Math 4399 Mathematics Instructional Design. Homework3. Please record all answers on the answer sheet for Homework 3.

Transcription

1 Math 99 nstructional Design Homework Please record all answers on the answer sheet for Homework.

2 DRECTONS Read each question carefull. For a multiple-choice question, determine the best answer to the question from the four answer choices provided. For a griddable question, determine the best answer to the question. Then fill in the answer on our answer document. 1 Four students are each tring to raise the same amount of mone for a class trip. The table below shows how much of each student's goal has been met. Fund-Raiser Progress Student Part of Goal Met Chelsea 0.7 Devon - 5 Huang - 8 Marcela 65% Which list shows the numbers in the table in order from least to greatest? A 0.7, 65%, ¾, ½ B 0.7, ¾, 65%, ~ C ¾, 65%, ½ 0,7 D ¾, ½ / 65%, 0,7 Page 8

3 Wh ich graph shows a proportional relationship between x and? F l,. '..ill J l ~ f 1_ 1- '-s 1-6 1_7,. ' 1-a l_.g J 1 H ' '\ 1 '\ ' l 1 1::.i '\, 1_7 '-s l '\ 1-9 ' G r ~" ~..,.,,. L.; _...-/ tl ' l _ _7 1-8 l_.g J l l ' '-7 '-s 1-9 Page 9

4 Point Mis located at (, 6) on a coordinate grid. Point Mis translated 8 units to the left and 9 units down to create point M' l ,i, Which measurement is closest to the distance between point Mand point M' in units? A B C D units 17 units 9 units 1 un its Tamara invested $15,000 in an account that pas % annual simple interest. Tamara will not make an additional deposits or withdrawals. How much interest will Tamara earn on her investment at the end of ears? F $1,800 G $600 H $50 J $1,87 Page 10

5 5 An aquarium is being filled with water. The graph shows the height of the water over time as the aquarium is being filled V) QJ..c u C:.._,,...,..c Ol a:; ), Aquarium 0 V / 15 V. / 10 V / 5 V V :/ ~ Time (seconds) Which statement best describes the rate of change for this situation? ~, A The height of the water increases 0 inches per second. B The height of the water increases 1 inch per second. C The height of the water increases 5 inches per second. D The height of the water increases.5 inches per second. Page 11

6 6 n the diagram a person who is 6 ft tall is standing on the ground ft awa from point P. A line segment drawn from the top corner of the building to point P creates two similar triangles. DOD DOD T 6 ft 1- ft ft Not drawn to scale Which proportion can be used to find h, the height of the building in feet? F = 18 h 6 G ~ -!!.._ 18 h H Page 1

7 7 Carnival M charges an entrance fee of $5.00 and $0.65 per ticket for the rides. Carnival P charges an entrance fee of $10.00 and $0.5 per ticket for the rides. How man tickets must be purchased in order for the total cost at Carnival M and Carnival P to be the same? A 5 B 10 C 50 D 75 8 The coordinate grid shows parallelogram PQRS. Q 9 j i', 8 tr P " r,..._ 5 _ {; {j Parallelogram PQRS is rotated 90 clockwise about the origin to create parallelogram P'Q'R'S'. Which rule describes this transformation? F (x, ) ~ (x, -) G (x, ) ~ (-x, ) H (x, ) ~ (, x) J (x, ) ~ (, -x) Page 1

8 9 The value of varies directl with x. When = 75, x =½ What is the value of when is ¼? A 8i 8 B 7~ C 16 D 168i 10 A triangular prism and its dimensions are shown in the diagram cm ----t What is the lateral surface area of this triangular prism in square centimeters? F 19 cm G 18 cm H 15 cm J 1 cm Page 1

