Answer Key 8 th Grade Geometry Honors Summer 2018 Mathematics Packet

Transcription

1 Answer Ke 8 th Grade Geometr Honors Summer 08 Mathematics Packet [] [B] [] You will never reach point B. [] a. raph 4. raph c. raph d. raph [4] $7.78 [] 4% [6] 6 4 % decrease [7] A population is a roup aout which we seek information. A sample is a portion of the population ein studied. Since it is inefficient, if not impossile, to collect information aout ever memer of a population, we select a sample of the population to stud. If we choose the sample randoml, it will represent the whole population. [8],000 [9] [A] [] 4 cup [] 0,064 ft [] 9.6 km/hr

2 [] Aout 900 inches [4] The -ounce cans cost.86 cents per ounce and a -liter ottle costs.84 cents per ounce. The cans are a etter u. [] a. 7. miles per allon. 40 miles c. $4.4, assumin 7. miles per allon [6] The data shows direct variation; 9; d = 9t [7] 0 pounds [8] a.. d d = 0. 4t 0 t Window: 0,,, 0,, c..8 meters [9] Software Sold a. Das in usiness Units sold = 08. [0] a. t = 0.d minutes [] $.48 [] r t = 80; hr

3 [] a. = 9. = 6 [4] a.. ( 4 ) = 6 ( + 4) 7 = [] 9 [6] 74 [7] The 8th term is 7. Sample eplanation: I used the routine ENTER, + 4 ENTER, then pressed ENTER 6 more times. [8] Toothpick Pattern Numer of heaons [9] The walker starts m awa from the motion sensor and walks awa from it at a rate of. m in s, or 0. m/s. [0] = + [] = 6 4 [] n = t; The input variale t is the time spent walkin. The output variale n is the numer

4 of laps walked. [] Possile answer: (9, ) and (7, ) [4] Stock Market Gains Research (h) Estimate should e close to 8.% dependin on the line of fit students use. [] = 0. 4 or.. [6] a. Usin 4, 8 and, the equation is. = 0 c. 7. = 0. d. The equation has prediction accurac within.9 ppm. = [7] 7 h 4 min [8] 4

5 [9] Sample answer: Solvin 7 + = for ields the slope-intercept form of the equation: = 7. Thus, the raph of this equation has the same slope as the raph of the other equation, ut the have different vertical intercepts. Therefore, the lines are parallel, indicatin that the sstem has no solution. [40] a. N P = 4. 08, P = $, 944. $, N $,000. The approimate solution is more meaninful ecause the numer of hot dos sold must e a whole numer. The approimate solution is N = 4, P = $94 c. Possile eplanation: When oth hot do vendors sell 4 hot dos, the each make a profit of $94. [4] a.. R S T = ( tuition for credits at Collee A) = + ( tuition for credits at Collee B) Total Tuition Credits c. Possile answer: (, ) is an approimate solution. d. When a student takes credit hours, the tuition at either collee is aout the same.

6 [4] [4] 6, 8, [44] 7 = 6 8 = 49 + = 0 8 = 49 7 = = 7 7 = 7 = 6 = 6 = 6 = = =, + = 70 [4] = = 0 pounds of cashews = 0 pounds of peanuts [46] [47] 6

7 [48] [49] [0] The reion is a tall, narrow paralleloram with vertices 0,,,,,, and,. The reion is shown elow

8 [] a.. ; 7; Jackets c. Yes; $0 aove [] a. 88, 0.7,. 4,.7, 7, [] a. 9 F. Aout 4 or minutes [4] 6,000 [] $88 [6] Added, multiplied, distriuted [7] a. 8.. ( ) 4 c. ( + 0. ) 8

9 [8] a. No; 9 is more than ; should e. Yes c. No; 0.7 is less than ; should e [9] a Use the associative propert of multiplication to reroup. Then multipl the numers and multipl the powers of addin the eponents. 6 6 c. (. )( 4 ) =. 4 = 8. 4 [60] a. 94, 80( ) 0. The population 8 ears ao c. 94, 80( ) 88, 968 [6] a.. c. [6] d 6 [6] Year Salar Simone s Salar $, 000 $7, 4 $4, 794 $, Simone s Salar Year [64]. hours 9

10 [6] 40 rams [66] a. SXBGF. SOLUTION c. Yes, each input matches no more than one output. d. The codin scheme is a letter shift of + for the letters A-P and a letter shift of 4 for the letters Q-Z. [67] a. Yes; domain: {0,,,, 4}; rane: {7}. Yes; domain: {,, 0,, }; rane: {0,, 4} c. No; domain: {0,, }; rane: { 8,, 0,, 8} [68] Answers will var. The raphs must pass the vertical line test, pass throuh the points, and 6,, and have, 7,. domain and rane [69] a. The independent variale is the numer of fans. The dependent variale is the numer of uses.. The independent variale is time. The dependent variale is the heiht of the rocket. c. The independent variale is the price of asoline. The dependent variale is the cost of fillin the tank. [70] Possile description: As heat is applied to ice, the raph shows a linear increase until 0 C. Here the temperature remains constant as ice melts. When approimatel 0 calories of heat has een added, the temperature of the water eins to rise. The raph shows a sharp linear increase as this temperature rises from 0 C to 0 C. At 0 C, water eins to vaporize and the temperature remains constant as heat is added to the sstem. After approimatel 700 calories of heat has een applied, all the water is vaporized and the raph aain increases in a linear fashion as the temperature of the steam continues to rise. [7] a. + 4 = 8, Y = =, Y = c. d. 8 =, Y = 8 = 0, Y = 0 [7] a. f =. Two c. Domain: 7, Rane: 0 6

