PPF 502 & PPF 504 Work Sheet Period Name CRS SKILL LEVEL DESCRIPTION Level 1 ALL students must R- NCP 505 Work with squares and square roots attain mastery at this level Level 2 MOST students will PPF 502 Recognize Pythagorean triples attain mastery of the focus skill in PPF 504 Use the Pythagorean theorem in isolation isolation. PPF 502 PPF 504 Level 3 SOME students will attain mastery of focus skill with other skills Level 4 SOME students will attain mastery of focus topics covered in a more abstract way Level 5 FEW students will attain mastery of the extension skill. PPF 602 Use the Pythagorean theorem when it is not in isolation Level 1 1. Multiply or divide, if so indicated, and write each answer so that there are no perfect square factors inside the radical. a. 28 b. 125 c. 162 d. 3 200 e. 20 120 f. 7 27 30 18 Level 2 2. Determine if each of the following are a Pythagorean triple. a. (14, 27, 50) d. (11,60,61) b. (9, 12, 15) e. (15, 36, 39) c. (13,84, 85) f. (28, 45, 53) 1
3. Find the missing side length. Reduce all radicals. 4. Find the missing side length. Reduce all radicals. 5. Find the missing side length. Reduce all radicals. 6. Find the missing side length. Reduce all radicals. Level 3 7. You're locked out of your house and the only open window is on the second floor, 25 feet above the ground. You need to borrow a ladder from one of your neighbors. There's a bush along the edge of the house, so you'll have to place the ladder 10 feet from the house. What length of ladder do you need to reach the window? 2
8. Scott wants to swim across a river that is 400 meters wide. He begins swimming perpendicular to the shore he started from, but ends up 100 meters down river from where he started because of the current. How far did he actually swim from his starting point? 9. In the Old West, settlers often fashioned tents out of a piece of cloth thrown over tent poles and then secured to the ground with stakes forming an isosceles triangle. How long would the cloth have to be so that the opening of the tent was 4 meters high and 3 meters wide? 10. You've just picked up a ground ball at first base, and you see the other team's player running towards third base. How far do you have to throw the ball to get it from first base to third base, and throw the runner out? 11. Find the area of the triangle below. 3
12. One route along flat terrain from Madison to South Bend is to drive south from Madison for 400 miles to Chicago, then at Chicago to drive east 500 miles to South Bend. If a straight flat road existed between Madison and South Bend, how many miles would it be? Madison 400 mi Chicago 500 mi South Bend Level 4 13. Mike and Sue are out looking for rocks for a Geology project, Mike takes a path that goes due North for 6 miles. Sue takes a path that heads due west for 7 miles. Mike radios Sue that he has found a rare fossil within the face of a cliff. (Draw a picture first) a. If Sue walks in a straight path to Mike, how far will she have to walk? b. If she walks at 4 miles per hour, how long will it take her to reach Mike? 14. Carroll bikes 1 kilometer east, 4 kilometers north, and then 5 kilometers east again. How far is Carroll from her starting position, to the nearest tenth of a kilometer? 4
15. Level 5 16. Aurora, Burlington, and Clifton are three cities. Aurora is 65 miles west of Burlington. Clifton is due north of Burlington and 97 miles away from Aurora. Clyde and Minnie leave Aurora at the same time. Clyde goes straight to Clifton at a speed of 25 miles per hour. Minnie goes from Aurora to Burlington to Clifton at a speed of 30 miles per hour. a. Who will get to Clifton first? b. How much longer will it take for the second person to arrive? Your answer should be accurate to within a tenth of an hour. 17. Kenosha county gets its salt for the winter roads delivered in August. When the salt is delivered, it is fed up a large conveyer belt that drops the salt into a large circular building. The dropped salt forms a cone on the ground as it falls. The circular building is 75 feet across and the salt pile has a slant height (the distance you would slide form the top of the salt pile to the bottom) of 70.75 feet before winter started. a) What is the volume of the salt? 5
b) If the county uses 1,500 cubic feet in the average snow fall, how many days of snow will the salt last? 18. Some magpies are nesting at the top of two trees, which stand 25 m apart. The two trees are 12 m and 8 m tall. Jane made a birdfeeder for the young magpies. Her brother Kevin installed it on a 3.5 meter tall pole. Where did the two children plant the birdfeeder into the ground so that the young birds from both nests have an equal distance to the birdfeeder? Mixed Review 19. Opposite vertices of a square in the standard (x,y) coordinate plane have coordinates (4, 16) and (20, 0). What are the coordinates for the center of this square? 20. Simplify: 21. At what point will the line below cross the x- axis? 6
22. What is the distance between points ( 4, 1) and (4, 3)? Leave your answer in simplest radical form. 23. Find the slope of the following equation: 24. On a real number line, the coordinate of a point A is 10 and the coordinate of point B is 6. What is the coordinate of the midpoint of AB? A) 16 B) 8 C) 4 D) 4 E) 16 25. Chris is drilling cylindrical holes in the ground that he will fill up with concrete to support the posts in his deck. Each hole is 6 inches in diameter and 4 feet deep. a) What is the volume of each hole? b) If each bag of concrete makes 1.5 cubic feet, how many bags of concrete will he need if he is drilling 8 holes? 7