1. Find the missing input or output values for the following functions. If there is no value, explain why not. b. x=1-1

Transcription

1 ALGEBRA 1 A1P2 Final Exam Review 1. Find the missing input or output values for the following functions. If there is no value, explain why not. b. x=1-1 f (x)= 3x -7 f (x) = x 10 f (x)= -1 f (4= -1 x f (x) = _Lza Kezt, So AA-4.1'M 2. a. For any graph, explain how you determine whether or not the graph is a function k ;,)r ),4-- tf Y +)-6,_&) b. For any table, explain how you determine whether or not the relation is a function ,i_t_eid 61 roe' A-tr_ept Vietta,44 e a ire G sii.itte e, 3. Write an equation for the given line. (There should be arrows on the ends of this line.) a. equation = ± b. slope = y-intercept = ( 1 )c. d. x-intecept = ( LC I 0) e. domain = r): 1R., f. range = 4. Simplify each expression. Final answers should contain no parentheses or negative exponents. a. b. C. (4x2y3 y ( >,-,:::1-2x3y-"-- d. x 7 e. (2 x5 Y- 3 1(5x) f. (16)% g. y i \I)/L L (2-)1

2 -o)( 5. Solve the following equations. Check your solutions. a. 3(c+4)2+2=14 2_ 2_ b. 1 46x + = 3x (x 12) 2dt 314c, k 3(,5( -3t0X ---- CI- -q -9 t, ''--,,,...,...,...-, ' 3 Ci-i) 4-2_,t. ),..f "3 7 X 0 ).i,---.,...,.../ &40 ( ) r.---, D (0 12) b + tz) C. (2x +1)(2x 5)= Ox + 1)(x 1) '). 5 X 144-v._ X I Litk. I /.../ tie d. 12x+1+10 =4 fal So , i- 1,.12. ',.., 4b50/61,t, vizitre 00,,p.., N-4 ', ---i,,, 64,4_ 1--- :-_-_ 4 Jut.1_411(e 5,..., 64) \...,,, /1 t.vt a-be r. 0 L AQ ) \11- I 00 kt i 9 s.. fi cr M'''' 6. Solve each equation for the specified variable. a. Solve for y: 5x + 3y = 15-6x b. Solve for x: 4x 3y = , -45)44 lq 7'519 ia 3

3 7. Solve the following systems of equations using the most efficient method. Be sure to check your solution in BOTH equations. a. y= 5x-4 y= 4x+23 L-4 i--h4 4- I:3 Solution: Check: Ii := 3) jl 44 x b. Solution: 40-1-y = 26 Check: X 312:) 36) v" /4/4) , 40 tip 2. c (3x + 2y =12 (5x-3y = -37) g 4 6, 3 4. Solution: Check: 1=,A1 2 (-2) 7-(41) ,c?).1? --)o

4 8. Mike spent $11.19 on a bag containing red and green candies. The bag weighed 11 pounds. The red candies cost $1.29 per pound. The green candies cost $0.79 per pound. a. Define your variables: Let r =- 4- ) /LaS 14' repe, , Let Lt.t..0 -s E. a,ree1 64.4,14$4.- b. Write two equations to represent the si uation then solve the system Y. 4-- r-.dt,, 5 1.iq ( lug; AA Pi /. z f /11. / /1 0.54( H./1 u / c. How much of each type of candy did Mike buy? Answer in a complete sentence. 9. For each of the following sequences, write an explicit equation, a recursive equation, then calculate the 25th term in the sequence. Show all work. a. f8 14, 10, 6,2 explicit: t to) v 4 /? recursive: (i ) th term: ( ).E-(1) 4-/ 25th term:.1 (g) v.- -t4 17 )4-f zy."1- c , 128, 256 explicit: recursive: `2--- t- ty,) ( )" f- (t)-- 32_ te(14+1) -L- ) b ,-13,-10,-7,... explicit: 61) : recursive: -fr 1 L. -tiet4-1) In) th term: explicit: recursive: 25th term: '&125) s (25) 5-5, 5, -5, (24 rt. tit+ kk) 143

5 10. It seems reasonable that there would be a relationship between the amount of time a student spends studying and their GPA. Suppose you were interested in predicting a student's GPA based on the hours they study per week. You were able to randomly select 12 students and have them record the number of hours they studied in a week. Hours GPA a. Create a scatterp of and sketch it below. b. Create a residual plot and sketch it below. c. Enter the data into your calculator and calculate the LSRL. (Round to the hundredth.) /` - 0 5"2--- X d. Interpret the meaning of the slope of the LSRL in context. Stop f: 0, t-vt tutcu t- 41.Q 6 ) -67PA 01 tie.,p1a40,,,of 62 e. Interpret the meaning of the y-intercept of the LSRL in context. &O. tt-oia rs Ipe_AL s-f PA [isas 2-'41Fts f. What is the value of r? (Round to the thousandth.) Interpret the meaning of r: DU ce_ J. -friketti tet49,6,- &Act 6 3 PA Describe the association between the variables. direction: p0 5) strength: 0,1 ri#le cadtt form: outliers: If I '674,S treet-lt her s h. Use the LSRL to predict the GPA for a student who studies for 8 hours a week. Include the margin of error in your answer. fo./57--(t) 4-7.-z-t-fi (-SPA i. Calculate the residual for a student who studied for 8 hours actually had a 3.9 GPA. (Do not include the margin of error for this.) r ottkal ez cilled p(ept 0. Lt --- 3, Li to

