Algebra 1 Semester 2. Instructional Materials for the WCSD Math Common Finals

Transcription

1 Algebra 1 Semester Instructional Materials for the WCSD Math Common Finals The Instructional Materials are for student and teacher use and are aligned to the Math Common Final blueprint for this course. When used as test practice, success on the Instructional Materials does not guarantee success on the district math common final. Students can use these Instructional Materials to become familiar with the format and language used on the district common finals. Familiarity with standards vocabulary and interaction with the types of problems included in the Instructional Materials can result in less anxiety on the part of the students. Teachers can use the Instructional Materials in conjunction with the course guides to ensure that instruction and content is aligned with what will be assessed. The Instructional Materials are not representative of the depth or full range of learning that should occur in the classroom

2 1. Which of the following graphs represents y = x? A. C. B. D.. Reflect the graph of f(x) = x over the x-axis and translate the function one unit up. Which of the following is the function after the translation? A. f(x) = x 1 C. f(x) = x + 1 B. f(x) = x + 1 D. f(x) = x Which of the following is the solution for x in the equation x = 10? A. x = 5 C. x = 1 B. x = 5, x = 1 D. no solution 4. Which of the following is the solution for x in the equation 3 x + 4 = 6? A. x = 6 C. x = B. x = 6 and x = D. no solution

3 5. If f(x) = x and g(x) = 1 x + 5, use the tables below find the x-value(s) where f(x) = g(x). f(x) = x x f(x) g(x) = 1 x + 5 x g(x) A. x =, 4, 6 C. x = 6, B. x =, 6 D. no solution 6. Which graph below models the solutions to the equation 3 x =? A. C. B. D.

4 7. What is the simplified form of (4g 3 h 4 ) 3? A. B. 1g 6 h 1 C. 64g 9 h 1 D. 1g 9 h g 9 64h 1 8. Let f(x) = 3c 1/ and g(x) = c 15/ d 8. Find h(x) = f(x) g(x). A. h(x) = 6c8 C. d 8 h(x) = 5c7 d 8 B. h(x) = 6d8 c 8 D. h(x) = 6cd 9. What is the simplified form of 36m 4 n 6 4mn? (Assume that m 0, n 0, and p 0) p 4 A. 9n 4 p 4 m 3 C. 9n 8 p 4 m 5 B. 9n 8 m 5 p 4 D. 9m 5 n 8 p Simplify: 18 4 A. B C. 3 D. 3

5 11. A moving company sells boxes for packing items. The large box has a volume of 6x 3 + x + 3 cubic units. The medium box has a volume of x 3 + 8x 5 cubic units. A customer purchases two large boxes and one medium box. What is the total volume of the purchased boxes? A. 14x 6 + 1x cubic units C. 14x 3 + x + 8x cubic units B. 14x 6 + 4x + 8x + 1 cubic units D. 14x 3 + x + 8x + 1 cubic units 1. What is the product of the binomials: (r 8)(r + 5)? A. r 40 C. r 3 B. r + 13r 40 D. r 3r What is the simplified form of (b + 7)? A. b + 14b + 49 C. b + 49b + 49 B. b + 49 D. b The polynomial x + 11x + 30 is factorable. One factor is (x + 6), what is the other factor? A. (x + 1) C. (x 5) B. (x + 3) D. (x + 5) 15. Which of the following is a factor of 3x 1? A. (x + 1) C. (x ) B. (x 4) D. (x + 4) 16. Which of the following is a factor of x + 7x 30? A. (x 5) C. (x 1) B. (x + 6) D. (x 6)

6 17. What is the solution to x + 8x = 84? A. x = 1, x = 7 C. x = 14, x = 6 B. x = 14, x = 6 D. x = 1, x = Solve for x in 16x 49 = 0. A. x = ± C. x = B. x = ± 7 4 D. x = The height (h), in feet, of a person jumping off a diving platform can be modeled by the equation h = 16t + 4t + 6 where t represents the time in seconds the person is in the air. After how many seconds does the person jumping off the platform enter the water? A. 1 second C. B. 4 3 seconds 3 4 second D. seconds 0. Given the equation and graph of y = x 1, what is the domain and range? A. Domain: all real numbers Range: y 1 B. Domain: all real numbers Range: y 1 C. Domain: all real numbers Range: y 1 D. Domain: 1 x 1 Range: y 1

7 1. Which of the following quadratic functions represents the function graphed below? A. y = 1 x 5 B. y = x 5 C. y = 1 (x + 5) D. y = (x 5). Which of the following graphs represents f(x) = (x 4)? A. C. B. D.

