the speeding ticket - sfusd mathematics · performance task the speeding ticket test 9 p 7"...
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Performance Task The Speeding Ticket Test 9 P 7"©"Silicon"Valley"Mathematics"Initiative"2013.""To"reproduce"this"document,"permission"must"be"granted"by"the"SVMI"[email protected]""
The Speeding Ticket Assessment Task
1. How far will the speeding car travel in one minute?
___________________ Show how you figured it out.
2. The next exit is 3.4 miles ahead. How much time will it take for the car to reach the exit?
___________________________ Show how you figured it out.
A traffic officer is monitoring traffic on a windy section of road that has a speed limit of 55 miles per hour. A car speeds past the officer and the radar gun indicates the car is traveling 68 miles per hour.
Performance Task The Speeding Ticket Test 9 P 8"©"Silicon"Valley"Mathematics"Initiative"2013.""To"reproduce"this"document,"permission"must"be"granted"by"the"SVMI"[email protected]""
The officer tries to start her motorcycle, but it won’t start. Thirty seconds later the motorcycle starts and the officer begins to pursue the speeder.
3. If t is the time the speeding car has traveled since passing the officer, write an expression to show the time the chasing officer has been traveling.
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4. What speed will the officer have to average if she is to catch-up to the speeding car before the exit?
_______________________________________ Show how you figured it out.
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Distance Versus Time
MAC Test 8 Distance Versus Time Page 9 © SVMI 2017. To reproduce this document, permission must be granted by the Silicon Valley Mathematics Initiative [email protected]
Steph and Draymond like to take different trips traveling across their hometown on foot. 1. Draymond was gone for 6 hours. He walked half the time and then rested for the same
amount of time. Sketch a graph to show the distance – time graph of his journey.
2. Steph traveled a distance of 20 miles. He ran at a fast pace for half the distance and then
walked at a pace twice as slow as he ran for the remaining half of the distance. Sketch a graph to show the distance – time graph of his journey.
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MAC Test 8 Distance Versus Time Page 10 © SVMI 2017. To reproduce this document, permission must be granted by the Silicon Valley Mathematics Initiative [email protected]
Steph and Draymond took a different trip. Below is a graph of the trip. Draymond’s trip is represented by the solid line and Steph’s trip is represented by the dotted line. 3. Explain what happened on this trip. Be sure to describe how it started, how it ended and
what happened in the middle of the trip. ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ On a new trip, they started in Rockridge and ended at Bayfair on foot. Draymond walked half the distance and ran half the distance. Steph ran half the time and walked half the time. They started at the same time, and walked at the same speed as each other and ran at the same speed as each other. 4. Who arrived first? ______________________________________ Show how you figured it out.
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Transforming Triangles
MAC Test 8 Transforming Triangles Page 9 © SVMI 2016. To reproduce this document, permission must be granted by the Silicon Valley Mathematics Initiative [email protected]
Antoinette is playing with a triangle (∆ABC) on this grid below.
1. What are the coordinates of Antoinette’s triangle (∆ABC)?
_________________________________________________________________
2. WhatisthelengthoflinesegmentAC?______________________units
Showhowyoufigureditout.
A
B C
MAC Test 8 Transforming Triangles Page 10 © SVMI 2016. To reproduce this document, permission must be granted by the Silicon Valley Mathematics Initiative [email protected]
Antoinettereflectedtriangle∆ABCoverthelinex=4.
3. Draw the reflected image on the same coordinate plane. Label the new triangle ∆DEF, where A maps to D, B maps to E and C maps to F.
Write the coordinates of the points D, E and F.
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Antoinettetranslatedtriangle∆ABC3unitstotherighthorizontallyand1unitupvertically.
4. Draw the translated image on the same coordinate plane. Label the new triangle ∆GHI, where A maps to G, B maps to H and C maps to I.
Antoinetterotatedtriangle∆ABC180ºaroundthepoint(3,3).
5. Drawtherotatedimageonthesamecoordinateplane.Labelthenewtriangle∆XYZ,whereAmapstoX,BmapstoYandCmapstoZ.Explainwhyreflectingtriangle∆ABCoverthelineACdoesNOTmapontotriangle∆XYZ.
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Course 1 Performance Test Spring 2012 (c) Silicon Valley Mathematics Initiative 2011. To reproduce this document, permission must be granted by the SVMI [email protected]
You are researching the relationship between the amount of time people surf movie and music sites on the Internet and how much they spend. Below is a graph of a study you found.
