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ACTIVITIES AND ASSIGNMENTS FOR COLLEGE ALGEBRAINTRODUCTIONThese are abridged versions of some of the assignments that I use in my College Algebra classes. If there are any notes/comments for the instructor, those are before the assignment in parentheses between the ***.SKETCH STORYSimilar to what we did in class today, create a different story of your own. Make sure you are measuring something that has increases, decreases, and constant parts. You should not use an example that is too similar to what we did in class. You should neatly draw your graph on a sheet of plain white (printer) paper. Make sure you label your graph properly and draw it as neatly and exactly as possible. Choose appropriate variables other than ‘x’ or ‘y’ to use. Identify the domain and range somewhere on the front. On the back, neatly write out the story of your situation. Use proper function notation to identify two points on your graph. Write out the explanation of what these points mean in words. You may write this on the back. CRYPTOGRAPHY1.Decode the following message. C(n) = 2n + 757 – 17 – 9 – 23 25 21 – 37 – 47 25 – 47 43 – 25 – 21 – 23 – 472.Create a code equation and a coded message. I will have to decode it. 3.At the beginning of the next class, you will be given a code and a message to decode. You will need to determine the formula to decode the message and then actually decode the message. You will need to fully decode the message for full credit. You may use your notes, but not get any help from another student. There will be a 10 minute time limit.CSI RAINING BULLETS(***I use a lot of these. Students are given the general information and data needed. Then they must take what they are given and use the skills from class to arrive at an answer. This one would include students needing to use Excel to make a graph. This particular problem was adapted from a case on the TV show CSI.***)Facts:During an autopsy, the coroner is suspicious at how shallow the penetration is of a bullet in the chest of a victim. The bullet is only 1.7 inches deep. His conclusion is that this bullet struck the victim from a long range and had slowed down considerably before striking the victim.Refer to the attached file relating the penetration depth for bullets at different speeds. Use the Excel program to create a scatter plot and determine the best formula. Use this formula to estimate the speed at which the bullet entered the body.Once you have that speed, use the formula Speed = 32*time to determine how long the bullet had been in the air.Next the formuladistance = 0.707*velocity*time will determine the distance that an object traveled. Assume the initial velocity is 165 feet per second.Write up an official-looking Police Report of your findings. This should only include relevant materials and results.Lab Analysis—Raining BulletsSpeed of Bullet vs. Penetration DepthTest Conditions:Bullets were fired with different speeds into a gelatin with the same thickness as a human body. The measurement of the depth of the penetration was recorded.Bullet Speed (ft. / sec)Penetration (inches)18003.8016003.5014003.0412002.8810002.68 8002.12OLYMPIC LINESFor this assignment, you need to use some information about an Olympic sport from the Olympic sheets given out in class. Each person needs to choose a different sport. You need to claim your Olympic event on the sheet provided. First come, first serve.Use all of the years for the male or female (minimum of 5). You should adjust your years so that you are starting with a zero. Make a scatter plot of your data using the Excel program. You should label each axis correctly and give the graph a title. You should display the linear regression equation. Edit it to use appropriate variables and function notation.Explain the rate of change. Extend your graph out to the length to tell the winning value for the 2016 Olympics. Estimate this value by putting a point on the graph and then calculate it using the equation. Write your answer using proper function notation and write the explanation out in words.OLYMPIC SYSTEMS(***This assignment would be a continuation of the previous example.***)Using the Olympic event from the last assignment, use all of the years in common for the male or female. You should adjust your years so that you are starting with a zero. Make a scatter plot of your data using the Excel program. You should label each axis correctly and give the graph a title.You should display both the male and female linear regression equations. Make sure that you show the intersection of the two lines.Neatly explain what both rates of change mean.Calculate the point of intersection and explain what it means. Write the point of intersection using proper function notation.HERCULES AND THE TRIBBLES(***The “Hercules and the Hydra” reading should be included here as a separate file.