8 3. Translate the graph of f(x) = x four units to the left, three units up and stretch the graph by a factor of. Which of the following is the function after the transformations? A. f(x) = 1 (x + 4) + 3 C. f(x) = (x + 4) + 3 B. f(x) = 1 (x 4) + 3 D. f(x) = (x 4) Which of the following quadratic functions represents the function graphed? A. y = (x 3) 1 B. y = (x + 3) 1 C. y = (x + 1) 3 D. y = (x 1) 3 5. Which of the following is the vertex for f(x) = 4(x 5) +? A. (5, ) C. ( 5, ) B. ( 0, ) D. (5, ) 6. What is the y-intercept of the graph of y = (x 1) + 3? A. (1, 3) C. (0, 3) B. (0, 5) D. (0, 1)

9 7. Given the graph of y = x, what is the solution for x after the transformation down four units and left three units? A. x =, x = B. x = 3 C. x = 5, x = 1 D. x = 4, x = 3 8. Which of the following are the x-intercepts for y = (x + ) 16 A. ( 6, 0), (, 0) C. ( 6, 0), (, 0) B. (, 0), (16, 0) D. (, 0), ( 16, 0) 9. What is the solution to h + 9h 4 = 0? A. h = , h = B. h = 9 65, h = C. h = 9 97, h = D. h = , h = 30. Which of the following is a solution to x + 14x = 18? A. x = 7 ± 85 B. x = 7 ± 13 C. x = D. x = 7 ± ± Which of the following is the vertex form for f(x) = x + 4x + 7? A. f(x) = (x + ) + 3 C. f(x) = (x + ) + 7 B. f(x) = (x ) + 4 D. f(x) = (x ) + 3

10 3. What is the y-intercept of the graph of y = x + 9x + 15? A. (0, 9) C. (0, 15) B. (9, 15) D. (0, 15) 33. What is the vertex of the function f(x) = x + 8x 9? A. ( 4, 73) C. (, 33) B. (4, 9) D. (, 1) 34. Before a truck can drive through a tunnel, it must be determined if the load can fit safely through the tunnel. The parabola f(x) = 1 4 (x 8) + 16 models the curve of the tunnel. If a truckload is 1 feet high what is the maximum width it could be? A. 4 feet B. 8 feet C. 1 feet D. 16 feet 35. Which of the following best describes the data in the table? x y A. Exponential with a growth rate of 3 B. Linear with a rate of change of 6 C. Quadratic with a second difference of 1 D. none of the above

11 36. Since the year 001 the population of community A grows exponentially as illustrated in the table. The exponential rate of growth is 1.3. What are the units for the rate of growth in the table? year people A. people per year B. years per people C. years D. people 37. Determine which of the following equations represent exponential growth or decay. Equation 1 Equation Equation 3 Equation 4 y = 1.5 x y = 0.8 x y = 0.5 x y =.7 x A. Equation 1: Growth Equation : Growth Equation 3: Decay Equation 4: Decay B. Equation 1: Decay Equation : Decay Equation 3: Growth Equation 4: Growth C. Equation 1: Decay Equation : Growth Equation 3: Growth Equation 4: Decay D. Equation 1: Growth Equation : Decay Equation 3: Decay Equation 4: Growth 38. If f(x) = 3 4 x and g(x) = 3 x, compare the functions and determine which of the following statements is correct. A. The x-intercept of f(x) is greater than the x-intercept of g(x). B. The y-intercept of f(x) is greater than the y-intercept of g(x). C. The functions increase at the same rate. D. The functions have the same y-intercept.

