2) What is the slope of the line that goes through points (5, -4) and (5, 4)? 1 and a y-intercept 3? 3) Which line has a slope of 2.

Size: px

Start display at page:

Download "2) What is the slope of the line that goes through points (5, -4) and (5, 4)? 1 and a y-intercept 3? 3) Which line has a slope of 2."

Abel Allen
6 years ago
Views:

$expressios ito math. Solvig equatios, icludig those with paretheses, like terms, ad fractios.$ Be able to verify solutios by pluggig them back ito the origial equatio. Solvig a equatio for a variable.

Be able to verify solutios by pluggig them back ito the origial equatio. Solvig a equatio for a variable.

Determiig whether a relatio is a fuctio, determiig domai ad rage of a relatio i set builder otatio, ad fidig zeros (x-itercepts) of a fuctio.

Determie whether a fuctio is a direct variatio, ad write direct variatio equatios (y = kx) give a poit o a direct variatio.

1 Algebra 1 Semester Exam Study Guide Name Date Block The semester exam will cover all material we have leared so far, icludig: Traslatig Eglish expressios ito math. Solvig equatios, icludig those with paretheses, like terms, ad fractios. Be able to verify solutios by pluggig them back ito the origial equatio. Solvig a equatio for a variable. Expressig radicals i simplest form, icludig radicals with umbers that cotai perfect square factors, radicals with variables i the radicad, ad radicals with variables i the radicad. Solvig problems with statistics, icludig iterpretig box-ad-whisker plots, fidig MAD, stadard deviatio, ad z-score. Determiig whether a relatio is a fuctio, determiig domai ad rage of a relatio i set builder otatio, ad fidig zeros (x-itercepts) of a fuctio. Graphig liear fuctios usig the slope-itercept method. Determie whether a fuctio is a direct variatio, ad write direct variatio equatios (y = kx) give a poit o a direct variatio. Evaluate word problems, icludig rate of chage ad direct variatio problems. Review your otes, homework, checkpoits, quizzes, ad tests to help you prepare. Practice problems: 1) What is the value of 5x 2 - y 2 if x = -1 ad y = 5? 2) What is the slope of the lie that goes through poits (5, -4) ad (5, 4)? ) Which lie has a slope of 2 1 ad a y-itercept? a) b) c) d) 4) Solve the equatios for the requested variable: a) Solve for y: b) Solve for x: c) Solve for k: d) Solve for h: 10x + 5y = 0 5x+ z y = 8 4 m = k 1 A = bh 2

Algebra 1 Semester Exam Study Guide Page 2 5) Solve for C: F = 5 9 C + 2.

6) The formula for the surface area of a cylider is SA = 2π r(h + r),

b) Use the formula you foud i part a) to fid the height of a cylider

7) Solve the equatios, if possible. VERIFY YOUR SOLUTIONS.

+ 6 e) 5(1 + 4x) + 2x = 2( + 10x) + 5 f) 6(2y + 6) = 4(9 + y) g) 2-15 =

r = k) r + 1 11 w = w + 24 8) For each graph below, determie whether the

2 Algebra 1 Semester Exam Study Guide Page 2 5) Solve for C: F = 5 9 C + 2. Use the formula you foud for C to covert 90 of to Celsius. 6) The formula for the surface area of a cylider is SA = 2π r(h + r), where r is the radius ad h is the height. a) Solve the equatio for h. b) Use the formula you foud i part a) to fid the height of a cylider give its surface area is 20π ad its radius is 2. 7) Solve the equatios, if possible. VERIFY YOUR SOLUTIONS. a) 5 10a = 1 b) (x + 2) = 6(x 1) c) 6(x ) = (2x + 4) d) 8(x 1) + 2x = x + 6 e) 5(1 + 4x) + 2x = 2( + 10x) + 5 f) 6(2y + 6) = 4(9 + y) g) 2-15 = 5(- + 2) h) (5y + 64) = (20 + 2y) i) 2-15 = 5(- + 2) j) r = k) r w = w ) For each graph below, determie whether the relatio is a fuctio. Explai your aswer. The write the domai ad rage of the relatio show i set builder otatio. a) b) c) d) e) f)

Algebra 1 Semester Exam Study Guide Page 9) Which of the followig relatios does ot represet a fuctio? Explai your aswer. a) b) c) d) 10) Which of these data sets represet a fuctio? Explai. There may be more tha oe.

