linear equations. 1:"" 5 S 3x + y = :')o -I S)'. - 5 j =- -(0 '*" CQvl,,{ ()..." 5.v v""- v..jl;t. -. (-5, 28) 6t. (-2,19) I/"'1JI,..U -3 (7,2) 'b j e (5,-2) { x + 5y = -5 + x+ SJ :=..- - 'J -70 Page 3 of 15

4 11. An ice cream store is keeping track of the number of chocolate and vanilla ice cream cones sold. One day, the number of chocolate cones sold was 10 less than twice the number of vanilla cones sold. A total of 140 cones w r sol that day. Write equations to determine the number of chocolate cones sold that day. Be sure to define your variables. Use the equations to determine the number of chocolate cones sold that day. Show your work using words, numbers, and/or diagrams. '--v---'" 3)< J-)( t I D - IS O :: 2(50) -10 /00-10 'f. SO - -;. C)D ) 12_ After soi vi ng the foil owing system 0 f equati 0 n,,_ (4 ; Sarah claimed that the system has no solution. Carl disagreed and said that the system has an infinite number of solutions. Who is correct and why? Who is correct? Show work to justify your conclusion. '1-2( '2)(- ;') I D L{)( -zt'f ' Explain how your work supports your conclusion: Page 4 of 15

5 13. A moving box can hold at most 40 pounds- I hav at least 50 boo to load into the box. On average, the hardcover books weigh twice as muc a ack books. Write system of inequalities to represent the situati o -t 50 Define your variables. =1f-l--.,t.-v-t.{ (C> 'I(/.R...r b 0 (> jl S u...jit.) S u etae.os 1- V..e.R. J-...-L..e ;;). hvt- CLWu u o":t 14. Tara's cell phone plan cost month, which includes 150 text messages. After she uses all of those text messages, it will cost her 0.12 er text message. Write an equation or inequality that could be used to determine the total cost of her cell phone bill if she sends more than 150 text messages. Be sure to define your variables. Equation/inequal ity: definition of variable: 0., I I ')( + S ::::. <j # -l--e 'f-+s po.. 5rl IS 0 v -=---o{....l <!..0 st- J Tara wants to spend no more than $48 -on her cell phone bill. How many text messages can she send, total? Support your answer with words, numbers, and/or diagrams. 0,, '2 )( -t- S - S - c; De I "")( 13. '-.. X < -- IO o 1'2 Explain what your answer means: -tf. YZ) To Le e f -I b, l LJ -1-<)'-t-c; be... r--j (SID ls)es. IO 2SY; "" Page 5 0/15

6 15. Fred, Thomas, and Zachary worked at the ice cream store in the mall. Last week, Fred earned more money than Thomas, but less than Zachary. The graph shows the money earned by Zachary a nd Thomas. :>', r< 1; WEEKLY PAY VS. NUM BER OF HOU RS W OR K ED ", ro 0 0 c ;>. r. a.. :.?OO Ho urs Worked Which area of the graph represents Fred's possible weekly pay, and why? P because that represents more than Thomas. T because that represents more than Zachary and less than Thomas. P because that represents more than both Zachary and Thomas. T because that represents more than Thomas and less than Zachary. 16. Which is the graph of the solution set of the system of inequalities? Se;Q- c.t G => - L.V -2y O r - J -'2 clj+.e J 2x + y > 0 G yo -:=d: _..x 5h l J '.0 t- be. b"sl J ;t -.:-- -. _-- 'Tf bovf..i Sko lj b - X -t ID 'o C{.D".It- Page 6 of 15

7 17. Look at the system of linear inequalities. _.1 <.. -! - 3 5oeDvJ ' { y <JJ -I -I -I J ol - ""e(" + y 8 > X - 3 }OCN Jt,:e s.o I.'--,x+g Which graph represents'1:he solutions to the system of linear inequalities?. s fos slo, Ch '" +' rj :, J, v.l 18. Graph A is the graph of y = 2cfi and graph B is the graph of Which statement about the two graphs is true? Both graphs A and B rise at the same rate. -t'-r-'..-l. Graph B rises at a faster rate than graph A. l s..e... Graph A rises at a faster rate than graph 8. --h-- v e... The y-intercept of graph A is above the y-intercept of graph B. :." L 19. In 2000, there wer 4800 p,eople who attended the state basketball tournament. The enrollment has been increasing 3% annually since then. Create an equation that would determine the total number of people who will attend after x years. (Let x = 0 represent the year 2000.) ( ) x Page 7 of 15

8 20. Solve the equation 2 x = c; 7 rj 0 x 5 :; G, 8 x=6,. J CO 7 o A. ifjr M.ecL-. o c. x = 34 0 o D. x = 64 2 (o 21. In the laboratory, a bacteria population grows in size every hour, as shown in the table. A new bacteria culture is started with 20 bacteria. Create a function that describes the size of the bacteria population, pet), in terms of the number of hours, t. Predict the number of bacteria in 7 days. ) After how many hours will the population first exceed 10,000? X a) 7 hours I OJ DOu ::- L/-O( 2 ') COT 8hou - Ov- 50 S; GLA el L.:...: c) 9 hours J '1 d) 10 hours if0 ('L-') '7 '= S U),0 B LiO(7.,J IOIl..J.10 t{o(z..) YO,O 22. The student population at a high school has been decreasing each year, as shown in the table. Years # students -5 Write a function, for t 2: 1 to represent the number of students, Set), based on the number of students from the previous year, Set - 1). S (t;) =- S[ t::- - I") - 5 SCI") = 1'2 30 Page 8 of 15