9 ~ 11 Julie made 5 international long-distance phone calls to London last month. The scatterplot below shows the length and cost of each phone call she made. vi'... ro 0 ~ Cost of nternational Long-Distance Phone Calls " - ro ~ 0..., - Vl ' Length of Call (minutes) ~ Which conclusion is best supported b the scatterplot? A B As the length of a call increases, the cost of the call increases. As the length of a call increases, the cost of the call remains the same. f D There is no relationship between the length of a call and the cost of a call. Ckb O il f~d D/\)._ ~ 'i) 1 lo~~ r a ( (_, h, 1 fv\.,. ( ; + "'>'1'/1,,_~.t.. '; 1 C As the length of a call increases, the cost of the call decreases. /,e_ f.,-(/""'j +o b,) 1,.(S 1--; bv\. 1 Page 15

10 1 What are the slope and the -intercept of the graph of the linear function shown on the grid?...,...(-6, 0)- f- 1 '-- ' ' l ""', -...! (, -) ""', -ll,,,. F Slope =, -intercept = -6 G Slope= -, -intercept = -1.5 H Slope= - ¼, -intercept = -1.5 J Slope = ¼, -intercept = -6 1 A preschool has a rectangular field and a rectangular plaground that are similar in shape. Each dimension of the field is. times the corresponding dimension of the plaground. Which statement is true? A The area of the field is 6. times the area of the plaground. B The area of the field is 10. times the area of the plaground. C The perimeter of the field is 6. times the perimeter of the plaground. D The perimeter of the field is 10. times the perimeter of the plaground. Page 16

11 1 Which function is best represented b this graph? "" ""i l... - cg ~ - 7 ~ l _a 9-1 ~ ~ -7 ~ cg F 1 = -x+ 6 G = -x+ H = x + 6 J 1 =--x+ Page 17

12 15 The set designer for a pla painted some background scener on a large piece of plwood. He used a 1-foot-long pole to hold the piece of plwood upright, as shown in the diagram below ft --i What is h, the total height in feet of the piece of plwood? Record our answer and fill in the bubbles on our answer document. Be sure to use the correct place value. Page 18

13 16 Which table contains onl corresponding x-values and -values where the value of is more than the quotient of x and? F H G 10 8 J Page 19

14 17 A ball shaped like a sphere has a radius of. 7 centimeters. Which measurement is closest to the volume of the ball in cubic centimeters? A 6.8 cm B.9 cm C 1.15 cm D 8.5 cm 18 Alejandra and her famil are discussing how to pa for her college education. The cost of tuition at the college that Alejandra wants to attend is $9,000 per ear. Alejandra's parents will pa 85% of the tuition cost ever ear, and she will pa the rest. Alejandra has one ear to save enough mone to attend her first ear of college. What is the minimum amount of mone she should save ever month in order to reach her goal? F $67.50 G $1,50.00 H $11.50 J $8.1 Page 0

15 19 The coordinates of the vertices of a quadrilateral are P (1, ), R (1, ), S (, ), and T (, ) l ' ~ l l l ~ '-9 Quadrilateral PRST is reflected across the -axis to create quadrilateral P'R'S'T'. Which rule describes this transformation? A (x, ) -t (x, -) B (x, ) -t (-x, ) C (x, ) -t (, -x) D (x, ) -t (-, x) 0 Which situation represents a proportional relationship? F The cost of purchasing a basket of oranges for $1.0 per pound plus $5.00 for the basket G The cost of purchasing peaches for $7.00 per box of peaches with a deliver charge of $.00 H The cost of purchasing grapefruit for $1.80 per pound with a coupon for $1.00 off the total cost J The cost of purchasing apples for $1. 75 per pound plus a shipping fee of $0.16 per pound Page 1

16 1 Jamie used a microscope to measure the diameter of a hair. She found that the diameter of the hair was meter. How is this number written in scientific notation? A S B C 7. x 10 5 D Triangles PQR and RST are similar right triangles. --P \ Q,- " ' R' -t\ - 9 B l ' '\ l B 9 ~, ' ~ 7... S ~T -8 '--9 Which proportion can be used to show that the slope of PR is equal to the slope of RT? F G H J = - - (- 7) - (- ) -(-) -5- = 7 - (-7) -(-) - - (-7) - {- ) = (- ) - (- 5) = Page