***)1.Read the article posted on MathXL called “Hercules and the Hydra” section 2.1.1 and 2.2.1. Is this situation linear or exponential? Explain your reasoning. If Hercules worked for 30 minutes, how many heads would there be? Show your work.2.Watch the video at . Determine how many heads spring up when Hercules slices one head off. Find a point later in the clip where you can see the hydra with its many heads. Count how many heads you see at this point (you will probably have to pause the video to do this). Based on this situation, could Hercules have cut off enough heads to arrive at this count? Explain your reasoning with proper calculations.3.(*adapted from a worksheet at *)Tribbles are cute furry creatures that exist in the world of Star Trek. One tribble can produce 10 babies in 12 hours. One tribble was trapped in the grain hold of the starship Enterprise for 3 days. Spock claims that there are 1,771,561 tribbles at the end of the three days. Is Spock correct? Show your work or explain your reasoning. ZOMBIE APOCALYPSE(***I have to admit. This is one of my favorite assignments. So much for the students to do and explore on their own in a fun way.***)Each student needs to sign up for a country on the sign-up sheet in the room. First come, first served.Using the website sent to your email, look up the current country population for your country and the current growth rate.Zombies have invaded the United States and sadly, we didn’t put up much of a fight. The zombies are chasing you. You see a helicopter in the distance bound for safety. You and your band of zombie fighters have been able to leave for the country you chose.Unfortunately, you have accidentally transported some contaminated hot dogs with you and four members of your group have eaten them. Fortunately, you have noticed this in time and the rest of your party has captured these people before they have turned in to zombies and thrown them off of the plane before landing. You live happily in your new country for a year when you hear a sobering report. The original group of contaminated people that you have thrown from the plane has grown into twenty. The zombification is spreading although slowly. You feel pretty safe that it is contained for the moment, but are worried that it might eventually overwhelm the country.Create an Excel graph showing the exponential equation for your country and for the zombie growth next to it. Using the graph, estimate how many years it would take for the zombies to completely take over your country. Set up and solve your system of equations to calculate the exact answer. BUFFY THE VAMPIRE SLAYER(***This is part of the same assignment with the previous example.***)Read the article at the following website: sure you understand the article and the math involved. You were able to eliminate all of the zombies, but now find out you have a vampire in your country. Determine how long it would take for your country to become all vampires. Show all work. PAWN STARS1.A person walks into the Pawn Shop claiming to have a wooden chair that was used during the draft of the Constitution. After a C-14 test, you determine that there is still 98.2% of the C-14 left. Could this chair have come from the session where the Constitution was drafted? Show all work. 2.A person walks into the Pawn Shop claiming to have a wooden barrel that was brought to the United States with Christopher Columbus. After a C-14 test, you determine that there is still 93.879% of the C-14 left. Could this barrel have come from that trip? Show all work. 3.You need to choose four famous historical events / civilizations / persons. These items all need to be before 1950. For the event, come up with an object that could have come from that time related to the event itself. Calculate the amount of C-14 that should still be present in that item today. Come up with a small “pawn shop” story for each problem. Neatly write each story out. SIMPSONS MATHLisa Simpson puts $100 in the bank…“I got their new Thrifty Savers savings account, with 2.3% annual interest instead of the normal 2.25% so a year from now, I’ll have an extra $0.05.”Is she right? Show your work. BUY ME A CAR(***In this activity, I ask the students to pick a kind of car that I should buy. We Google it and find the price. I then tell them to pair up and they are my financial advisors. They need to determine the best way for me to finance this car. I give them Excel spreadsheets which can quickly calculate monthly payments using the two interest rate formulas. I don’t give them specific information. They need to figure out what questions to ask me (such as ‘how long do you want to finance this?’, ‘what kind of car will you trade in?’, ‘do you have a down-payment?’, etc.). We take about a half hour and I give full credit to the team who gives me the best finance plan.