Mrs Browne's Algebra One and Two - Home



Name_______________________________________ Algebra TwoProblem Set Project2014Due date: One problem is due on the first day. Two completed problems are due by the third class of this week for a quiz grade, and the remaining will be due at the end of two-hour class. Keep in mind that we will be doing another problem during that class so you will not have the whole two hours to finish your individual problem project paper.Directions: Each problem is worth a different number of points. You must do at least 60 points worth of problems, and no more than 110 points worth of problems. Your grade will be the total points you earn divided by the points attempted. Each problem is a four part word problem, which follow the problem-solving steps of the famous mathematician George Pólya – details below. You may work with a partner but you must tell me whom you worked with for each problem. You must type your project and send it to me in a document. You may use mathematica if you like or you can take a picture of your work (refers to part 3) and put it into your document. Polya’s Problem Solving Steps.Understanding the problem. (Recognizing what is asked for – explain what the problem is talking about.)Devising a plan. (Tell me how you are planning on solving the problem.)Carrying out the plan. (Actually do the math of the problem.)Looking back. (Reflect on your answers.)DETAILED VERSION (possible elements to include in each step)Understand the problem.You may need to rewrite the problem in your own words.What is the missing information that is needed?Is there information given is not needed?Devise a plan.Make a list of information provided.Make a list of information needed.Draw diagrams or make a table.d) Look for a pattern.Carry out the plan.Work carefully.Do not skip steps. Show all your work even if done on a calculator.State the solutionReview your solution. Is the solution feasible in terms of the problem? (Does the answer make sense?)Are there generalizations from this problem that could apply to other similar problems?Are there other ways to arrive at the same solution?Why did you pick this problem?1. (10 points). Pat races at 10 miles per hour, while Kim races at 9 miles per hour. When they both ran in the same long distance race last week, Pat finished 8 minutes ahead of Kim. What was the length of the race, in miles? 2. (5 points) (Continuation) Assume that Pat and Kim run at p and k miles per hour, respectively, and that Pat finishes m minutes before Kim. Find the length of the race, in miles.3. (20 points) A bug moves linearly with constant speed across my graph paper. I first notice the bug when it is at (3, 4). It reaches (9, 8) after two seconds and (15,12) after four seconds.Predict the position of the bug after six seconds; after nine seconds; after t seconds.Is there a time when the bug is equidistant from the x- and y-axes? If so, where is it?4. (5 points) An airplane 27000 feet above the ground begins descending at the rate of 1500 feet per minute. Assuming the plane continues at the same rate of descent, how long will it be before it is on the ground?5. (5 points) (Continuation) Graph the line y = 27000 ? 1500x, using an appropriate window on your calculator (or on paper) With the preceding problem in mind, explain the significance of the slope of this line and its two intercepts. Reminder that if you graph it on the Nspire, you need to send me your document. Or install the software on your computer and take a screen shot.6. (15 points) An airplane is flying at 36000 feet directly above Lincoln, Nebraska. A little later the plane is flying at 28000 feet directly above Des Moines, Iowa, which is 160 miles from Lincoln. Assuming a constant rate of descent, predict how far from Des Moines the airplane will be when it lands.7. (20 points) In a dream, Blair is confined to a coordinate plane, moving along a line with a constant speed. Blair’s position at 4 am is (2, 5) and at 6 am it is (6, 3). What is Blair’s position at 8:15 am when the alarm goes off?8. (10 points). Golf balls cost $0.90 each at Jerzy’s Club, which has an annual $25 membership fee. At Rick & Tom’s sporting-goods store, the price is $1.35 per ball for the same brand. Where you buy your golf balls depends on how many you wish to buy. Explain, and illustrate your reasoning by drawing a graph.9. (15 points) If you were to drop a ball from a height of 50 feet, how high would it bounce? To make such a prediction, you could gather data by experimenting with smaller heights, where it is easier to measure the rebound. Gather several data points (drop, rebound), using a meter stick and a sufficiently bouncy ball. If you use the top of the ball for your measurements, remember to take the diameter of the ball into account when recording your data.10. (5 points) An estate of $362880 is to be divided among three heirs, Alden, Blair, and Cary. According to the will, Alden is to get two parts, Blair three parts, and Cary four parts. What does this mean, in dollars and cents?11. (20 points) Sam and Kirby were out in their rowboat one day, when Kirby spied a nearby water lily. Knowing that Sam liked a mathematical challenge, Kirby announced that, with the help of the plant, it was possible to calculate the depth of the water under the boat. While Sam held the top of the plant, which remained rooted to the lake bottom during the entire process, Kirby gently rowed the boat five feet. This forced Sam’s hand to the water surface. When pulled taut, the top of the plant was originally 10 inches above the water surface. Use this information to calculate the depth of the water under the boat.12. (20 points) Preparing to go on a fishing trip to Alaska, Sam wants to know whether a collapsible fishing rod will fit into a rectangular box that measures 40 inches by 20 inches by 3 inches. The longest section of the rod is 44.75 inches long. Will the rod fit in the box? (KEEP IN MIND THIS IS 20 POINTS AND NOT AS EASY AS YOU THINK-IT’S A 3D BOX, NOT A FLAT SURFACE!)13. (5 points) Three softball teams ordered equipment from the same catalog. The first team spent $285 on 5 shirts, 4 caps, and 8 bats. The second team spent $210 on 12 shirts and 6 caps. The third team spent $250 for 7 shirts, 10 caps, and 3 bats. What were the catalog prices for shirts, caps, and bats?14. (15 pts) Alex, the geologist, is in the desert, 18 km from a long straight road and 72 km from base camp, which is also 18 km from the road, on the same side of the road as Alex is. On the road, the jeep can do 60 kph, but in the desert sands, it can only manage 32 kph. Sketch a picture of the situation.Describe the path that Alex should follow to return to the base camp most quickly.How long would the trip be in hours and minutes?If the jeep were capable of 40 kph in the desert, how would your answer be affected?15. (10 points). There are 396 persons in a theater. If the ratio of women to men is 2:3, and the ratio of men to children is 1:2, how many men are in the theater? ................
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