2 nd Term Final Revision Sheet

Transcription

1 nd Term Final Revision Sheet Name: Grade: 10A/B Subject : Math Teachers Signature

2 ( nd Final Revision Gr-10) Select the best answer. 1. Which equation is represented by the graph below? A x (y 1) 6 B x (y 1) 36. On the design of a new car, the steering wheel has a diameter with endpoints at (4, 9) and (1, 3). What are the center and radius of the wheel? A Center (8, 6); r 5 B Center (8, 6); r 10 C Center (6, 8); r 5 D Center (6, 8); r The graph of which equation would be a circle with a center at (0, 3) and a radius of 3? A x (y 3) 3 B x (y 3) 9 C x (y 3) 9 D x (y 3) 3 4. A tape measure is coiled in a circular roll described by the equation (x 1) y 5. The tape is pulled out in a line tangent to the circle at the point (3, 3). Which equation models the line of the extended tape measure? A 4 y x 7 3 B 4 y x Which is the length of the major axis for x y the ellipse with equation 1? A 1 C 36 B 14 D A cow pasture is in the shape of an ellipse with vertices at (5, 3) and (5, 3) and foci at (3, 3) and (3, 3). Which equation models this ellipse? A B C D x y x y x 3 y x 3 y Which equation represents the graph below? A y x 9 y B x 1 9

3 8. What are the vertex and axis of symmetry for the parabola with equation y (x 3)? A (3, 0) and x 3 B (0, 3) and x 3 9. The height of a toy rocket is graphed below. 1. A vulture is circling an area of a desert in a path modeled by the equation (x 5) y 5. A horse walks in a 1 path modeled by y x x. At what points is the vulture above the horse? A (4, 1) and (, 4) B (0, 0) and (, 4) C (4, 1) and (5, 5) D (5, 5) and (0, 0) 13. Which are the solutions of the system shown below? Which equation models the height of the rocket? A y 16x 100x B y 16x 100x C y 16x 100 D y 16x Which conic section is represented by the equation x y 4x 5? A circle B ellipse C hyperbola D parabola 11. Find the standard form of the equation for the conic section represented by y x 10x 6y 5. A (y 3) (x 5) 81 B y 3 x 5 C 9 9 y 3 x D y 3 x A (0, 5) and (, 0) B (, 1) and (5, 5) C (5, 5) and (5, 0) D (8, 0) and (, 0) 14. What are the solutions of the system y x 3? x 1 y 4 4 A (1, 4) and (1, ) B (0, 3) and (1, 3)

4 Chapter Test Form B Select the best answer. 1. Which equation is represented by the graph below? A x 4y 16 C 4x y 16 B x 4y 16 D 4x y 16. A civil engineer has laid a graph down over the sketch of a new road system. A circular rotary has a diameter with endpoints at (3, 5) and (5, 11). What are the center and radius of the rotary? F Center (8, 1); r 5 G Center (8, 1); r 10 H Center (1, 8); r 5 J Center (1, 8); r The graph of which equation would be a circle with a center at (, 3) and a radius of 7? A (x ) (y 3) 7 B (x ) (y 3) 7 C (x ) (y 3) 49 D (x ) (y 3) A ball is spun in a circle described by the equation (x ) (y 1) 10. The ball is released at the point (1, 4) and proceeds to travel in a line tangent to the circle. Which equation models the flight of the ball after it is released? 1 11 F y x H y 1 x G y 3x 7 J y 3x 7 5. What is the length of the major axis for the ellipse with equation 64x 5y 1600? A 10 C 0 B 16 D A race track is modeled with the graph of an ellipse with vertices at (, 3) and (8, 3) and foci at (1, 3) and (7, 3). Which equation models this ellipse? F x 3 y G x 3 y H x 3 y J x 3 y Which equation represents the graph below? A x 1 y B x 1 y C x 1 y D x 1 y 1 4 9

5 8. What are the vertex and axis of symmetry for the parabola with equation y 6 (x 4)? F (4, 6) and x 4 G (4, 6) and y 6 H (4, 6) and x 4 J (4, 6) and y 6 9. The height of a thrown ball is graphed below. 1. The path swum by the captain of a synchronized swimming team is modeled by the equation (x 3) (y ) 5. One of her teammates swims in a path modeled by 1 1 the equation y x x. At what points are the two swimmers in danger of colliding? F (0, 6) and (0, ) G (1, 1) and (3, 7) H (5, 17) and (0, 6) J (1, 1) and (3, 1) 13. What are the solutions of the system shown below? Which equation models the height of the ball? A y 16x 60x B y 16x 60x C y 16x 56 D y 16x Which conic section is represented by the equation 6x 9y 1x 7y 19 0? F circle H hyperbola G ellipse J parabola 11. Find the standard form of the equation for the conic section represented by x y 10x 6y 47. A (y 3) (x 5) 9 B (y 3) (x 5) 81 C y 3 x D y 3 x A (3, 0) and (0, 3) B (7, 0) and (1, 0) C (6, 3) and (0, 3) D (3, 4) and (3, 7.5) 14. What are the solutions of the system y 4 3x 48? y 4x 4 F (1, 0) and (, 4) G (0, 4) and (1, 0) H (0, 4) and (1, 0) J (1, 8) and (3, 8)

