AP Precalculus Unit 1 Review Problems Name______

1. Page 77 in the textbook: Problems 73-76, 81 and 82 2. Page 99 in the textbook: Problems 1-4 and 6-13

3. Julia is hiking near the Circular Forest, which has the shape of a perfect circle, 20 km in diameter. Julia starts her hike from a point 3 km SOUTH and 2km EAST of the SOUTHERNMOST point of the forest. She then walks in a straight line to a point 4 km EAST and 6 km NORTH of the NORTHERNMOST point of the forest.

a). If Julia hikes at a constant speed of 4km per hour, how much time did she spend in the forest? b). On Julia’s hike, where is she when she is closest to the EASTERNMOST point of the forest? You may give your answer in x and y coordinates in whatever coordinate system you used to solve the problem.

4. Maddie painted a bright yellow circle on Red Square. The circle had a radius of 25 feet. She then walked from a point 31 feet due south of the center of the circle directly to a point 8 feet north and 37 feet west of the center of the circle. If Maddie walked at a constant speed of 5 feet per second, how long was she inside the circle?

5. The line y - x = 4 cuts the circle x2 + y2 -12x -8y + 16 = 0 at points A and B. Find the length of chord AB.

6. Find the equation of the tangent to the circle x2 + y2 -6x -8y - 9 = 0 at point (0, -1) on the circle.

7. Write the equation of a line that passes through points and .

8. Mrs. Lindeback left Woodinville High School to watch her daughter’s volleyball game at Finn Hill Middle School. She stopped at WFC after driving 6 miles to pick up cupcakes for the team. When Mrs. L. left QFC she worried that she would be late, so she increased her average speed by 10 Mph for the remaining 2 miles. It took Mrs. Lindeback 8 minutes longer to drive to QFC than to Finn Hill. What is the average speed she drove to QFC?

9. Find the equation of the tangent line to circle x2 + y2 -6x -8y - 9 = 0 at point (0, 1) on the circle.

10. Determine the equation of the line that is perpendicular to the line 5x – 2y + 8 =0 and goes through the point (-5, 2). Express your answer in point-slope form.

11. Solve each equation.

a). b) c) Solve for y:

12. Kayla leaves Woodinville high school at 3:00 and heads due north at 3 mph. Lauren leaves at 3:05 and heads due east at 3.5mph. What time are the girls 2 miles apart?

13. What is the length of the tangent from the point (5, 5) to the tangent point on the circle given by the equation ?

Problem Solving Extension Problems:

12. Circles with centers O and P have radii 2 and 4, respectively, and are externally tangent. Points A and B on the circle with center O and points C and D on the circle with center P are such that AD and BC are common external tangents to the circles. What is the area of the concave Hexagon AOBCPD?

14. Yesterday Han drove 1 hour longer than Reid at an average speed 5 miles per hour faster than Ian. Jan drove 2 hours longer than Ryan at an average speed of 10 miles per hour faster than Ian. Han drove 70 miles more than Ian. How many more miles did Jan drive than Ian?

9. Bricklayer Brenda would take nine hours to build a chimney alone, and Bricklayer Brandon would take 10 hours to build it alone. When they work together, they talk a lot, and their combined output decreases by 10 bricks per hour. Working together ,they build the chimney in 5 hours. How many bricks are in the chimney?