11 [7] a. f = = 7, f = 7. f 0 c. Two d. If < or >, then f > = $. 60 [74] P = , [7] [76] 9, 7, 7 =, = 9 [77] [C] [78] 7

12 [79] a. Possile comparison: The raph for f ( ) = forms a paraola with curved lines. The raph for f ( ) = is V-shaped. Both functions have their verte at the oriin of the raph. When >, >.. Both functions share the points,,, 0, 0, and,. [80] > when > or < 0. [8] 0 = + 6 [8] a. A reflection across the -ais. A translation riht units followed a reflection across the -ais c. A translation left 6 units and up units d. A reflection across the line =

13 [8] a. The raph of = + 4 is the raph of = with a vertical stretch a factor of and a translation up 4 units.. The raph of = is the raph of = with a vertical stretch a factor of 6, a translation riht 4 units, and a translation up unit. c. The raph of = + is the raph of = with a reflection in the -ais, a translation left units, and a translation down units. d. The raph of = is the raph of = with a vertical shrink a factor of and a translation down units. [84] Move down units; multipl each -value. 0 Vertical asmptote: = 0 (-ais); horizontal asmptote: = [8] a. F k q q = d F 9 N m = / H G9. 0 C/ = 4 N. F k q q = d F HG 9 N m. N = 9. 0 C/ 0. 4 N m. N = d 0. 4 N/ m d =.N/ I KJ 6 c. C/ hc 6. 0 C/ h 0.0m/ / I KJ d = m d = m 0.0 m 6 6 c6. 0 C/ hc6. 0 C/ h d d = m

14 [86] a. Concentration of MCl Added amount of water (L) Amount of MCl (L) Whole solution (L) Concentration of MCl = c = = = = = = You would need to add aout.7 liters of water to have a 0. 0% MCl solution. 4 [87] a., where 0., where 0 7 c., where + 4 d., where 0 4 [88] a. 9., where 0 4 c., where 0 [89] rational numers, real numers 4

15 [90] a. 6 feet. At time t = second c. 0. seconds (as the oject is oin up) and.87 seconds (as the oject is comin down) [9] [A] [9] = = = =. 7 + = ±. 7 + = ±. 7 = ±. 7 The two solutions are and [9] = + h t 6t 4t [94] Approimations for the -intercepts are = and = The averae of these values,., is the approimate -coordinate of the verte of the paraola. Sustitute =. into the equation = + to et =.. The approimate coordinates of the verte are.,. = h, k. Therefore, the equation can e written as =... [9] Verte form: = 8 General form: = 4 6 Factored form: = + [96] = 4, + 6 [97], where and

16 4 + [98], + 6 9, 7 [99] +,, ± [0] [C] + [] =, [] = 4, [] = 0 ; = 6 + 8, 6 8 [4] 6 4 = 0, so there is one -intercept. [] Yes [6] a c. =, = 7 cm e j = , 68 = 6 cm = 4, 6 or. 4 = 4, 6 =. cm 6

17 [7] a. V = w w w + = w + w w Width (cm) Volume (cm ) v Volume of a Bo 4 Width (cm) w The volume is reater than 0 cm when the width is at least. cm. [8] a. 60 cm. 80 cm c. 48,000 cm d. w = 40 or w = 70 e. l = 80 or l = 90 f. V = V = or [9] [] =

18 [] a. Favorite Colors Color Numer of students Blue Red 0 Purple Orane Yellow 7 Other. c. students d. Red; Possile answer: is % and 4% of the students named red. 4 e. 4% or less [] [A] [] [D] [4] [] a. 0.. P(landin in shaded area) = 0. ecause the shaded area is of the circle. 4 [6] 8 8

19 [7] a [8] H H C H C H C C H C H C H C [9] a. comination. permutation [] [C] [] 47,60 [] a. 6. [] a. 80,

20 [4] 4 4 W G 4 0 W G W G 0 [] 6 0 [6] Independent; the first name drawn and replaced doesn t affect the proailities for the second choice. [7] [8] a [9] a. $.7. No, it is not a ood deal, ecause over the lon run ou will come out $0. ehind per spin. [0] Perpendicular [] Perpendicular 0

21 [] Possile equations: = 4 4, = 4, =. 4 [] ( 9, ) [4] a. A, 4 B 4, E, 8 F, H, C 6, 8 0 G 7, D 8,. Equation of the line throuh F and G: = + ; slope = Equation of the line throuh E and H: = + ; slope = The slopes are equal so these lines are parallel. [] 7 square inches [6] a. 7. sq. units. 7. sq. units c. 7. sq. units

22 [7] 7 [8] a. Areas: Square = 8 sq. units, Square = 8 sq. units, Square = 6 sq. units. Lenths: AC = 8, BC = 8, AB = 4 c. Area of Square + Area of Square = Area of Square [9] Three answers are possile: D 0,, D 6, 6, or D 6, 6. Check students raphs. [40] AB = 6 ; BC = 6 ; CD = 6; AD = 6 7 [4] 9,, and [4] [4] [44] a. = 6. = 6 7 [4] a., 4

23 . Possile answer: The intersection of the raphs of Y = + 0 and Y = occurs once, at =. c. = is a solution; = 4 is not a realistic solution ecause a square root cannot e neative. [46] AB = ; EF = [47] a. cosine. tanent c. 0.74; 0.9 d. approimatel. ft [48] a. = tan68. The raph is a direct variation. c d. 4. [49] 8 [0]. ft