6 Select the best answer. 1. Which equation is represented by the graph below? G y x 5 J 3 y x 5 3 A 4x y 16 C 4y x 16 B 4x y 16 D 4y x 16. On a map, a circular reservoir has a diameter with endpoints at (7, 13) and (, 5). What are the center and radius of the reservoir on the map? F Center (1.5, 19.5); r 7.5 G Center (.5, 19); r 7.5 H Center (8, 8); r 15 J Center (0, 15); r The graph of which equation would be a circle with a center at (9, 9) and a radius of 13? A (x 9) (y 9) 13 B (x 9) (y 9) 13 C (x 9) (y 9) 169 D (x 9) (y 9) A circular gear is modeled by the equation (x 10) (y 3) 5. The gear pushes a piston that runs tangent to the gear, attaching at the point (6, 9). Which equation models the path of the piston? 3 3 y x 5 y x 5 F H

7 5. Which is the length of the major axis for x y the ellipse with equation 4? 9 16 A 6 C 16 B 8 D A model of the White House shows the oval office as an ellipse with vertices at (5.5, 3) and (.5, 3) and co-vertices at (1.5, 5) and (1.5, 1). Which equation models this ellipse? F x 3 y G x 1.5 y 3 H 16 9 x 3 y x 1.5 y 3 1 J Which equation represents the graph below? Conic Sections 8. What are the vertex and directrix for the parabola with equation 1 x 3 y 3? F (3, 3) and y 3.5 G (3, 3) and x 3.5 H (3, 3) and x.5 J (3, 3) and y.5 9. The height of a water balloon thrown from a building is graphed below. A x 4 y 9 4 B x y 4 C 9 4 x 4 y 4 9 D x y Which equation models the height of the balloon? A y 16x 180 B y 16x 180x C y 16x x 180 D y 16x x Which conic section is modeled by 4x 9y 4x 54y 81? F circle H hyperbola

8 G ellipse J parabola 11. Write x y 4x 8y 48 in standard form. A (x ) (y 4) 36 B (x ) (y 4) 36 C x y D x y At a renaissance faire, horses are ridden in a complex pattern as part of a show. A stallion rides a path modeled by the equation x 5 y 1 and 4 5 another horse rides a path modeled by the equation y (x 7). At what points are the two horses in danger of colliding? F (4, 5) and (7, 0) G (5, 4) and (7, 0) H (4, 5) and (7, 0) J (5, 4) and (7, 0) 13. What are the solutions of the system shown below? A (6, 4) and (0, 4) B (6, 4) and (1, 0) C (5.5, 5.5) and (0, 4) D (3, 4) and (5.5, 5.5) 14. What are all the solutions of the system y 4 9x 0 4 9? y x 4 F (1, ) and (1, ) G (0, 4) and (1, ) H (1, ), (1, ), and (0, 4) J (0, 4), (0, 4), and (1, )

9 1. Sketch a graph of the function (x 1) y 36 and identify the conic section it describes. 5. What is the length of the major axis for the ellipse described by the equation x 4 y ? 6. On a map of an amusement park, a ride has a track in the shape of an ellipse. The ellipse has vertices at (5, 1) and (5, 1) and foci at (3, 1) and (3, 1). Find the equation that can be used to describe the path of the ride. 7. Find the equation that describes the graph below.. On a map, the circular mouth of a volcano has a diameter with endpoints at (, 5) and (8, 13). Find the center and radius of the volcano s opening. 3. Find the equation to a circle with a radius of 10 and a center at (1, 7). 4. A hose is coiled in a circle described by the equation (x 5) (y 4) 5. When it s pulled out, the hose runs tangent to the circle at the point (8, 8). Find the equation of the line that the hose makes with the circle.

10 8. Find the vertex and axis of symmetry for the parabola with equation 1 y 3 x The height of a thrown ball is graphed below. 1. A supply truck is circling an area in a path described by the equation (x 3) (y 1) 5. A troop needing supplies travels a path described 1 by y x 3. At what point or points 4 will the troop meet the supply truck? 13. List all solutions of the system shown below. Find the equation that models the height of the ball against time. 10. Which conic section is represented by the equation y x y 4x 109? 11. Complete the square and find the standard form of the equation for the conic section represented by x 10x 3y List all solutions of the system y 3 x 9. x y 3 5

11 1. Sketch a graph of the function 5x 64y 1600 and identify which conic section it describes. 5. What is the length of the major axis of the ellipse described by the equation x 5 y ? 6. On a map of the night sky, an elliptical galaxy has vertices at (16, 3) and (10, 3) and foci at (8, 3) and (, 3). Find the equation that can be used to model the shape of the galaxy. 7. Find the equation that describes the graph below.. On the diagram of a computer, a circular disk drive has a diameter with endpoints at (9, ) and (15, 1). Find the center and radius of the disk drive. 3. Find the equation to a circle with a center of (3, 3) and a radius of A pitcher s arm makes a circle described by the equation (x 5) (y 5) 100. He releases the ball at the point (1, 13) and it then travels tangent to the circle. Find the equation of the line that describes the ball s path after release.

12 Chapter Test Form B continued

13 8. Find the vertex and axis of symmetry for the parabola with equation 3 x 4 y A construction worker throws a sandwich to his coworker below, and the height of the sandwich is graphed below. Find the equation that models the height of the sandwich over time. 10. Which conic section is represented by the equation 16y 9x 96y 54x 81? 11. Complete the square and find the standard form of the equation for the conic section represented by 9y x 18y 6x 9 0.