9 stv'---. (t- J v 23. Consider a sequence given by the formula: fen) = 5-8(n - 1) Which of the following is an equivalent sequence? u i o,j e.( fen) = 5n - 1 with [(1) = 8 fen) = fen - 1) + 5 with [(1) = 8 &--wrv 5f-v.-t : ) fen) = fen - 1) - 8 with [(1) = 5 7'>. fen) = fen - 1) - 8n with [(1) = Given the functions: [(x) = x + 5 and g(x) = 5 Gf Select all he statements that apply to the functions: (4 [(x) and g(x) have the same y-intercept; -+VII i!...,. b) [(x) and g(x) are linear functions; +Vue fo... f) j u.h,v- <) c) [(x) and g(x) are decreasing functions; ll:w<. --c. y 1;-) {yve fur C'cr Jd) [(x) is an increasing function, g(x) is a decreasing function. C/ --t-<" v e.. tv.) e., 25. The graph of a function is shown. Which of the following equations is o represented by the graph? (1 ptj [(x) 2Gr «; - I" [(x) = (2)X 26. Given the function [(x) = Ixl + 3, for what values of x is the function positive? ( 3J always ' ,4e A / r when x > -3 )%11->'(;' whenx>3 never Page 9 of15

10 c1c.)", f j.-s 5h fet.t letr 3 V-s sr-lfj JvwV" y o..-v--j.s.tvhke( 27. Graph A is the graph ofy = Ix and graph B is the graph of y = 31xl - s. 6cr Which statement about the two graphs is true? 2 2S. Given the functions: g(x) = -(x - 3)2 + 2 and {(x) = x, describe the graph shifts needed to create the graph of g(x) from the graph of {(x). v(w' 3 rr< J (re 0kc+.e(.A) tn(!:y- '?< -C-'.)l-I S 29. A group of functions are shown. J p 2 a(x) = Ix + SI l{...",2. I hex) = 31xl c(x) = Ixl + S d(x) =. -Ixl - 3 wf' e(x) = Ix ,.. {(x) = Ixl -, v-. (V. {J;., '"' v Sort the functions based on the graph shifts compared to the parent function. Write the function's letter in the correct category below. You may need to write a letter in more than one box. " 30. Choose the equation that matches the graph: -2. '/-- y = -Ix s if-'! skc,ql- y=-lx+21-s Graph A and B have the same slope...g-...ls-< Graph A is Jess steep than graph B. -YvL r ll Graph B has a y-intercept that is 4 units above the y-intercept of Graph A. l.- lrs Graph B has a vertex that is S units,abov] the vertex of Graph A. -V -t v p -C-c,-l'>e-- ',h" elo...).t-- o 1& +ko.:::;r /( y = - (x + 2) 2 +.S "'-k.(a V '/<.. y = -(x - 2)2 + S f, Page 10 0/15

11 31. You are a full time employee at a marketing firm. In order to maintain full-time status you must work.minimum of 25.hours a week, and you cannot work more than 45 hours in a week. You make $20 per hour. Define the domain and range variables in the context of the problem. Express the domain and range as inequalities. Define domain...- {:/ l _ Define range variable: "f: /" ':::> variable: :::. a t-. Domain inequality: --"'- "-- SOD - ':J fa, c1 < l - 9uv 32. Given that {(x) = 3(5x - 2), find x when {(x) = -18. '-l3'l) -1 <& -:: - S )< -<a 33. Given the function: f( f(xre -Ie : valuate -2). - + I '1.. +I -:::Ci) - -->.r 34. Look at the function. ekt 1-0 ", :) L A.....-,1..) v - -.J What are the doc 8 n and raa Domain: -5 ::; x ::; 8, Range: -3 ::; Y ::; 3 Domain: -5 ::; x ::; 8, Range: -4 ::; Y ::; 4 Domain: -3 ::; x ::; 2.5, Range: -4 ::;y::;3 Domain: -4 ::; x ::; 4, Range: -5 ::; Y ::; 8 Page 11 of15

12 r c(<.tv!+- re ed- a.,... "1-' v?.l J e Which of the following is ll.q!a function? bvt- ClLV'-.(e.r-e A.. L..J Vc lve... Domain Range 2 9 t:; {(4, 1), (7, -2), (-2,4), (1, 2)} > ,--. L) ' -y-vc.lve. J 2 l. lljs The graph shows the functions { (x) = (x - 1)2-4 and g(x) = x Identify the value(s) of for which {(x ) = g(x) )(--d- 37. Over which interval(s) is {(x) < g(x )? SR,---K ce",-te x - c,yc.s ( ') 38. Over which interval(s) 'f-j}, is fc: mcreasin; ) i , 6 5 : 3, I 1 1 ', - 3-5,. (x) I I I, J f'.v I 1f' ;',! I "" Sv f I': fi N x, f' U d ilts" ) I If'-c... -<. ;;x-'f 39. Identify the vertex, x-intercepts, and y intercept of {(x). 'j U x-'f- Lt) - 4 ') 6 'j(-ivd- (-1 / 0') (/») II) - ', N- (' 0) -"3) Page 12 of15