17 The scatterplot shows the average number of hours each of 1 people spends at work ever week and the average number of hours each of them spends on recreational activities ever week.,..., ~ 0 :::, _g 5 ~ 0 E > 5 B <l'. 0 ro 15 :;:::; ro ~ 10 u ~ 5 '", Working and Relaxing., ; so Work (hours) Based on the scatterplot, what is the best prediction of the average number of hours a person spends at work ever week if that person spends an average of 10 hours on recreational activities ever week? ~ - A B C h 85 h 50 h D 65 h Page

18 Four triangles are shown. 10 Based on these triangles, which statement is true? F w = 75, because = 105 and = 75 G w = 105, because ( ) = 75 and = 105 H w = 85, because = 105 and = 85 J w = 165, because = 10 and = Which set of ordered pairs represents as a function of x? A {(, -1), (, -), (6, -), (8, -)} B {(0, 0), (1, 1), (1, 0), (, 1)} C {(, ), (, ), (, ), (, )} D {(1, -5), (1, 5), (, -10), (, -15)} Page

19 6 Circle was dilated with the origin as the center of dilation to create Circle. ~ 9-7, V 6 "" 5 / ' \ ' ' Circle \ Circle -,,,.. """-:. \ {j \. j - \ '- _.; -- \. -5 / '- ~ --{j r / ~... ' -~ Which rule best represents the dilation applied to Circle to create Circle? --9 F G (x, ) ~ (Bx, B) 8 8 (x, ) ~ (x, ) H (x, ) ~ (x + 5, + 5) l (x, ) ~ (x- 5, - 5) Page 5

20 7 The manager of a restaurant recorded how man people were in different groups of customers and how much those groups spent on food and beverages. The scatterplot below shows the data she recorded ''..., ~ vi' 100 Cl.... <fl ~ 80-0 fl-o ~ '--' Food and Beverages!., Number of People Based on this scatterplot, about how much mone would a group of 10 people be expected to spend on food and beverages at this restaurant? A $15 B $115 C $105 D $150 -,. Page 6

21 8 Which statement describes the mapping? F G The mapping represents as a function of x, because each -value corresponds to exactl one x-value. The mapping does not represent as a function of x, because two of the x-values correspond to the same -value. H The mapping represents as a function of x, because each x-value corresponds to exactl one -value. J The mapping does not represent as a function of x, because there are more x-values than different corresponding -values. Page 7

22 9 A clinder and its dimensions are shown below. 1.1 cm.8 cm One equation for calculating the volume of a clinder is V = Bh, where B represents the area of the base of the clinder. Which expression can be used to find the value of B, in square centimeters, for this clinder? A n(1.1) B n(1.1) C n(.8) D None of these Page 8

23 0 Three groups of students used different methods to estimate the diagonal length of a patio in feet. Their results were: f1 t 1 ft 5 1. ft Which list shows these diagonal lengths in order from greatest to least? F G H J 1., 15, f1 1., ill, 15 15, 1., f1 ill, 15, 1. Page 9

24 1 The model represents an equation What value of x makes the equation true? Record our answer and fill in the bubbles on our answer document. Be sure to use the correct place value. Page 0

25 The diagram below shows the side view of a ramp used to help load and unload a moving van. ft 9 ft Which measurement is closest to the length of the ramp in feet? F G 8.5 ft 10.5 ft H 9.5 ft J 1.5 ft Which representation of a transformation on a coordinate grid does not preserve congruence? A 1 1 (x, ) ---+ ( 7 x, 7 ) B (x, ) ---+ (x + 7, + 7) C (x, ) ---+ (x, -) D (, ) ---+ (, -) Page 1

26 A tree in Dante's neighborhood grew 18 inches in the first ears after it was planted. f the tree continues to grow at this same rate, which graph best represents the growth rate of the tree in inches per ear? 1, 90 81,... 7.!:: 6.._,.c 5 F ~ 5 e 6 l j ) j Tree Growth,. j J Year - H 90 81, _,.!:: 6.c... 5 ;: 5 e 6 l ,, j ~ Tree Growth -, Year , _,.!:: 6 5 G.c... ;: 5 e 6 l Tree Growth,, /f / / / / V V / / V -, Year / J " 90 81,..., 7.._,.!:: 6.c 5 ~ 5 e 6 l ~ Tree Growth -, Year Page