3 Algebra 1 Semester Exam Study Guide Page 9) Which of the followig relatios does ot represet a fuctio? Explai your aswer. a) b) c) d) 10) Which of these data sets represet a fuctio? Explai. There may be more tha oe. a) b) c) d) 11) If f(x) = -5x 7, what is the value of f(-7)? 12) What is the rage of the fuctio f(x) = 4x 2 whe the domai is {-1, 0,1}? 1) Jerri wrote the steps whe solvig a equatio: 17(x + ) = 6 4 Step 1: 17x + 51 = 6 4 Step 2: 17x + 51 = 2 Step : 17x = Step 4: x = 17 Which property justifies Step 4? a) Distributive Property b) Multiplicatio Property of Equality c) Divisio Property of Equality d) Commutative Property of Additio 14) Which statemet illustrates the trasitive property of equality? x + y a) x + (-7) = -7 + x b) (a + b) + c = a + (b + c) c) 0 = 0 z d) if a = b ad b = c the a = c

4 Algebra 1 Semester Exam Study Guide Page 4 15) For the equatios below, fid the slopes ad y-itercepts, the graph the equatios usig the slope-itercept method. a) x + 7y = 14 b) -4x + 10y = 20 c) -5x 2y = 10 16) What is the slope of the lie show? 17) The membership fee for joiig a campig associatio is $45. A local campgroud charges members of the campig associatio $5 per ight for a campsite ad omembers $40 per ight for a campsite. a) Write a equatio that describes each situatio. b) Whe is the umber of ights spet by both members ad omembers the same cost? 18) A public pool charges $8 every time you visit their pool to swim. They also charge $2 to ret a bathig cap, which every perso with log hair must wear. Margie wet to the pool all summer, ad reted a bathig cap each time she wet. Margie spet $150 over the summer visitig the pool. a) Write a equatio that describes the umber of times Margie wet to the pool, ad solve it to fid how may times she wet. b) If Margie had brought her ow bathig cap rather tha retig oe, how may more times could she have visited the pool with the savigs? 19) Give the table at right, is the relatio show a direct variatio? Explai your aswer.

20) Use the graph at right to aswer the questios: a) Write a direct variatio equatio for the graph. b) Idetify the costat of variatio.

b) Does oe graph show more savigs for Stacy? Explai why. 22) The poit (, 8) is part of a direct variatio. Write the direct variatio equatio. What are two other poits o this direct variatio?

05 per gallo i February, fires ad mechaical failures that shut dow four Califoria refieries drove up prices to aroud $1.67 per gallo i April.

5 20) Use the graph at right to aswer the questios: a) Write a direct variatio equatio for the graph. b) Idetify the costat of variatio. Algebra 1 Semester Exam Study Guide Page 5 21) The graphs below show two possible savig optios for Stacy where Dad s deposits vary directly with Stacy s earigs. a) Write a equatio for each graph. b) Does oe graph show more savigs for Stacy? Explai why. 22) The poit (, 8) is part of a direct variatio. Write the direct variatio equatio. What are two other poits o this direct variatio? Sketch a graph with the origial poit, ad the two poits you foud. 2) I Sacrameto, Califoria, gasolie prices fluctuated dramatically durig the first half of After recordig ear record lows of $1.05 per gallo i February, fires ad mechaical failures that shut dow four Califoria refieries drove up prices to aroud $1.67 per gallo i April. The cost of gasolie at a gas statio varies directly with the umber of gallos of gasolie that you pump. It cost $27.95 to fill a 1 gallo tak at a statio i Sacrameto at that time. a) Write a direct variatio model that relates the umber of gallos g to the total cost c to fill the tak. b) How much it will cost to fill up a truck with a 50 gallo tak. 24) Write the equatios that represet the lies o the graphs show below. a) b)

