Alg 2 Honors 2018 DRHS Unit 1 Practice Problems
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1 Essentil Understnding: Cn ou represent liner situtions with equtions, grphs, nd inequlities, nd model constrints to optimize solutions? Assignment Clendr D Dte Assignment (Due the next clss meeting) Mond 8/06/18 (A) 1.1 Functions Tuesd 8/07/18 (B) 1. Function Nottion nd Compositions Wednesd Thursd 8/08/18 (A) 8/09/18 (B) HW: 1. Prctice, Sign sllbus nd p $ lb fee 1. Equtions of Lines 1.4 Sstems of Equtions HW: 1. & 1.4 Prctice, hve ou pid our lb fee? Frid Mond Tuesd Wednesd 8/10/18 (A) 8/1/18 (B) 8/14/18 (A) 8/15/18 (B) 1.5 Set nd Intervl Nottion & Review HW: Prctice Test, hve ou pid our lb fee? Next clss is the lst d ou cn turn in n lte ssignments for this unit. Unit 1 Test Notes: Simplifing Rdicls HW:.1 1 P g e Be prepred for dil quizzes Need help? Tr Check in order to get informtion on how to ccess the textbook website, copies of notes, nd other hndouts. Students who complete ever ssignment for the semester re eligible for % grde bonus. Students with no lte ssignments lso get pizz prt! Show the originl problem, ll work, nd solutions on our own pper! 1. Prctice Problems: Use f(x) = -6x + 9; g(x) = 5x ; h(x) = -; d(x) = -x 1) Find g(-). ) Find f ( 1 ). ) Find x if d(x) = -1. 4) Find x if g(x) = 11. 5) Find f(x) + g(x) h(x). 6) Find g(x) f (x). 7) Find f(x) h(x) 8) Find f(x) g(x). 9) Find f (g(x)). 10) Find g(d(x)). 11) Find d(g(x)). 1) Find g (x + 4). 1) Find f(f(x)). 14) Find g(f (d(x))). 15) Find g(d(4)). 16) Betriz is plnning rodtrip, nd she usull drives 65 miles per hour. Which sttement below is true? ) The domin is distnce, nd the rnge is hours. b) The domin is speed nd the rnge is distnce. c) The domin is hours nd the rnge is speed. d) The domin is hours nd the rnge is distnce. For #17-1, solve ech eqution for the vrible. 17) x 5( 4x) = 18 18) 6x+9 b 4 = 7 19) = x 4 0) = 5 1) 4(x 1) 5x = +4( x) ) Solve for : x = 1 7 x x+1 For #-8, Fctor ech expression: ) x x 1 4) x + 1x + 4 5) 4x 81 6) x + 4x 99 7) x + 11x + 5 8) x 7
2 1. Prctice Problems For #1 9: Grph ech line on coordinte sstem. 1) f (x) = -x 4 ) + = 8 ) + = 6(x 5) 4) 1x = -6 5) = x 1 6) - 1 = (x 7) For #7 10, write the eqution of ech line (in slope-intercept form.) 7) A line hs slope of - nd psses through the point (1, -5). 8) A verticl line psses through the point (, -8). (specil line) 9) A line is prllel to = 1 x 1 nd goes through the point (10, -). 5 10) A horizontl line psses contins the ordered pir (-5, -15). (specil line) 11) Angelfish cost $7 ech nd tetrs cost $8 ech. Ptt spent $ on fish. Write liner eqution in stndrd form to model this sitution. 1) Three students were chosen to show their solutions for solving the eqution = (x h) + k for x. Their work is shown below. Determine which students were correct. Student #1 Student # Student # = (x h) + k = (x h) + k = (x h) + k k = (x h) ( k) = x h ( k) + h = x = (x h) + k k = x h k + h = x = (x h) + k k = x h k + h = x A. Students #1 nd # B. Students # nd # C. Students #1 nd # D. All were correct 1) Which of the following is NOT n equivlent form of the line represented in the tble: x A. = 1 x + 9 B. = 1 (x + 5) + 7 C. = 1 (x ) + 6 D. 1.4 Prctice Problems For #1, solve ech sstem of equtions b grphing. 1) x + 4 = -8 ) 1 + x = 8 = 1 x = -5 For # 18, solve ech sstem of equtions b n method of our choice. ) = 6x x 4).5x +.5 = 4 9x = 4.1x.5 = -. P g e