27 5 An artist joined three square regions at their vertices to create the figure shown in the diagram. Region Z The artist will use small congruent square tiles to cover each region without an gaps or overlaps. Based on the information, which statement is true? A B C The number of tiles needed to cover Region is the same as the number of tiles needed to cover both Region Y and Region Z. The number of tiles needed to cover Region Y is the same as the number of tiles needed to cover both Region and Region Z. The number of tiles needed to cover Region Z is the same as the number of tiles needed to cover both Region and Region Y. D None of these Page

28 6 Mr. Leonard is renting a car for one da. The table below shows the total amount he will be charged for the car based on the number of miles he drives. Car Rental Number of Miles, m Total Amount Charged, c 5 $ $ $ $.00 Which equation best represents c, the number of dollars Mr. Leonard should be charged for driving m miles? F c = 0.10m + 0 G c = 0m H c = 0.50m + 0 J c = 0m + a.so Page

29 7 Which list shows the numbers below in order from least to greatest? 5.78, -5.9, 58%, A -5.9, -, 5.78, 58% B -, -5.9, 58%, 5.78 C -5.9, D 58%, -, -, 58%, , A storage container for oil is in the shape of a clinder with a diameter of 10 ft and a height of 17 ft. Which measurement is closest to the volume of the storage container in cubic feet? F 5 ft G 1,5 ft H 691 ft J 1,696 ft Page 5

30 9 The graph of a linear function is shown on the coordinate grid. 10 ~ J 9 i\ a \ 7,-~(-, 6) - 6 \ 5 \ \ ! a 9 10 \ 1 - \ -6 7 \ -a -9 - t(1, -9) -10 1"'1 1 What is the -intercept of the graph of the linear function? Record our answer and fill in the bubbles on our answer document. Be sure to use the correct place value. Page 6

31 0 Triangle ABC was translated units to the right and units down. Which rule describes the translation that was applied to triangle ABC to create triangle A'B'C'? F (x, ) ~ (x-, + ) G (x, ) ~ (x +, - ) H (x, ) ~ (x, -) J (x, ) ~ (-x, ) 1 Nicolas has $650 to deposit into two different savings accounts. Nicolas will deposit $00 into Account, which earns.5% annual simple interest. He will deposit $50 into Account, which earns ¼% interest compounded annuall. Nicolas will not make an additional deposits or withdrawals. Which amount is closest to the total balance of these two accounts at the end of ears? A $67.1 B $ C $69.5 D $69.51 Page 7

32 On a field trip, there are adults for ever 5 students. Which graph models a relationship with the same unit rate? F )~ --,1.-l"..,.....,...r-,., '~ H / V V -~ / V / / V V ljf / G ), ~ j j J! -~ ), J ~ ~ Page 8

33 Pentagon ABCDE is rotated 180 clockwise about the origin to form pentagon A'B'C'D'E'. 9 8 :~- 7 6 A B- 1-D ~ i. ~ - ;..g g ' Which statement is true? A Pentagon ABCDE is congruent to pentagon A'B'C'D'E'. B C The sum of the angle measures of pentagon A'B'C'D'E' is 180 more than the sum of the angle measures of pentagon ABCDE. Each side length of pentagon A'B'C'D'E' is times the corresponding side length of pentagon ABCDE. D Each side length of pentagon A'B'C'D'E' is½ the corresponding side length of pentagon ABCDE. The measures of two angles are (5x + ) 0 and (9x- 17) 0 What is the value of x if these angles are congruent? F 1.75 G 1. H 0.5 J 10.5 Page 9

34 5 A rectangular prism and its dimensions are shown in the diagram.,,,,,,, ~ in. What is the total surface area of this rectangular prism in square inches? Record our answer and fill in the bubbles on our answer document. Be sure to use the correct place value. Page 0