Internet Surfing for Media
DOLLARS SPENT
HOURS SPENT SHOPPING ONLINE
Performance*Task*
Media!Surfing!
Course 1 Performance Test Spring 2012 (c) Silicon Valley Mathematics Initiative 2011. To reproduce this document, permission must be granted by the SVMI [email protected]
1. What was the most money anyone spent? ______________________ How many hours did they spend shopping on line? _____________________. Circle the point you are referring to on the graph.
2. Draw a line that best fits the data set on the graph. 3. Approximate the amount of money people spend when they shop for 7 hours. Explain your
answer. 4. A person not in the study spent $55 shopping on these music and video websites. Estimate
the number of hours they probably spent shopping. Explain how you determined your answer.
5. What is the relationship between the two variables in this study?
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Sports Medicine Storage
MAC Algebra 1 Test Sports Medicine Storage Page 5 © SVMI 2017. To reproduce this document, permission must be granted by the Silicon Valley Mathematics Initiative [email protected]
You are a teacher’s assistant for the Athletic Trainer at your school. The training room needs cleaning up because of all the new training equipment and supplies your Athletic Trainer has acquired. You need to buy some cabinets for the room. You look at two different brands. You know that the Trainer’s Closet cabinet costs $10 per cabinet. The Medicine Chest cabinet costs $20 per cabinet. You have been given $140 for this purchase, though you don't have to spend that much. Your job is to research the numbers of each type of cabinets you should buy, in order to maximize storage volume and stay under the total cost and space restrictions. Let x be the number of Trainer’s Closet cabinets. 1. Write an expression to show what it would cost to buy x number of Trainer’s Closet
cabinets. _______________________________________________________________________ Let y be the number of Medicine Chest cabinets.
2. Write an inequality to show that the amount you can spend on the two types of cabinets
is less than or equal to the total money you have for this purchase.
_______________________________________________________________________ 3. Sketch a graph of the inequality of the amount you spend on the two cabinets.
MAC Algebra 1 Test Sports Medicine Storage Page 6 © SVMI 2017. To reproduce this document, permission must be granted by the Silicon Valley Mathematics Initiative [email protected]
Now that you have an equation for the total costs of the two types of cabinets, you are considering the amount of space needed in your training room for the cabinets. You would like the cabinets to fit in an area of no more than 72 square feet. The Trainer’s Closet cabinet requires six square feet of floor space. The Medicine Chest cabinet requires eight square feet of floor space. 4. Write an inequality to represent the space the two cabinets would require.
____________________________________________________________________
5. On the same axis, sketch a graph of the inequality that represents the space the two
types of cabinets would require.
6. What are the coordinates of the intersection of those two lines? _________________
Show how you figured it out. Remember, the goal of your job is to maximize the volume of storage space and stay under the total cost and space restrictions. The Trainer’s Closet cabinet holds eight cubic feet of sports medicine supplies. The Medicine Chest cabinet holds twelve cubic feet of sports medicine supplies. 7. If you selected the optimum numbers of each type of cabinet for the training room,
what would the total storage volume of the cabinets be? __________________ cubic feet
Show how you figured it out.
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MAC Test Algebra Linda’s Tiles Page 3 © SVMI 2016. To reproduce this document, permission must be granted by the Silicon Valley Mathematics Initiative [email protected]
Linda’s Tiles Linda has taken up ceramics. She has created tile patterns with light and dark tiles. The first tile pattern she made is shown below:
1. How many light and dark tiles wide is the pattern?________________ tile(s)
Linda makes the next bigger pattern below:
2. How many total light and dark tiles appear in Linda’s second pattern?
______________________tile(s)
Linda decided she wants to make a tile pattern, using the same structure as the first two she built, but smaller than her first tile pattern. She labels this pattern Zero Tile Pattern.
3. How many tiles would be in Zero Tile Pattern?
___________________________tile(s) Explain how you figured it out.
___________________________________________________________________
___________________________________________________________________
Linda’s First Tile Pattern
Linda’s Second Tile Pattern
MAC Test Algebra Linda’s Tiles Page 4 © SVMI 2016. To reproduce this document, permission must be granted by the Silicon Valley Mathematics Initiative [email protected]
Linda continues to build a third, fourth and fifth tile pattern.