6 25) Use the graph at right to aswer the questios below: a) What is the domai ad rage (i set builder otatio) of the fuctio show at right? b) What are the zeros of the fuctio? Circle them. Algebra 1 Semester Exam Study Guide Page 6 26) Give f(x) = 5x + 10, what is the zero(s) of the fuctio? 27) Circle the zeros of the fuctio give the graph below: 28) O Jauary rd, the price of a gallo of gas was $2.89 ad o Jauary 12 th, the price had rise to $.19 per gallo. What is the average rate of chage of the price of a gallo of gas over this time iterval? 29) Accordig to cesus figures, the populatio of Clovis was 1,194 i 1980 ad 4,506 i What was the average rate of chage of the populatio over that time? 0) Joes ad Swill deliver 12 cubic yards of gravel for $240 ad 0 cubic yards for $575. What is the average rate of chage of the cost per yard? 1) Whe a load of 5 pouds is placed o a sprig, its legth is 6 iches, ad whe a load of 9 pouds is placed o the sprig, its legth is 12 iches. What is the average rate of chage of the legth of the sprig? For the questios below, use formulas: µ = i= 1 ( x µ) i 2, ad z = x µ σ i=1 x i MAD =, i= 1 ( xi µ, σ 2 = If ecessary, roud to the earest hudredth. 2) Fid the mea, MAD, stadard deviatio, ad variace: {8, 22, 0, 20} i= 1 ( x µ) i 2, σ = ) For a give dataset, µ was calculated as 15, ad σ = 4. How may stadard deviatios from the mea would data poits 21 ad be?

7 Algebra 1 Semester Exam Study Guide Page 7 4) Mary s job is to buy light bulbs for street lamps i the city she lives i. She goes to two compaies. The first compay claims that the mea average life spa of their bulbs is 5 moths with a stadard deviatio of 5.6. The secod compay claims the mea average life spa of their bulbs is 4 moths with a stadard deviatio of 2.1. Mary decides to buy bulbs from the secod compay, eve though their mea average life spa is shorter. Why might she choose to do this? 5) Adrea ra a survey o the effectiveess of her ew cold medicie ad received 50 results. Rosella coducted a similar survey for her ew cold medicie ad collected 50 results. Both sets of data are represeted below i the box-ad-whisker plots. Based o the box-ad-whisker plots, which of the followig statemets must be true? Select ALL of the correct aswers (there may be more tha oe). a) Exactly ¼ of Adrea s data lie i the secod quartile. b) The rage of Rosella s data is greater tha the rage of Adrea s data. c) Rosella has the same amout of data i the secod quartile as Adrea has i her fourth quartile. d) The upper quartile of Adrea s data is greater tha the upper quartile of Rosella s data. e) The iterquartile rage of Rosella s data could be calculated if the axis was labeled. f) The mea of Adrea s data could be calculated if the axis was labeled. 6) The followig data represets the umber of phoe calls that two compaies, Apple ad BetaMax, received i four days. Apple = { 20, 22, 17, 25 } BetaMax = { 40, 20, 15, 45 } Which compay, Apple or BetaMax, had a larger variatio i the umber of calls per day? Explai why. 7) Three baseball teams, (the Bobcats, the Firehawks, ad the Zebras) each had three games this week. The followig data represets the umber of rus that each team received i their three games. Bobcats = { 6, 10, 11 } Firehawks = { 10, 2, 15 } Zebras = { 5, 4, 9 } Which team is most cosistet i terms of how may rus scored per game? Explai why.

8 Algebra 1 Semester Exam Study Guide Page 8 8) Michelle made a 80 o her Biology test ad a 8 o her Geometry test. The average score o the Biology test was a 84, with stadard deviatio. The average score o the Geometry test was a 88, with stadard deviatio 5. Relative to her classmates, o which test did Michelle do better? Explai WHY. 9) Joe is a track athlete that is cosiderig movig to Georgia or Ketucky. Joe also just ra the 400-meter race i 100 secods. The average 400-meter time i Georgia is 110 secods with stadard deviatio 4. The average 400-meter time i Ketucky is 111 secods with stadard deviatio 5. I which state would Joe be the better ruer relative to where he lives? Explai why. 40) I Phillip s math class, the average score was a 90 with stadard deviatio. I Abby s math class, the average score was a 80 with a stadard deviatio 4. If Phillip scored a 95, ad Abby scored a 90, who did better o their test relative to their class? 41) Maddie is a attorey that charges a fixed fee o $250 for a iitial meetig ad $150 per hour for all hours worked after that. a) Write a equatio i slope-itercept form. b) Fid Maddie s charge for 26 hours of work. 42) Baxter s store, Video Retal-O-Rama, charges a $20 membership fee ad $2.50 for each video reted. a) Write a liear equatio to model this situatio. b) If a ew member paid the store $67.50 i the last moths, how may videos were reted? 4) For babysittig, Nicole charges a flat fee of $, plus $5 per hour. a) Write a equatio for the cost, C, after h hours of babysittig. b) What do you thik the slope ad the y-itercept represet? c) How much moey will she make if she babysits 5 hours? 44) Simplify the radicals below: a) 81x 6y x y z b) w x c) 6 8 4y z d) 16 e) 64x