35 6 The scatterplot shows the number of hours that 1 people spent learning to tpe on a keboard and each person's average tping speed. Tping Speed Data 'fil- 80 QJ QJ 0..., <fl ~ ~ E L.. >- QJ F- o.. 50 QJ Vl Cl E 0 e o QJ ::: ~,..., !~ 1-. ',-, Number of Hours of Learning Based on the scatterplot, what is the best prediction of a person's average tping speed in words per minute (wpm) if the person has spent 70 hours learning to tpe? F G H J 100 wpm 55 wpm 85 wpm 70 wpm Page 1

36 7 Caroln will bu the same number of stamps ever month to add to a stamp collection her grandfather gave her. The table shows the number of stamps Caroln will have at the end of x months. Caroln's Stamp Collection Number of Months, x Number of Stamps, How man stamps was Caroln given, and how man stamps will she bu ever month? A B C Caroln was given 00 stamps, and she will bu 50 stamps ever month. Caroln was given 180 stamps, and she will bu 70 stamps ever month. Caroln was given 180 stamps, and she will bu 50 stamps ever month. D Caroln was given 00 stamps, and she will bu 70 stamps ever month. 8 Which point on the number line best represents the location of J9? M N p Q,( > F G Point M Point N H Point P J Point Q Page

37 9 The list shows the number of songs that five students each downloaded last week.,, 8, 8, 51 What is the mean absolute deviation of the numbers in the list? A. B 6.88 C 8. D The graph models the linear relationship between the charge for a trip and the number of miles driven for two taxis. -V) L.. ro '~ "C...,, Q) Cl L.. ro..c u i--- V" ~ / Taxi Charges ~-.,,r Taxi 1 / ~~ ---r -~ Taxi Distance (miles driven) - - Based on the graph, which statement appears to be true? F The charge for a trip with a distance of 5 miles is $5 greater for Taxi 1 than for Taxi. G The charge for a trip with a distance of 5 miles is $5 less for Taxi 1 than for Taxi. H The charge for a trip with a distance of 5 miles is $0 for both Taxi 1 and Taxi. l The charge for a trip with a distance of 5 miles cannot be determined for either Taxi 1 or Taxi. Page

38 ~ 51 Figure S, the small arrow, was dilated with the origin as the center of dilation to create Figure T, the large arrow Flg 1 u~e 1 T Figure.:::i l -9 " !"'i;. / 1" 1 '-. / / ~ V -5 1\.. V 1'- / -6-7 "" -9 Which rule best represents the dilation that was applied to Figure S to create Figure T? A (x, ) ~ (x, ) B C D (x,) ~ (x,) 1 1 (x, ) ~ (x,) 1 1 (x, ) ~ (x, ) 5 Veronica is ordering trophies for her school. Compan P charges $.50 for each troph and a one-time engraving fee of $5. Compan R charges $7.50 for each troph and a one-time engraving fee of $17. Which inequalit can be used to find x, the minimum number of trophies that can be ordered so that the total charge at Compan P is less than the total charge at Compan R? F.5+5x<7.5+17x G.5+5x> x H.5x+ 5 < 7.5x+ 17 J.5x+5 > 7.5x+ 17 Page

39 5 Which scatterplot suggests a linear relationship between x and? " A 5 1 ' " " ' ~ 8 " 7 6 C ~ ;, B 5 1 -, i D 5 1 ~.~ Frankie bought a new computer. He made an initial pament of $50 to the store, and he will pa $0 each month until the computer is paid off. Which equation represents the relationship between m, the number of monthl paments Frankie has made, and t, the total amount that Frankie has paid the store? F t = 50m + 0 G t = 0m- 50 H t = 50m- 0 J t = 0m + 50 Page 5

40 55 A part hat is shaped like a cone. The dimensions of the part hat are shown in the diagram in Which measurement is closest to the volume of the part hat in cubic inches? A B C 8.8 in. 9.9 in. 5.7 in. D 1, in. Page 6

41 ~ 56 Which graph represents as a function of x? J' r--... F ~ H ~ i--~ / w G j \ \ \ -- \ \ / \ 1 \ J \ \ \ \ Jf \ ' ' -~ ~ J Page 7 BE SURE YOU HAVE RECORDED ALL OF YOUR ANSWERS ON THE ANSWER DOCUMENT.