***)Participate in the class Car Buying Activity. CSI CASEAt the beginning of the next class, you will be given a sample CSI-related case. You may work with a partner if you want. You will need to use the skills learned in this class, your own imagination, and thinking ability to try and solve the case. Grades will be based on not only how correct you are on the case, but how well you organize your solutions and write up your “report” to turn in. Note: If you choose to work with a partner and I get the impression that one person is doing all of the work, I reserve the right to ask the other person to come to the front of the class to explain the answer to everyone. Therefore, make sure you are both working together if you choose to go that route.CASE #1—Calculator ConcussionFacts:Prof. Pat Riley was found dead in his office, beaten over the head with a graphing calculator. The front desk of the building his office is in has a camera that marked the times various students entered the building. All of the students have an obvious motive. Your job is to determine the time of death. Here is the information you have:Temperature in the room:75 degreesTemperature of the body when it was found:94.1degreesTemperature of the body 10 minutes later:93.8degreesFirst find the cooling rate and then use this information to estimate the time of death. The professor was found at 5pm. Be VERY careful with rounding off! Rounding off too much may miss the actual time of death. Case #2:Stop Thief!Facts:On Monday, September 28th, Ms. Fifi LaRue contacted authorities about possible abuse of her banking account. Her estranged husband, Dr. Leon LaRue, has apparently disappeared. Shortly after his disappearance, Ms. LaRue noticed that her savings account has been drained and closed. Apparently, due to carelessness on the part of the bank and clever scheming, Dr. LaRue used fake documents and an alias to retrieve the money. The Bank had a log of all of the savings account withdrawals from the day in question (Friday, September 28th). Ms. LaRue was not sure about the money that was in the account at the time. Here is what she remembers:Initial Deposit:$4500Interest Rate:Either 3.5% or 5.3%Length of Account:Either 4, 6 or 8 yearsCompounding:Either Continuously or QuarterlySince Ms. LaRue cannot be more specific, you need to calculate all possibilities for the amount that should have been in the account. Once you have this information, refer to the BANK LOG on the screen to determine the alias that Dr. LaRue used.BIG BANG THEORY MATHWatch the following clip from the TV show The Big Bang Theory this is a prime-time TV show, it is acceptable for a general audience, but I do give a caution that it is probably PG-13. In this clip, Leonard estimates the height of the elevator shaft. Determine whether his estimation was correct or not. Verify with the proper calculations.DROP DISTANCE COYOTE VIDEOYou need to work with a partner and get another person to help you. These people may be part of the class, but do not have to. If you work with a partner from the class, you will need to do this part twice….one for each person. You need to use your phone (or another video camera) to create a video where you demonstrate the falling object formula. You will need to drop something from a height over 6 feet outside and time how long it takes to hit the ground. You need to drop it five times and get an average of your times. Then from your average, you will need to calculate how high you dropped the item from. Your video also needs to include the written explanation of the actual answer. If you know how to properly email the video to me, you may. Otherwise, you can just show it to me either in my class or my office. Be creative and have fun!WILE E. COYOTE CARTOONYou have been hired as a story-writer for an episode of the Wile E. Coyote and Roadrunner cartoons. Your job is to write a segment of the cartoon which involves falling objects. Your cartoon needs to have two different examples of falling objects which use the quadratic formula. It needs to be two of the following three types:1.Something launched from a height to the ground2.Something launched from ground level up to a height3.Something launched from one height to another height (not ground level)Design the segment. Determine what will be launched into the air, from what level, ending on what level, what the initial velocity would be, and the story behind the falling object (ie how does it fit into the cartoon).The producers are looking for creative stories as well as ones that will reasonably fit into their cartoon based on the length of the clip, so you might want to know how long your part will run in the cartoon. They are also looking for realistic situations (time-wise) if possible. All times need to be between 5 and 15 seconds.For each situation, you need to calculate how long it will take for your object to fly from one place to the other. Show all the steps for all calculations.You will need to design a half poster with your story plot, a rough sketch of both situations, and the calculations neatly included.NERF DART GUNS(***I have purchased several Nerf Dart Guns to use in class. If you do not have the means for that, you would have to ask students to bring their own.