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CHAPTER 3: LESSONS 3.1-3.4 CHAPTER 4: CHAPTER 5: LESSONS 4.1 - 4.6, 4.8 o 4.9 LESSONS 5.2 - 5.8 CHAPTER 6: LESSONS 6.1,6.3 - 6.6 CHAPTER 8: LESSONS 8.2 - 8.6 Date Standardized Tes For use after Chapter 3 Multiple Choice 1. The graph of a linear system is shown. How can you classify the ’system? ¯ 6. What is the solutionol~the system of ~quations be!qw? x=7y+ 12 2x- 14y=ll @ (12.5, 1) ® (5, -1) (~) many ~olutions (~) no solution " 6. Which system of inequalities is represented by the graph below? @ consistent and independent ,(~) ~o~sistent and dependent ¯ (~) inconsistent (~ inconsistent and independent How many sointions does the system in Exercise 1 have? (g) none ® one @ imSnitely many 3. What is the solution of the system of equations below? 3x + 4y= -6 x-2y=8 @ (-2, -3) @ (2, -3) 4= (~ (-2, 3) @ ’(2, 3) You haveS123.50 in quarters and dimes. ’There are 1202 coins altogethe;. Which system of equations can yo~ use to find the rmmber of each type of coin you have? @ x + y = 1202 0.1x + 0.25Z = 123.5 (~) x + y = 123.5 0.1x + 0.25y,= !202 (~)x+y= 1202 0.1x + 0.25y = 12,350 (~)x+y= 1202 10x + 25y = 123.5 Chapter 3 Assessment,Book @x+y<3 -4x + 2y>.1 (~) x + y > 3 -4x + 2y<_l ’ (~)x+y>_3 -4x + 2y> 1 (~ x + y<_3 -4x + 2y~l 7. What i~ the solution of thesystem o~ equations below? -x + 3y -.2Z = 19 2x+y-z=5 =3x =-y + 2,z= -7 @ (-1, -4, -3) (~) (-1, -4, 3 @ (-1,.4, -3) @ (1, 4, 3) A high school,s enro!lment i~ 950 students, which includes sophomores, juniors, and ~eniors. Twlce the sQphomore enrollment is three times the senior enrollment, and the total number ofjuninrs and seniors enrolled is 200 more than the number of sophomores e~olied. How many se~ors are enrolled? @ 250 geniots (~) 375 seniors ¯ ~ ]Standardized Tes condnued ~ "lForuse afterChapter3 What is the sum of the mat~ces? Short Response F7 31 + I--9 -41 ~ L1-2J. L 1 llJ Matrix M gives the number of minutes Amy and Renee spent on three types of long distance calls last month. Matrix C gives the cost per minute for each type of call. Which product is defined, MC pr’CM? Explflin. ¯Find this matrix and explain what itg elements represent. MatrixM Amy ¯ Renee What is the product? -3 5 Local ’ State International ’L 4 -6] 20 4 I0 Matrix C L~cal State International Costp~rnfin [0.05 0.1 1.2] 9 Extended Response What is the determinant of the matrix? ~ 5 ¯ a. Write a system of linear equations with two equations and t~o variables to represent the si ,tFation. What do the variables represent? Grldded Answer You earned $141 last week babysitting and cleaning: You earned $5 per hour babysitting and $7 per ho&r cleaning. You worked 9 more hours babysitting than cleaning. How many hours did you work last week? The student cou#. cil is having a bake sale. They spend $40 for the ingredients to make brownies mad cookies. It costs $1.25 to make a d0zen brownies and $1.50 to make a dozen cookies. The brownies seI1 for $6 per dozen and the cooldes sell for $7.50 per dozen~ The ¯ student council sells a total of $195in baked goods. NUse an ifiverse matrix to ’solve the system of linear equations. (i3 c. What profit did the student council make for the brownies ’sold? for the cookies sold? Algebra 2 Chapter 3 Assessment Book ’ ’~i.