4. How many total light and dark tiles are in the fifth pattern?
_____________________ tile(s) Show how you figured it out.
5. Linda continues to build larger tile patterns with the same structure. Write a function f(x), to determine the total number of light and dark tiles in the xth pattern. _________________________________________________________________
Explain how you know your function is correct. ________________________________________________________________ _________________________________________________________________ _________________________________________________________________
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Exponents and Rectangles
MAC Algebra 1 Test Exponents and Rectangles Page 9 © SVMI 2017. To reproduce this document, permission must be granted by the Silicon Valley Mathematics Initiative [email protected]
Janice and Janet are making sense of algebraic expressions with exponents. Janice draws the following figure, comprised of four small rectangles inside a big rectangle. Janice said, “The length of this big rectangle is x + 3 and the width is x + 2.” She asked Janet, “What is the perimeter of the big rectangle?” 1. What answer should Janet give? ________________________________ units Janet then asks Janice, “What is the area of the big rectangle?” 2. What answer should Janice give? _____________________________ sq. units
Show how you figured it out.
Janice now asks a new question, “A different big rectangle has an area of x2 + 7x + 12. What does it look like?” 3. Draw this new big rectangle and label the dimensions of the four smaller rectangles
contained in the big rectangle.
x
2
x 3
MAC Algebra 1 Test Exponents and Rectangles Page 10 © SVMI 2017. To reproduce this document, permission must be granted by the Silicon Valley Mathematics Initiative [email protected]
Janet says, “What if we combined the areas of these two big rectangles into an even bigger rectangle. What would be the area of the new bigger rectangle be?” 4. What answer should Janice give? ____________________________________
Show how you figured it out.
5. Draw a rectangle that would have the new area of this bigger rectangle and label the dimensions of the four smaller rectangles that comprise it.
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Performance Task Consuelo’s Graph Test 9 P 9"©"Silicon"Valley"Mathematics"Initiative"2013.""To"reproduce"this"document,"permission"must"be"granted"by"the"SVMI"[email protected]""
Consuelo’s Graph Assessment Task
Melissa helps Consuelo work on a math problem involving a parabola. They examine the graph below.
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1. What are the coordinates of the vertex point? _____________________
Performance Task Consuelo’s Graph Test 9 P 10"©"Silicon"Valley"Mathematics"Initiative"2013.""To"reproduce"this"document,"permission"must"be"granted"by"the"SVMI"[email protected]""
2. List the zeros of the parabola. _____________________________________
Explain how you know the zeros.
3. Write a function of the parabola. __________________________________
Melissa writes the following function, y = -2x - 1
4. Draw a graph of Melissa's function on the same coordinate axes.
5. Consuelo wants to find where the line and parabola intersect. Determine the points of intersection of the two functions.
___________________________________________
Show how you figured it out.
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Microorganisms
MAC Algebra 1 Test Microorganisms Page 3 © SVMI 2017. To reproduce this document, permission must be granted by the Silicon Valley Mathematics Initiative [email protected]
Amari is studying three different microorganisms in biology. Amari has put each microorganism on a separate Petri dish labeled A, B and C. Each day he looks through a microscope and counts the number of microorganisms on each dish. He made a table of the numbers of microorganisms he counts on each dish.
Microorganisms Dish/Day Day 1 Day 2 Day 3 Day 4 Dish A 6 6 6 6 Dish B 1 7 13 19 Dish C 1 3 6 10
Assume the microorganisms continue to grow at the same rate from day to day.
1. How many microorganisms will be on Dish A on Day 5?
_______________________ microorganisms
2. On the coordinate plane, sketch a graph of the three functions: the function of the number of microorganisms on Dish A, the function of the number of microorganisms on Dish B, and the function of the number of microorganisms on Dish C. Label each function.
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MAC Algebra 1 Test Microorganisms Page 4 © SVMI 2017. To reproduce this document, permission must be granted by the Silicon Valley Mathematics Initiative [email protected]
3. At what point(s) do the Dish B and Dish C functions intersect?
_____________________________________________________________________
Explain the meaning of the point(s) of intersection in the context of the situation.
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4. On Dish B, how many microorganisms appear on Day 8?
_______________________ microorganisms
Show your work.
5. Write a function to determine the number of microorganisms on Dish B for any given day, where x is the day number.
_____________________________________________________________________
6. