Foundations of Math II - Final Exam Review - Fall

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1 Foundations of Math II - Final Exam Review - Fall Multiple Choice Identify the choice that best completes the statement or answers the question. Write your answer in the blank left of the number!! 1. If find the values of x, EF, and FG. The drawing is not to scale. E F G 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 find the values of x and ST. The diagram is not to scale. S T 9x 6x + 18 U A. x = 11, ST = 70 C. x = 6, ST = 54 B. x = 11, ST = 54 D. x = 6, ST = bisects and Solve for x and find The diagram is not to scale. A. x = 10, C. x = 11, B. x = 10, D. x = 11, 4. Each unit on the map represents 5 miles. What is the actual distance from Oceanfront to Seaside? y 8 6 Seaside x 2 Landview Oceanfront A. about 8 miles C. 50 miles B. 10 miles D. about 40 miles

2 5. Find the midpoint of 10 y 5 Q x P 5 A. ( 1, 2) B. ( 1, 3) C. ( 2, 3) D. ( 2, 2) 6. and are complementary angles. m =, and m =. Find the measure of each angle. A. = 46, = 44 C. = 46, = 54 B. = 54, = 46 D. = 54, = Find the value of x. 10 (6x + 7) (7x 9) Drawing not to scale A. 103 B. 77 C. 16 D. 16

3 8. Which of the following is the rule for the transformation of to. 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. 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) 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)

4 15. Which graph shows a triangle and its reflection image in the y-axis? A. y C. y x x 2 4 B. y D y x x is the image of after a transformation. Which choice describes the transformation shown. A. a reflection over the x-axis C. B. a reflection over the y-axis D.

5 17. Determine whether the figures are similar. If so, state the scale factor. A. similar, scale factor: B. similar, scale factor: C. similar, scale factor: D. not similar 18. Determine whether the figures are similar. If so, state the scale factor. A. similar, scale factor: B. similar, scale factor: C. similar, scale factor: D. not similar

6 19.. 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 In each pair of triangles, parts are congruent as marked. Which pair of triangles is congruent by SAS?

7 22. Use the information in the diagram to determine the height of the tree. The diagram is not to scale. 190 ft A ft B. 190 ft C ft D. 95 ft 23. Find the value of k. The diagram is not to scale k A. 84 B. 109 C. 96 D Find the value of x. The diagram is not to scale x 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. Building 100 ft A. 308 ft B ft C. 72 ft D. 33 ft

8 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 to the nearest degree. 100 ft A 249 ft A. 35 B. 45 C. 68 D 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? x 4.1 m 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? 1066 ft x Not drawn to scale 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. 15 cm 7 cm A. 49 cm B. 98 cm C cm D cm

9 Factor the expression Solve by factoring. = 0 A. 6, 2 B. C. D. 6, 1 7 6, 3 2 7, Solves: A. B. C. 31,,, What are the x-intercepts of the graph of? A. and C. D. 2, 10 3 B. and D. and 37. 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)

10 38. What is the equation of the line of symmetry for the quadratic equation graphed below? A. x = -3 C. x = 2 B. y = -3 D. y = Identify the parent function name and describe the transformations: 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: 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. 42. 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.

11 43. Find the domain and range of the quadratic function graphed below. A. domain: all real numbers range: B. domain: all real numbers range: C. domain: all real numbers range: all real numbers D. domain: range: 44. Choose the pair of statements which accurate describe the end behavior of the quadratic function graphed below.

12 45. Express in terms of. 46. Identify the range of. 47. Write the equation that is the translation of left 9 units and up 6 units.

13 48. A. y C y x x B. y D y x x A lunch menu consists of 8 different sandwiches, 3 different soups, and 5 different drinks. How many choices are there for ordering a sandwich, a bowl of soup, and a drink? A. 120 choices B. 160 choices C. 16 choices D. 109 choices 50. How many 8-letter permutations are possible for the letters S, T, U, D, Y, H, A, R, D? A. 43,046,721 permutations C. 362,880 permutations B. 181,440 permutations D. 362,880 permutations 51. In how many different ways could a committee of 4 students be chosen from a class of 26 students? A. 456,976 B. 14,950 C. 104 D. 358, Ms. Wong is redecorating her office. She has a choice of 7 colors of paint, 4 kinds of curtains, 7 colors of carpet, and 3 styles of furniture. How many different ways are there to redecorate if she can choose two different colors of paint, one kind of curtain, one color of carpet, and one style of furniture? A. 588 ways B. 4,116 ways C. 3,528 ways D. 28 ways 53. In how many different ways can you arrange 4 books on a shelf? A. 10 ways B. 256 ways C. 6 ways D. 24 ways

14 Does the problem involve permutations or combinations? Explain. 54. In how many ways could six horses come in first, second or third in a race? A. Combinations; the order does not matter. B. Combinations; the order matters. C. Permutations; the order does not matter. D. Permutations; the order matters.

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