12 39. What is the solution for x in 4 x = 64? A. x = 16 C. x = 3 B. x = 4 D. x = 40. What is the solution for x in 5 x 9 = 15? A. x = 6 C. x = 5 B. x = 4 D. x = What is the solution to the system graphed? A. (, 4) B. (4, ) C. (1, ) D. no solution 4. What is the solution for x in the system? { y = 8 y = x A. x = 1 3 C. x = 1 B. x = 1 D. x = 3

13 43. Which of the following represents the function f(x) = 3 x 5? A. C. B. D. 44. Write a recursive formula for the sequence below, assuming f(1) is the first term in the sequence: 3, 6, 1, 4, 48 A. f(1) = 6 and f(n) = f(n 1) ( ), for n B. f(1) = and f(n) = f(n 1) 3, for n C. f(1) = 3 and f(n) = f(n 1) ( ), for n D. f(1) = 3 and f(n) = f(n 1) 9, for n 45. Write an explicit formula for the geometric sequence given a 3 = 1 and a 5 = 0.5. Assume the common ratio is positive. A. a n = 8(0.5) n 1 C. a n = 0.5(4) n 1 B. a n = 4(0.5) n 1 D. a n = 0.5(8) n 1

14 46. A supervisor at a factory is testing the company s packaging machines for accuracy. The machines are labeled X, Y, and Z. The company standard for packaging a product is that each bag should contain 6 to 10 ounces. The supervisor randomly chose 10 bags from each machine and recorded the results in the table below. Based on the dot plots below, which statement is correct? A. Machine X is both the most consistent and the most accurate. B. Machine X and Y are equally consistent, but Machine Y is the most accurate. C. Machine Z is both the most consistent and the most accurate. D. Machine Z is the most consistent, but Machine Y is the most accurate. 47. A fast food chain took a random survey of some of their stores to find the average number of sodas they sell per day. The data collected is given below. Which measure of central tendency best represents the data? Justify your answer. {165, 14, 153, 160, 135, 140, 155, 30, 16, 157} A. The mean would be best because there is an outlier. B. The mean would be best because there is not an outlier. C. The median would be best because there is an outlier. D. The median would be best because there is not an outlier. 48. The two-way frequency table shows all of the grades for males and females in a science class. If the females were to have the same percent of B s as the males, how many more females would need to get a B in the class? A. B. 3 C. 4 D. 5 A B C D F Females Males

15 49. Use the table below to help determine which function has the greatest value as x gets larger and larger. x f(x) = x + 3 g(x) = 3x h(x) = x 3 i(x) = 3 x A. f(x) has the greatest value as x gets larger and larger. B. g(x) has the greatest value as x gets larger and larger. C. h(x) has the greatest value as x gets larger and larger. D. i(x) has the greatest value as x gets larger and larger. 50. The maximum height reached by a bouncing ball is given by h(x) = 10(0.75) x where h is measured in feet and x is the bounce number. Describe the domain of this function and what it means when x = 0. A. The domain is all real numbers. When the bounce number x = 0, the height h of the ball is 10 feet, which represents its original height of the ball before it is dropped and bounces. B. The domain is all real numbers. When the bounce number x = 0, the height h of the ball is 7.5 feet, which represents its original height of the ball before it is dropped and bounces. C. The domain is all nonnegative integers, or 0, 1,, 3,. The domain represents the bounce number x and does not have units. When x = 0 the height h of the ball is 10 feet, which represents its original height of the ball before it is dropped and bounces. D. The domain is all nonnegative integers, or 0, 1,, 3,. The domain represents the bounce number x and does not have units. When x = 0 the height h of the ball is 7.5 feet, which represents its original height of the ball before it is dropped and bounces.

16 Algebra 1 S Instructional Material Answers D 11. B 1. B 31. A 41. A. D 1. D. A 3. C 4. D 3. B 13. A 3. C 33. D 43. B 4. D 14. D 4. B 34. B 44. C 5. C 15. C 5. D 35. A 45. B 6. A 16. B 6. B 36. A 46. D 7. D 17. C 7. C 37. B 47. C 8. A 18. B 8. A 38. D 48. D 9. C 19. B 9. D 39. C 49. D 10. A 0. C 30. C 40. A 50. C