~! "7~or ~se after Chapter 4 1. For the ftmcfiony = -x2 - 6x - 7, find the v6rtex and axis of s.ymmetry. @ vertek (3, -2); axis of symmetry x = 3 (~) vertex (-3, 2); axis of symmetry x = 4 @ vertek (-3, 2); axis of symmetryx = -3 (~) vertex (3, -2); axis ofsymmeti-yx =-4 If the graph ofy = ax2 q2 bx + c opens down, which of the following ’must be. true? -@ a~O @ c<O ® a>O @ c>O Which function does not have a maximum value? @y = -x2,- 5x- 6 (~) y = -x2 -2.- 6 @’y=3x2-15x+2 ,# @ y = 49 - X2 @ -3, 2-14 (~) 3,-I4 -3, 14 @ 3, 14 9. Factor the expr,,ession 8xz + ~8x + i2. @ 2(x + 2)(4x + 3) (g) 2(x + 3)(2x + 1) @ 4(x + i)(2x ÷ 3) @ 4(X + 3)(2x + 1) Simplify the expression 2 2+ ~-’ @ 4 _ 2~/~- @ (2, 4) What are the x-intercept~ of y = -2(x - 7)(x + 2)? @ -7 and 2 ~ + and -2 @ 14 and -4 @ 14 and -2 6. Factor the expression m2 -- 4m - 21. @(m-7)(m-3) (~) (m -- 75(m + 3). @(m+7)(m-3) (~) (m+7)(m÷3) -5 ’11. What are the solutions of the equation W2 = -9w? @ -9, 3 ’ 4-- Wha{ is’tlie vertex ofy = -3(x - 2)2 - 4? -~@ (-2, -4) ~ (~).(-2, 4)" (2, -4) 8. What are the root~ of the equation " Z2 q- 1 IZ -- 42 = O? 00,9 (~) O, -9 01,9’ What are the solutidns of 23=2(x-3)2+7? @ -+3. (~) 3~2J~ What are the s~lutions of -3 - y2 = 24? @ -+3~f~ ~ -+3i~/~ @ -+9~/~ @ -+9i~/~ 14. What is the standard form of the i9 . expressmn ~. N Which value of c makes the expression x2 - 5x + c a perfect square trinomial? 5 5 i 2. 1 Algebra 2 Chapter 4 Assessment Book Date Name For use after Chapter What is the absolute value of 3 - 4i? ¯ Short¯ Response ~ -18. What is the vertex ofy 3x2 - 30x +. 77? ® {-5, -.2) ® (-5, 2) (~ (5,-2)’ ,(~) (5, 2) "17. What is the value ofc ift~e discrimant of -2x} - 3x + c is 41? @ -4 .A bottle ro~et travels along ~ parabolic path and reaches a maximum height of 2r feet after traveling a horizontal distance of 7.feet. a. Write a quadratic function of the form y =: a(x - h)2 +/c that models the bottle rocket’s path; assttming it leaves the grmmd at the point (0, 0). b. Describe how ~hanging the’values of a, h, and/~ affect the flight path 0fthe bottle rocket. (~) 4 /\ 18. Which’ineq~alityrepresents the graph below? Extended Response 2-1. A rectangular garden is 25 feet long by 10 feet wide. You have enough mulch to cover 1000 square feet. @2X2+X-- 15>-0 a. You would like to extend both the length and the width of the .garden by ¯ x feet to use up all of the mulch. Write an equation to represent the area of the new garden. I~. Solve the equatioh frompart (a). c. Which solution do you have to reject? Explain. (~) --2X2 q-X- 15>_0 (~(2x+S)(x+3)~O’ (~) 2x2-x- 15>0 Grldded Answer -19. 12Iow many real number solutions does the equation 7x2 - 5x + 1 =0 have? Algebra2 ~-’ " Chapter 4 Assessment Book (D Date , . Name Standardized Test For use after Chapter 5 at i~ the simplified form of 8a~be-19 Which polynomial represents the volume of the cone show~? 