9 Study guide aswers: 1) -20 2) udefied ) d) 4) a) y=-2x+6 b) 5) C ( F 2) Algebra 1 Semester Exam Study Guide Page 9 8y z x = c) 5 5 SA = ; 90 9 o F 2.2 o C 6) a) h = r b) uits 2 π r 4 7) a) a= b) x=4 c) o sol. d) x=2 e) x= 5 f) all R g) = 5 8 h) y=-24 i) o sol. j) r=2 k)w=12 4 k = d) m 2A h = b 8) yes reaso: every iput has OAOO output; o reaso: there exist iputs with more tha oe output a) yes; D={x -6 x -1};R={y -5 y } b) yes; D={x x}; R={y y 0} c) o; D={x x 0}; R={y y}; d) yes; D={x x 0};R={y y 0} e) yes; D={x x}; R={y y}; f) o; D={x x -1 or x 1}; R={y y}; 9) b, sice there is a iput with more tha oe output (2) 11) f(-7) = 28 12) R={-6, -2, 2} 1) c) divisio property of equality 14) d) if a = b ad b=c the a=c 10) Oly c is a fuctio sice each iput has OAOO output 15) a) m= 7 1 ; b=2 b) m= 5 2 ;b=2 c) m=- 2 5 ; b=-5 16) m=-2 17) a) y=45+5x; y=40x b) 9 ights 18) a) 8x + 2x = 150; 15 times b) times 19) No, there is o cosistet costat of variatio 20) a) y = 2x b) k = 2 21) a) y = 2x; y = x b) graph a shows more 7 savigs because it has a bigger costat of variatio (steeper slope) 8 2) a) c=2.15g b) $ ) y = x ; (0, 0); (9, 24) (aswers may vary) 24) a) x = - b) y = 4 25) a) D={x x}; R={y y 15} b) circle x-itercepts x=0 ad x=8 26) x=-2 27) circle x-itercepts x 1, x 2, x, ad x 4 28) about $.0/day 29) people/year 0) $18.61/yd 2 1) lbs/ich 2) µ=20, MAD= 6, σ=7.87, σ 2 =62 ) 21 is 1.5σ above the mea; is σ below 4) The s.d. was smaller, meaig there was 5) a, b, c, e less spread i the data, so they will more cosistetly reach the average lifespa tha the first compay. 6) BetaMax (use either MAD or s.d. to compare: 7) Both the Bobcats ad Zebras show the same BetaMax MAD=12.5/σ=12.74 is much bigger cosistecy i rus scored, sice their tha the same for Apple (MAD=2.5/σ=2.92) MAD/stadard deviatios (MAD=2/σ=2.16) so it has more variatio i umber of calls. are the same ad less tha those of the 8) Geometry (z-score was -1; z-score o Bio test was 1., so closer to mea o Geo. test) Firehawks (MAD=4.67/σ=5.5) 9) Georgia (z-score is -2.5; i KY it is -2.2, so he is further below the mea (a good thig!) i GA)

10 Algebra 1 Semester Exam Study Guide Page 10 40) Abby (her z-score=2.5; Phillip s is 1.67; she 41) a) y=150x+250 b) $4150 is farther from the mea i her class tha he is i his) 42) y=2.5x+20 b) 19 videos 4) a) C=+5h b) slope=cost per hour; y-it=flat fee c) $ ) a) 4x y z xy b) 5 9x 6y 2 wx c) 4 2y z x d) 4 d) 4x

multiplies all measures of center and the standard deviation and range by k, while the variance is multiplied by k 2.

multiplies all measures of center and the standard deviation and range by k, while the variance is multiplied by k 2. Lesso 3- Lesso 3- Scale Chages of Data Vocabulary scale chage of a data set scale factor scale image BIG IDEA Multiplyig every umber i a data set by k multiplies all measures of ceter ad the stadard deviatio