***)Weather permitting, at the beginning of next class we will go outside. Students will be put into pairs. Each pair will be given a Nerf Dart Gun. They will shoot ten darts straight up into the air and time how long it takes to hit the ground. They will need to measure their initial height. When they get their 10 times, they will need to find the average. Use this as your value for time. Plug what you know into the falling object formula to solve for the initial velocity. Once you have done that, you will have enough information to be able to calculate the maximum height that the darts went into the air.Write up your calculations neatly to turn in. You will have a total of 15 minutes to do this activity, so the more prepared you come to class (i.e. the less you will have to refer to your notes), the better chance you will have for full credit.ROLLER COASTER(***This is not a very intensive assignment. It is mostly artsy and creative. For students not going into STEM fields, all I really think they need to know is what polynomials are and how to identify the end behavior. They would make the graph on Excel.***)You need to design a 500-foot straight stretch rollercoaster. Plan your rollercoaster by determining the height every 10 feet. Make sure your rollercoaster is reasonable (this will be a judgment call on my part). Make a sketch of your rollercoaster using the Excel program. Your roller coaster needs to be designed to fit a preferred theme. You need to list what the leading coefficient would be for your coaster. Display all of this information on a half poster. It needs to be very neat and organized. Any other material that doesn’t easily and neatly fit on the front should be neatly displayed on the back. DRAW AN ELLIPSEAt the beginning of class, students will be paired up to draw an ellipse. Students will be given the total length and width that the ellipse needs to be. They will need to determine how much string they will need. They will then take some chalk and go outside (weather permitting) and draw the ellipse on the sidewalk. They will need to determine where to put the focus points and then draw the ellipse.There will be a 15 minute time limit.Points will be based on accuracy of calculations. REAL LIFE PARABOLAFind an example of a parabola that you see in the real-word. Take a photo of it and copy the photo to a Word document. Measure the parabola to find the values needed to calculate where the focus is. Place the focus points in the proper place on the parabola. Show all steps.REAL LIFE ELLIPSEFind an example of an ellipse that you see in the real-word. Take a photo of it and copy the photo to a Word document. Measure the ellipse to determine the “a” and “b” values. Calculate the “c” value. Place the focus points in the proper place on the ellipse. MAKE ELLIPSE(***I usually cover this topic near the end of the course. If you have a “last day party” or something like that, this is good to have due that day as a lot of students make edible ellipses.***)You are going to make your own ellipse. Find a sheet of paper, poster board, wood, etc. that you want to make your ellipse on. Clearly mark where you want the two focus points to be on your material. Take a tack, nail, etc. and put one at each focus point. Using a string of some kind, cut a length of it (long enough to reach the two focus points and a little beyond) and attach it to each tack that you used. Stretch the string tight and trace out the boundary of the ellipse lightly. Once you are done, cut it out. Make sure you properly label the focus points, the measurement for ‘a’, ‘b’, and ‘c’. Find the eccentricity and write it somewhere on the ellipse. (*Ellipses made out of edible food can earn +5 extra points*) QUIDDITCH PITCH(***Once again, this is not a very intensive assignment. It is mostly artsy and creative. It gives students a good chance though to use computer technology to make geometric shapes and see how circles and ellipses can be used and made on the computer. I ask students to download Google Earth (free) at the beginning of the course.***)Quidditch is a sport created in the world of Harry Potter. It is played on an elliptical pitch that is 500 feet long and 180 feet wide. Hopkinsville has been granted a team provided that it can find a place to build a pitch and stands. You need to do the following:1.Open Google Earth and zoom in on the Hopkinsville and surrounding area.2.Under the VIEW menu, make sure SCALE LEGEND is checked.3.Scroll around the Hopkinsville area for a clear area to build a potential Quidditch pitch. You need to zoom in until the scale is as close as possible to 500 feet.4.When you get it to this level, use the Snipping Tool to make a copy of this screen. Make sure to include the SCALE LEGEND for verification. Copy this to a Word file. When you get it into Word, enlarge the picture so it fills the page. (*You may need to change to Landscape mode.