12abac : @2abac2 2a V= ~rr h (~ 3bac2 2x+ 5 212 3b2 , ~ What is (~.2 X 105)(I.4-X i0-2) written in ¯ ~ " scientific ttotation? (~) 4.4~ × 107 ,@ 4.48 x iO3 (~) 44:8 X 103 x-2 (~ 44.8 X 107 3. Which equation is the graph of the polynomial function shown?" ~ (~) x2-}" 3 ,rrx 107r 3 7. What is the complete factorization of 3x4 -- 3x2? ¯ @ 3~(x~- 1) @ f(x) = -Z~3 + x2 -- 2 (!~ 3x~(x -- 1)(x + 1) @. 3x(x 7 ~)(x + 1) @ ~(x~ - ~) 8.’ Ifx + 3 is d factor ofx3 - x2 - 17x - 15, whist is another factor? 4. What’is the degree of the polyaomial h(t).= -St2 + 5 - 3t37 @1.-®2 @3 5. Wl~at is the greatest common monomiaI factor ofgx3y2 + 15x2y - 6xya? @ 3x2 (i~ 3y= (g) x+ 1 9. Ifx - 2 is a facior.ofapolynomialf(x), whicl~ of the following statements does not have to be true? @ f(2)= .0 "" . (~ f(-2) = 0 (~) 2 is a root off(x). (~ 2 is a zero off(x). ~ ~ Fo~use~qfterChapter5 " ’10. Which is not a possiNe ration!! sohition of f(x) = 3x3 - 1 lx2 + 5X -- 6? (~) _+2 (!~ _+6 Ba~e~ upon D;scartes’ l~uIe of Signs,’ which of the following is the only possible ¯classification df the rogts of the function u(k) = -3k3 ÷ 5k~- k + 4? ~ @ (~ 3 positives, 0 negatives, 0 i~:aaginar~, 0 positives, 3 negatives, 0 imaginary 1 positiye, 1 negative, i imaginary (~) 2 positives’.1 negativ4, 0 imaginary A package has a length 10 inches greater than its width and a height 12 inches less than its width. . a. Determine the polynomial funStio~ that will calcqlate’the volurne of a package with width w. b. To carry this package onto an airplane, it cannot be larger ’than 4800 cubic inches. What should its dimensions be if you "$vant to havethe maximum allowable volume? (~ "12. What is (are) the local’minimum value(s) for v(x) = 2x3 - x2 ÷ 1? (~) There are none. students who use a.college lab is tracked for several academic yem-s. The results are summarized in the table below. St~d~I 1287 I i365 11402 11693 -1994 1995 1996 1997 GHdded Answer 13; How many solutions does j(m) = -7m3 - m4 + 1 have? @ ~= "/ a. Let 1990 correspond to year x = 0, 1991 to year x = 1, and so on. Enter the data into your graphing calculator arid make a scatterplot. Which polynomial fimction does it seem to model? Use polynomial regression to obtain a model. Romad to tw6 decimal places What is the regresgion equation you obtained? b. Graph the model mad predict what the nmnber of students wili be i~-20~,6. ~. Graphy =. 500 in the same’ viewing window. F~nd the intersection point(s). Explain the, ’ °~ ~ ¯ ~ignificance~o~:ou_r res~Jts ¯ Algebra 2 ’Chapter 5 Assessment BoOk 71 Name ¯ ’ Date Standardized Test Fofi~se_qfter Chapte~ 6 Mu~lLiple Choice 1. What is the valne of (-243)3/5? @ -27 (~) -3 (~3 (~ 27 2. What is the solution to 3x5. + 350 = -379? 729 ¯ 729 ~ Which expression is the simplest form of 4~ ([~) 3"~- 8. Given u(x) = ~ - 1 and v(x) = x - 5r what is the domain of u(v(x))? @ All real numbers (~ x 2 0 @x>¼ 4 9. Which function represents the inverse of the graph shown? ([~) 6~ x ~what i{ the simplified expression of the ~’." length of the triangle’s hypotenuse? , /t 3X112 (~)y= -5x + 3, 2x3/2 @ ~ 3x1/2 (~ ~ + 9x 1 ®y=gx-3 @y=~x+3 .(~) y= 5X+3 (~) 2x3/2 + 3x1/2 @ 4x3 -t- 9x2 Assuming gll variables are positive, what is the simplified form of 10. What is the inverse of the power function ¯ g(t) = .2-~qTt37 " (~ h(t) = 2 3 = ’-z2@ + 3~? @-z3~zz ~ 14z3~zz (~ ]4z4~zz (~) 92z3~zz Ifh(O = t2/3 9 andj(t) = 3t + 5t2/3, what is h(O -j(t)? 