13 40. At a particular company, every employee ceceives a 4%cD I ;v;cease to:c al 5": " What impact does this have on the mean and on the range of employee salar;es at the company? '/.. I, o' The mean increases but the range does not change..j 'Y'2-- '7.2A.) 'X Jjj The mean does not change but the range increases. ts..e- The mean and range both increase. --v v e... o D. The mean and range do not change. IOVi:> f. 1.0"" 10' A company decides to give everyone of its employees a $1000 raise. What happens to the mean and median of the salaries as a result? --v-v; S () ':::. " Mean stays the same, median increases by $1000 SO) GOD ' 7(,1 D Mean increases by $1000, median stays the same (Vt-la..", ') L""""" ta..-(a."",-, t- I ()a Mean and median stay the same -t!.9l- {' B Mean and median both increase by $1000. I I.? 0... (,1 0 1.) G:1-{l 42. A company decides to pay its employees the following salaries: VI'-Q... t l:0.-.. $200 per week $250 per week $350 per week $8000 per week tsllrvje, Which statistical measure best describes the typical salary, and why? The mean, because it is not affected by extreme values. J. c;.l The mean, because it is the average of everyone's salary. --Yv The median, because it is not affected by extreme values. - The median, because it is the average of everyone's salary. ls--e- 43. The box plot below shows the ages of football players on a school's football team. 0.., M I Select all of the statements that are supported by the box plot: j)4.. The youngest player on the team is 15. l The median age of the players is 17. %-.1 25% of the players are between 17 and 18 years old. +V- U e... 02»0% of the players are between 15 and 17 years old. ' ve... Ll *'I..-.. Q (:. au/,-") - The Q.:!ean ag,e of the players is 16.5 ye?rs old. cev-..: +- h' vo tvv-- -. S, Only one player is 14.5 years old. fo-- s-v'-o V' (L S(f" h Page 13 of 15

14 44. The two-way frequency table below shows the results of a survey regarding transportation to ( school at a high school: '70 Ride the bus Walk or ride bike Drive a car total Freshmen Sophomores Juniors Seniors Total , L' C, U D -z.-.c.o Select ALL of the statements that are supported by this data: "J.>O -;" :/,/ '1' W"" iy' -s 2- R. 0/ 'V'" vr y c (; ":>. i> '>(-.'0' -N) e v ' c,jl9 e..,ii) v,/ (,9.. The relative frequency of thhmen riding thgher than the relative frequency of. the combined other classes riding the b lj,s....:- 5D () _ 2-7, " I{).e",, $: The joint frequency of,sophomores driving iwer than the joint frequency of en D=..oalking or ridi9 their bikes. ::'> 2s SO CI -::..0 S The marginal frequency of seniors is higher than the marginal frequency of students drivin to school. ""' I 5 '? :, SbC) :::. O. 7.- ;, -;- 5DV :::... ::>. The relative frequency of juniors who DON'T drive is lower than the relative frequency of s 10 -= c. O..-lL,,,0 -;' 0, I The graph shows the stock value for a technology company. 45. Which equation represents a line to fit the data?.""'/ 1 lb Y=2x+20 7 Vi' 60 Y=8X+20..'t 'IS cldses+....!!! 50 '0 40 y = 0.125x vO. M.l S s (,If 30 til y = lox +20 > 20.--tN <" 0 t;.!)rf What is the most likely value of the stock in year 10? cvv-. 0 A. $60 Uf- 0 B. $1b 0 C. $70 l Stock Value years since D. $ Lucy did a study on the number of hours students spend studying and their grades. She found that there was a strong positive correlation between the two. Page 14 of 15

15 rs'x: -to,ee/ ( ' c.v la- Which scatterplot shows the strong, positive correlation of her data? -G. CO.J(? <; v j)? Samantha surveyed a group of adults to gather data on their height and weight. She put her results into this graph: 300 }',O + 50 () o Height beyond 50 inches tall The line of best fit for this graph is: y = lox + 50 where x = # inches taller than 50 incn and y = weight in pounds I 0 po I.' ""L-:;. ( 1-)) CN y 1.. ""c. ()<:) Which of the foilowing statements is a generalization of the slope of the line's equation? For every inch a person grows, he will gain 10 pounds, -..4;. -r '-b() v t- pe-.--s C'I A' -- Irr--.e.. For every inch a person grows, he wil1lose 10 pounds Ifperson A is one inch taller than person B, it is likely that person A is 10 pounds heavier than person B. If per Qn A is one inch taller than person B, it is likely that person B is 10 pounds heavier than person A. JVVV.A Page 15 of15