*)5.Go to INSERT and choose the ELLIPSE (OVAL) shape. Using the SCALE LEGEND, draw your ellipse the length of the scale bar (close to 500 feet).6.180 feet is roughly one-third of the 500 foot distance. Measure about one-third of the scale bar (using a ruler) and stretch your ellipse to that length. This is the size of your Quidditch pitch.7.Rotate and move your shape to the appropriate place on your map.8.In order for people to be able to watch the Quidditch Pitch, you need to create stands. The stands must be circular around the Pitch with a radius of 300 feet. INSERT another oval shape. Stretch its width so the oval becomes circular and 300 feet in radius.9.Right-click on the circle and select FORMAT SHAPE. Change the TRANSPARENCY to 100%. Change the LINE STYLE to a width of 10.10.Move the Circular stands around your Quidditch Pitch. You may have to move the Quidditch Pitch around too in order to get both shapes to fit in your area.11.Print out a copy of this to turn in.12.Copy your Ellipse to another Word file. Expand it so it keeps its shape, but fills the screen. Measure the ellipse to determine the “a” and “b” values. Calculate the “c” value. Place the focus points in the proper place on the ellipse.DESIGN BALANCE BEAM(***Excel spreadsheet for this is saved as a separate file. I teach in a computer lab. If you do not have that luxury, you might ask students to bring laptops. Hopefully you can get at least one laptop for every two students. There is a “catch” to this. Students can make infinitely ‘thin’ beams and get the price down to almost zero. Obviously this is impractical in reality, but it is good to have students think about the relationship between the variables and discover this. It makes for good post-activity discussion. For grading purposes, I give students who realize this full credit, but then give the best “practical” solution top credit as well.***)Playing around with the Beam Spreadsheet to understand how the variables relate. Bringing a laptop to use during class or bringing a list of possible results to use.You may work with a partner on this activity if you choose. You will have to design a beam to be able to hold a certain weight. The weight carrying capacity of a rectangular beam varies directly with its width and the square of its height and inversely as its length.Using the ‘k’ value developed in class, you will be told how much weight your beam needs to hold and the minimum length and/or width for the top. You will have to find the dimensions of the beam that will meet these criteria. In addition, you know that the wood costs $0.05 per cubic inch. The team with the best value for the beam that meets the conditions will be “hired” and earn the full 10 points. Points for the rest of the class will be distributed in ratios based on the lowest cost.You are free to use any technology that you wish to use during the class activity provided that you and your partner work alone. You may bring your own laptop, calculators with programs, etc. You should check with me first to make sure that you aren’t violating the spirit of the assignment (i.e. you will be getting the answers from your own knowledge/effort). You will have 10 minutes to (a) determine the dimensions (b) minimize the cost and (c) prepare a well-written proposal to submit. PROJECTILE MOTION VIDEOYou need to work with a partner and get another person to help you. These people may be part of the class, but do not have to. You need to use your phone (or another video camera) to create a video where you demonstrate the falling object formula that is launched at an angle. You will need to launch/throw something in the air and (a) time how long it takes to hit the ground, (b) determine the angle it was launched at, (c) the height you launched it from, and (d) how far away from the launcher it landed. There are two projectile motion formulas:d = v0*t*cos(angle) (--where ‘d’ is the distance away from the launcher)andh = -16t2 + v0*t*sin(angle) + h0You need to use the first equation to calculate the initial velocity. Once you have that, you have the information to use in the second equation to calculate the highest point that the object was in the air.Perform these calculations and determine the highest the object was in the air. Show all work.If you know how to properly email the video to me, you may. Otherwise, you can just show it to me either in my class or my office. Be creative and have fun! ................
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