1 I. Which of the following paJ~s of functions are not thverses of one another? (g) u(x) = x - 2; v(x) = x + 2 @ --4t~/3 -- 3t - 9 (~) .4t2/3 + 3t + 9 ® u(x) = 5x - 1; v(x) = ~x + ~ @ 3t + 6t4/3 " ® u(x) = x3 + 1; v(x) = ~xx - i (~) -7t713 - 9 Algebra 2 Chapter 6 Assessment Book 85 Date Name CSAPTE" ]Standardized Test. continued 12. The graph ofy = ~ is shined 2 ~its up ~d 3 ~its to &e leA. ~ch is the equation of the tr~slated Nnction? Short Response You are digging a garden in your bacl~ard. You would like the length to be 5 feet grea~er than th~ width. Determine the fomction A(x) to calculate the area of the g~rden. What should the dimensions of the garden be if you’would like your garden to cover 104 square feet of gro}~,nd? @y = ~3 +’2 13. What are the domahl and range of the functiony = 5~xx - 22 @ Domain: all real numbers; range: all real numbers ~=x~e~ded Response "17. The XYZ Widget Company determines that it costs them $4 to produce each widget plus " an initial fixed cost of $2250. a, Determine the cost ftmcf!on C(x) for producing x number.of widgets. Un~’ortunately, the sharp increase in fuel prices.have led the company’s pricing analysts to believe that. costs vail increase overall by 10%. Determine the functionf(x) which represents a 10% increase. Which composition of functions makes sense to calculate the total cost with the 10% increase, C(f(x)) or f(C(x))? Why? Hay< much will .it cost the company to produc~ I 0q,000 widgets before and aftei the increase? (~) DOmain: x .-> 2; range: all real numbers @ Domain: all real numbers; range: y > 0 " @ Do~aain: X -> 2; range: y > 0 14. What is (are) the solution(s) to x-2=~x=l? @x=l (~) x= 5 @ x = ! and 5 (~ No solution What is the solution of (x - 5)~/3 - 2. = 2? 86 Algebra 2 _- - .... ...... Chapter 6 Assessr~ent Book ..... - <-~ ~ ~’ Name Date Standardized Test For use after Chapter 8 ’ Multiple Choice ¯ " ~. Which equation represents inverse variation? 5 @~-=x ,(!~ y=x+ 5 (~) y ~ 5x ~Ifx v~es directly Wi~y andy = -12 when ~ ~ x = 4, what is the value ofy whenx = -3? 6. Whicfi function has the domain of all real numbers except -2? x-2 @Y~x+2 .(~ Y = x , x-2 (~)y x+2 x-2 y=x~2 7. What ar~ the asymptotes of the ftmction 4x2 + 3x + 19 Y = x2- 1 . @x=0, y=0 1 ~ Let r v~y ~rectly with s and inversely wi~ t. ~ich equation represents t~s relationship? at a (~) st Which function represents the graph shown? (~) x = 0,~c= 1,y=4 (~)x=-,1,x= 1,y=~ What ~s the simplified form of 2x - 9x+109 x2+xs-6 Z-c - 5. 2x-5’ @ x-3 (~) x+3 2)+5 @ 2x+5 9. Which expressionis theproduct of 24a?b ¯ 39a~c37 13abc’ 8b2c~" 7 "@ Y- x2- 9’ @Y=x2_9 7x (~y= .. @y 9 7x3 ¯ 2 -9 _ x~ What is (are) the vertical asYmptote(s) of the function in Exercise 4? " (~) x=3 @x=_+3 118 Algebra 2, - .... Chapter 8 Asses~-r~nt Book There are none, ~ b~ " (~ 9aab2 2 .