3 5) Hrold is going to purchse t-shirts for school fundriser, nd he is considering two compnies. Compn A chrges $8 per shirt, plus set-up fee of $100. Compn B chrges $6 per shirt, plus set-up fee of $140. Set up sstem of equtions. DO NOT SOLVE. 6) Brend hs 1 coins in her wllet, consisting onl of nickels nd qurters, nd the hve totl vlue of $.00. How mn qurters does she hve? 5x = 7 7) { x + 5 4z = 1 x + 5z = ) [ ] 16 9) A lndscping compn plced two orders with nurser. The first order ws for 1 bushes nd 4 trees, nd totled $487. The second order ws for 6 bushes nd trees, nd totled $. The bills do not list the per-item price. Wht were the costs of one bush nd of one tree? 10) Two smll pitchers nd one lrge pitcher cn hold 8 cups of wter. One lrge pitcher minus one smll pitcher constitutes cups of wter. How mn cups of wter cn ech pitcher hold? 11) A test hs twent questions worth 100 points. The test consists of True/Flse questions worth points ech nd multiple choice questions worth 11 points ech. How mn multiple choice questions re on the test? 1) Solve: x + + z = 4 x z = 1 x z = -1 Unit 1 Prctice Test Problems For #1 6: h(x) = 5x, f(x) = x 11, nd g(x) = -x 5 1) Find f ( 5 ). ) Find x if g(x) = -7. ) Find g(x) + f (x). 4) Find h(x) g(x). 5) Find h(g(x)). 6) Find f(f(-)). For 7 1, grph ech line. 7) 6 = 5(x + ) 8) = x + 5 9) = 4x + 10) = -(x - ) + 1 For 11 1, write the eqution of ech line described (in slope-intercept form unless otherwise specified.) 11) A line is prllel to = x 1 nd goes through the point (-10, -). 1) A verticl line psses through the point (-, 7). (specil line) For 1 14, solve ech sstem of equtions b n method of our choice. x + z = 5 x + 6 = 1) { 14) { x + 4z = (x 1) = + x x + + z = 7 15) Gr hs 14 coins comprised entirel of dimes nd nickels, totling $1.00. How mn of ech tpe of coin does he hve? For 16 19: Use the function f (x) = x. 16) Wht is the domin nd rnge? 17) Is the function incresing or decresing? 18) Wht re the intercepts? 19) Wht is the slope? For 0-1: Stte the domin nd rnge in both set nottion nd intervl nottion. 0) 1) P g e
4 For #-, mtch ech domin nd rnge to one of the grphs lbeled A to L on the lst pge of the prctice pcket. Domin: [-4, 4] Rnge: [-4, 4]. Domin: {x < x 5} Rnge: { = 1} 4. Domin: [-4, ] Rnge: [-, 4] 5. Domin: {x x > 0} Rnge: { = 4} 6. Domin: {x 6 x 6} Rnge: { 0 6} 7. Domin: [-5] Rnge: (-, 6) 8. Domin: {x x 0} Rnge: { is R} 9. Domin: [-, 4] Rnge: [-, 4] 0. Domin: (-, ) Rnge: (-, ) 1. Domin: {x 7 x < 5} Rnge: { < 1}. Domin: (-, ) Rnge: [0, ). Domin: (-, 4) Rnge: [0, 5) Prctice Problem Answers 1. Answers 1) -17 ) 7 ) ± 4).6 or 1 5 5) -1x ) 11x 11 7) x 8) -0x + 57x 18 9) -0x ) -15x 11) -75x + 60x 1 1) 5x ) 6x 45 14) 90x ) -4 16) D 17) x = 8 18) b = 9 19) x = 9 0) x = 4 1) x = 18 ) = x ) (x 4)(x + ) 4) (x +6)(x + 7) 5) (x 9)(x + 9) 6) (x )(x + 11) 7) (x + 1)(x + 5) 8) (x )(x + ) 1. Answers 1) ) ) 4) 5) 6) 7) = -x 8) x = 9) = 1 5 x 5 10) = ) 7x + 8 = 1) C 1) C 4 P g e
5 1.4 Answers Alg Honors 018 DRHS Unit 1 Prctice Problems 1) grph IMS ) grph (7, -5) ) No solution 4) (8, 4) 5) 8s+100=C nd 6x+140=C 6) 7 qurters 7) (, -, 1 ) 8) (-1, -, 8) 9) $ per bush, $47per tree 10) smll pitcher: cups, lrger pitcher: 4 cups 11) 5 multiple choice questions 1) (, -1, ) Prctice Test ANSWERS 1) -16 ) 11 ) x 16 4) -10x 5x 5) 0x + 100x ) -6 7) 8) 9) 10) 11) = x ) x = 1) (15, -8) 14) (, -, 1) 15) 6 dimes nd 8 nickels 16) D: ll rel #s; R: ll rel #s 17) incresing 18) -int t 0; x- int t 0 19) (or /1) 0) Set- D: {x x < } R: { 7 < 8} Intervl- D: [-, ) R: [-7, 8) 1) Set- D: {x x > 1} R: { 4} Intervl- D: (-1, ) R: [-4, ) ) D ) G 4) H 5) F 6) A 7) C 8) E 9) J 0) L 1) B ) K ) I 5 P g e
6 USE THESE FOR QUESTIONS - IN Prctice Test 6 P g e
1. Twelve less than five times a number is thirty three. What is the number
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