6 11. Based on the tables below, find the equation of the exponential function y = ab x by hand. Check your equations using your calculator. a. x 0 ) f{ x) 1600) equation: 2Sco _ ioco 20, triv Based on your equation, what is the percent of increase or decrease? 2)5 9a (ow (l.25, b. v equation: So (0.2) 2 3 /25 *4--/00 2S% g L a( Based on your equation, what is the percent of increase or decrease? 2-0 * In seven years, Seta's son Stu is leaving home for college. Seta hopes to save $8000 to pay for his first year. She has $5000 now. If her bank pays 6.75% interest annually, how much money will Seta have for Stu's first year of college? (Round to the nearest penny.) Will she have enough?.0010 b , :10 o =. 1 01,1 S 0t)0 (1.041C"))-1?e/7 5 / tut v-e Tungsten has many chemical and commercial uses, but some forms of it need to be combined with heavy alloys. W-187 has a half-life of 23.9 hours. If a manufacturer has 100 g sample, but won't be receive the necessary heavy alloys for 3 days (72 hours), how much W-187 will remain? a- =Jo b 0. /oo (0.;) 14. Calculate the equations of a line and an exponential through the two points (1,21 --,, a. Line:. ::: 23/14 X-23-)3 -'"N b., Exponential: / 174)3 Li /4 -A -?7Aq IT re\ )e e +19 2:7-Aq + b b 2-3 LI

7 15. Factor the following expressions COMPLETELY. Do not solve for xl a. X 2 + 5x+ 6 b. C. 3x2 +30x (6( '13 (e v2". (X.1- (4-2:) 16. Solve the following equations using the most appropriate method. a. O=x2+7x+2 qq- Li (I) (2.,) X V LI 1- t 0) Isuirmotrarauunt.474 2t )2-0 e ) 17. Solve each inequality and graph the solution. a. 2(x- 5) <8 b. -Fr o + 5)4,- 4--/ _ rres+- 4, 0 = 3 )e, :7, I o *Z.( L.? es)i-15 Tr tok Am A. r 7-7 to HH11 i`> ) 2--

8 18. Write an inequality for each of the given graphs: > J X I- 3 cp. X > ';"=> 19. Use the equation x 2-9x-10 = y to answer all of the following questions: Use Factoring and the Zero Product Property to solve for x. Circle your answers se-4-- I : 0 X t 0 ' Use Completing the Square to solve for x. Circle your answers. to 0 ) ) 7 `) on(-,z5 x- Lt. Use the Quadratic Formula to solve for x. Circle(ioan-ale5rs) -b b 2-4ac,x = 2a 4 1 tfir: t 1)1-10) z(t) c31, t5:147471:0 I j: 11;4 91- )) et:/_ 1. Graph the equation by providing the following information;,-/ "--- ' t?. y-intercept: ( 0, 10 ).,..,... x-intercepts: ( I 0, O ) and ( _", 0 ) vertex: (,. 2,e2_-5) 40 kilaa domain: Y, range: R(-71 3co shape: 12 a., trtti.-1194,

9 20. Graph ti=re-se6tiewie-te each of the following systems. Pay attention to the signs! a. b. y<1x-1-5..(x+2)2-1 TeSt- (610) D 7":6$ 4- (0 40) -I c. Check your solutions to these systems in your calculator. A. ( /- ait.,9l (-5 0 to 21. Solve the following equations for x. Show all work. c5t) wit)" UK Cu a.cx + 2 = X XS b. 16' =8x-1 X I = 20x 4 5-x 5 3x-3./9( + /0 7; 10 X 4 )C /0 = 2/ X 3X *3, X- 3

10 22. A survey of 155 recent high school graduates found that 130 had driver licenses and 58 had jobs. Twenty-one said they had neither a license nor a job. a. Create a two way table, No License b. What is the probability that a high school graduate has both a job and a license? 31--/q c. What is the probability that a high school graduate with a license has a job? 61.1 = 0. Lit I -_,.. LI I. 1? d. What is the probability that a high school graduate has. either a job or a license? + l o, t-i I , _..., if; wpmw., evial"...img mm..., 1GS i 5 5' e. Create a relative frequency table. License NO License Sc4 b No Job 0 q ) = ",q 67.0 O. NM 41'4 = 2)60 2t,t. s?, / GLS kivt. ajo6 44