(~) 13bll7aab~ 117a3ba @ 7 i~ 1.O. The least common multiple of .which pair of expressi6ns is 3x(x + 2)(x+ 1)? @ x~ +3x + 2;x ~ 2 (~) x~ +3x + 2; 3x + 6 @ x2 +3x + 2; 3X2÷ 6x @ x2 +3?c + 2; ’3x3 + 6x~ @ IFor~’~eoiterChepter8 The legs of a right triangle have lengths ) and x~. What is ~e sin~plified ratio of the area of the triangle to the hypotenuse? x,/g X Sh~rt Response You join a health club which charges you a $175 regisb’ation fee plus a $25 per month charge. a." Determine the equation which calculates the total amount y you have paid in fees for your membership through month x. . b. Determine the equation which calculates the average montl’fly payment y you hav~ made through month x. Which is the firs{ month you average less than $40 per month for membership? Ex~ended Response. 12. "fiNch expression represents the simplified form of 3x .? 1 - 25" @x . 3x - 2 ~-2 ~ 2{~x -T) (3x - 2)(x - 2) ¯ x(3x - 2)(x .2 2) ’{~) 3x - 5 (~ 2(3x - 5) Gridded Answer What is the solution of x--] 2= .Q A pack}ging engineer for the Bubble Beverage Company is given the task of designing a new can. The company would like to minimize the surface area of the can in order to min’tmize overall packaging cost.. a. What is the surface area ofa cari with radios r and height h? What is the volume of a can with radius rand height h? la, If the can must h~ld 35~ mL, determine the formula for the surface area 0fthe can in terms of radius r. (Hint: Use the fact that the volume is 355 mL and delve for h in terms ofr.) ,, For what value of’r is the surface area. a minimum? Rotmd to one decimal place. (Hint: 1 cm3 = 1 mL) d. If aluminum costs the company $.001 per square centimeter, how much will it cost the company to supply the aluminum for the can? Algebra 2 Chapter 8 Assessment Book StandardizedTest 1.A 2. B 3. C 4.A 5.D 6:B’ 8. A’9. D !0. C 11.D’:12.25 13. CMis defined. I~ is possible to multiply a 1 × 3 matrix by a 3 × 2 matrix, but not the other way around. CM ~epresents the dollar amount spent byAmy and Kenee on all long distance calls. ¯ 14. a. 1.25x + 1.5y = ~0; 6x + 7.5~ ~ 195; , ., x represents the. dozens of brownies¯ ~old, y represent~ the dozens of cookies so!d, b. x = 20 dozen; y = 10 dozen c. $95 pro~t for the brownies; $60 profit for the cookies. Standardized -Test "14. a. V = w3 - 2w~ - 120w b. ~vidth: 20 in., length: 30.in., height: 8 ih. ¯ ’15. ~dratic;y = -2p.17x~ + 262.56x + t 144.~1_b. 182 c. There ar~ two, intersection points atx U" -2 andx ~15. This means that the num)er of students was 500 in about¯ 1988 " and 2005. Standardized Test I.A 2. C 3. B 4. C 5. C 6. A2.7. D.8. B 9. A’10, C ~I;B 12. D’~3.3 14. a-y = "175 + 25x b.y = 1~ + 25; month 12 15. a: s~face area =.2~r: + 2~rh, " ’ vol~e ~ ~r:h b, s~face ~da ,=2vr: -t-710 c. 3.8 cm d. abou~ $.28/~ _ _ Standardized Tes~ ’I.C 2. A 3. C 4. C 5. B 6.~ 7. C 8. B 9. D 10. C 11.B 12. B 13. B 14, D 15]C 16. D ~7. B ~8~A 19.0 3 20. a.y = -~(x -- 7)2 +21 b. ~swers will v~. 2t a. 100’0 = (10 +’x)(25 +x) b.~ = 15 orx = =50 c.x = -50 becanse you c~ot have a negative len~. Standard~zed Test ¯ . ’1.A 2. B 3. B 4. C 5. B 6. A 7. B 8. D 9. C 10. C 1~.C ’12. D 13. D I~.B 15. 13 16.A(x)=x(x-5)i13ftby8ft 17. a. C(x) = 4x + 2250 b.f(x) = 1.10x ¢.f(C(x)~ because the I0% increase will not ’affect the $2250 otherwise, d. before: $402,250; after: $442,475 .