Foundation of Math II - Practice Exam

Transcription

1 Name: Date: Foundation of Math II - Practice Exam Multiple Choice Identify the choice that best completes the statement or answers the question. Write your answer in the blank on the left of the number!! 1. If EF = 2x 10, FG = 4x 20, and EG = 30, find the values of x, EF, and FG. The drawing is not to scale. A. x = 5, EF = 0, FG = 0 C. x = 10, EF = 30, FG = 60 B. x = 5, EF = 10, FG = 20 D. x = 10, EF = 10, FG = If T is the midpoint of SU, find the values of x and ST. The diagram is not to scale. A. x = 11, ST = 70 C. x = 6, ST = 54 B. x = 11, ST = 54 D. x = 6, ST = MO bisects LMN, m LMO = 8x 29, and m NMO = 2x Solve for x and find m LMN. The diagram is not to scale. A. x = 10, m LMN = 51 C. x = 11, m LMN = 118 B. x = 10, m LMN = 102 D. x = 11, m LMN = 59 1

2 4. Each unit on the map represents 5 miles. What is the actual distance from Oceanfront to Seaside? A. about 8 miles C. 50 miles B. 10 miles D. about 40 miles 5. Find the midpoint of PQ. A. ( 1, 2) B. ( 1, 3) C. ( 2, 3) D. ( 2, 2) 6. DFG and JKL are complementary angles. m DFG = x + 8, and m JKL = x 10. Find the measure of each angle. A. DFG = 46, JKL = 44 C. DFG = 46, JKL = 54 B. DFG = 54, JKL = 46 D. DFG = 54, JKL = 36 2

3 7. Find the value of x. A. 103 B. 77 C. 16 D Which of the following is the rule for the transformation of ΔABC to ΔA'B'C'. A. (x,y) (x 4,x + 9) C. (x,y) (2x, 4x) B. (x,y) ( 2x,9x) D. (x,y) (x + 4,x 9) 9. The vertices of a triangle are P(5, 7), Q( 3, 1), and R(4, 3). Name the vertices of the image reflected over the y-axis. A. Pʹ ( 5, 7), Qʹ (3, 1), Rʹ ( 4, 3) C. Pʹ (5, 7), Qʹ ( 3, 1), Rʹ (4,3) B. Pʹ ( 5, 7), Qʹ (3, 1), Rʹ ( 4, 3) D. Pʹ (5, 7), Qʹ ( 3,1), Rʹ (4, 3) 10. Which is a rule to describe the transformation that is 90 counterclockwise rotation. A. (x, y) ( y, x) C. (x, y) ( x, y) B. (x, y) (y, x) D. (x, y) (x, y) 11. Which is a rule to describe the transformation that is a reflection in the line y = x. A. (x, y) (y, x) C. (x, y) ( x, y) B. (x, y) ( x, y) D. (x, y) (x, y) 3

4 12. The vertices of a triangle are A(1, 3), B(3, 0) and C(4, 5). Find the vertices of the image reflected over the x-axis. A. A (3, 1), B (0, 3), C (5, 4) C. A (-1, 3), B (-3, 0), C (-4, 5) B. A (-3, -1), B (0, -3), C (-5,- 4) D. A (1, 3), B (3, 0), C (4, 5) 13. The vertices of a triangle are E(2, 3), F(-3, 2) and G(5, -4). Find the vertices of the image rotated 180. A. E (-3, 2), F (-2, -3) and G (4, 5) C. E (3, -2), F (2, 3) and G (4, -5) B. E (3, 2), F (2, -3) and G (5, -4) D. E (-2, -3), F (3, -2) and G (-5, 4) 14. The vertices of a triangle are R(5, 3), S(2, -3), and T(-2, 1). Find the vertices of the image reflected across the line y = 3. A. R (5, 3), S (2, 9), T (-2, 5) C. R (5, 6), S (2, 0), T (-2, 4) B. R (1, 3), S (4, -3), T (8, 1) D. R (8, 3), S (5, -3), T (1, 1) 15. Which graph shows a triangle and its reflection image in the y-axis? A. C. B. D. 4

5 16. ΔG'H'I' is the image of ΔGHI after a transformation. Which choice describes the transformation shown. A. a reflection over the x-axis C. (x,y) (x,y 8) B. a reflection over the y-axis D. (x,y) (x 8,y) 5

6 17. Determine whether the figures are similar. If so, state the scale factor. A. similar, scale factor: B. similar, scale factor: 4 5 C. similar, scale factor: 1 2 D. not similar 18. Determine whether the figures are similar. If so, state the scale factor. A. similar, scale factor: 3 7 B. similar, scale factor: 1 2 C. similar, scale factor: 2 5 D. not similar 6

7 19. ΔABC ΔFED. Find the value of x. A. x = 9.95 C. x = 2.6 B. x = 6 D. x = The pair of figures are similar. Find the value of x. A C. 143 B D

8 21. In each pair of triangles, parts are congruent as marked. Which pair of triangles is congruent by ASA? A. C. B. D. 22. Use the information in the diagram to determine the height of the tree. The diagram is not to scale. A ft B. 190 ft C ft D. 95 ft 23. Find the value of k. The diagram is not to scale. A. 84 B. 109 C. 96 D. 46 8

9 24. Find the value of x. The diagram is not to scale. A. 145 B. 47 C. 102 D The students in Mr. Collin s class used a surveyor s measuring device to find the angle from their location to the top of a building. They also measured their distance from the bottom of the building. The diagram shows the angle measure and the distance. To the nearest foot, find the height of the building. A. 308 ft B ft C. 72 ft D. 33 ft 26. A large totem pole in the state of Washington is 100 feet tall. At a particular time of day, the totem pole casts a 249-foot-long shadow. Find the measure of A to the nearest degree. A. 35 B. 45 C. 68 D. 22 9

10 27. A slide 4.1 meters long makes an angle of 35 with the ground. To the nearest tenth of a meter, how far above the ground is the top of the slide? A. 7.1 m B. 5.0 m C. 2.4 m D. 3.4 m 28. To approach the runway, a small plane must begin a 8 descent starting from a height of 1066 feet above the ground. To the nearest tenth of a mile, how many feet from the runway is the airplane at the start of this approach? A ft B. 148 ft C ft D. 7,659.5 ft 29. Find the angle of elevation of the sun from the ground to the top of a tree when a tree that is 8 yards tall casts a shadow 15 yards long. Round to the nearest degree. A. 32 B. 65 C. 44 D Find the area of the triangle. Give the answer to the nearest tenth. The drawing may not be to scale. A. 49 cm 2 B. 98 cm 2 C cm 2 D cm 2 10

11 31. Find the value of x to the nearest tenth. A. 7.2 C. 6.7 B. 3.4 D To find the length of a lake, a surveyor starts at one end of the lake and walks 245 yards. He then turns as shown and walks 270 yards until he arrives at the other end of the lake. About how long is the lake? A. 296 yards C. 314 yards B. 260 yards D. 422 yards Factor the expression. 33. x x + 40 A. (x 10)(x 4) C. (x + 10)(x 4) B. (x + 4)(x + 10) D. (x + 4)(x 10) 34. x 2 7x 18 A. (x + 9)(x 2) C. (x 9)(x 2) B. (x + 2)(x + 9) D. (x + 2)(x 9) 11

12 35. 3x x + 10 A. (x + 5)(3x + 2) C. (3x + 5)(x + 2) B. (3x + 2)(x 5) D. (3x + 5)(x 2) 36. Solve by factoring. 2x 2 + 5x 42 = 0 A. 6, 2 B. 6, 1 3 C. 6, 7 2 D. 7 2, 1 3 Use the Quadratic Formula to solve the equation x 2 + 2x + 5 = 0 A. 31 3, 11 B. 5 3, 1 C. 1, 5 3 D. 2, What are the x-intercepts of the graph of y = 2x 2 9x 5? A. Ê Ë Á 2,0 ˆ and Ê ËÁ 6,0 Ê 1 ˆ C. ËÁ 2, 5 ˆ Ê B. Ê 1 ËÁ 5, 0 ˆ and ËÁ 2,0 ˆ Ê D. 1 ËÁ 2,0 ˆ and Ê5,0 ËÁ ˆ 39. Use the graph below to identify the vertex of the quadratic model. A. (-3, 2) C. (0.3, 3.7) B. (0, 1) D. (2, -3) 12

13 40. What is the equation of the line of symmetry for the quadratic equation graphed below? 41. 5y 6 y 11 A. x = -3 C. x = 2 B. y = -3 D. y = 2 Simplify the expression. A. 6y 17 B. 5y 66 C. 5y 17 D. 6y y 4 y 9 A. y 13 B. 1 y 13 C. 1 D. y 5 y Suppose you invest $1700 at an annual interest rate of 4.6% compounded annually. How much will you have in the account after 5 years? Use the formula y = 1700(1.046) t where y is the amount of money in the account after t years. A. $ B. $ C. $ D. $ Suppose the population of a town is 2700 and is growing 4% each year. Use the equation y = 2700(1.04) t, where y is the population after t years, to predict about how long it will take for the population to reach A. 2.5 years B. 7.3 years C. 8.5 years D. 6.4 years 13

14 45. Suppose a laboratory has a 26 g sample of polonium-210.the half-life of polonium-210 is about 138 Ê days. How much polonium is in the sample 414 days later? Use the formula y = 26 1 ˆ n where y is the ËÁ 2 amount left after n half-lives. A. 26 g C g B. 13 g D. 6.5 g 46. A boat costs $10,000 and decreases in value by 10% per year. How much will the boat be worth after 15 years? Use the equation y = 10,000(0.90) t. A. $1, B. $9,850 C. $2, D. $41, Solve: 6 2x + 5 = 80 A C B D Solve: 4 10 x = 71 A C B D Identify the parent function name and describe the transformations: f(x) = 3x 2 5 A. quadratic; right 3, down 5 C. quadratic; vertical stretch, down 5 B. cubic; right 3, down 5 D. cubic; vertical stretch, down Identify the parent function name and describe the transformations: f(x) = x A. square root; right 4, down 6 C. absolute value; left 4, up 6 B. absolute value; right 4, up 6 D. square root; left 4, down Choose the equation whose parent function is the square root function that has been flipped across the x-axis and moved left 7 units. A. f(x) = 7 x C. f(x) = x 7 B. f(x) = x + 7 D. f(x) = x Choose the equation whose parent function is a base 3 exponential function that has a vertical stretch by 4 and has moved down 2 units. A. f(x) = 4 3x 2 C. f(x) = 4 3 x 2 B. f(x) = 4 3 x 2 D. f(x) = 3 4x 2 14

15 53. Find the domain and range of the quadratic function graphed below. A. domain: all real numbers range: y 0 B. domain: all real numbers range: y 0 C. domain: all real numbers range: all real numbers D. domain: 5 x 5 range: 0 y Choose the pair of statements which accurate describe the end behavior of the quadratic function graphed below. A. f(x) 0 as x f(x) as x + B. f(x) + as x f(x) + as x + C. f(x) as x f(x) + as x + D. f(x) as x f(x) as x + 15

16 55. Express t(x) in terms of f(x). A. f(x 2) + 5 C. f(x 2) 5 B. f(x + 2) 5 D. f(x + 2) Identify the range of t(x). A. 4 y 6 C. 1 y 5 B. y 5 D. 6 y 4 16

17 ID: A Foundation of Math II - Practice Exam Answer Section MULTIPLE CHOICE 1. D 2. C 3. C 4. D 5. A 6. D 7. D 8. D 9. A 10. A 11. A 12. C 13. D 14. A 15. D 16. C 17. D 18. A 19. D 20. C 21. B 22. D 23. A 24. D 25. A 26. D 27. C 28. D 29. D 30. A 31. C 32. A 33. B 34. D 35. C 36. C 37. C 38. D 39. D 40. C 1

18 ID: A 41. C 42. C 43. D 44. D 45. C 46. C 47. D 48. C 49. C 50. B 51. B 52. B 53. B 54. C 55. D 56. C 2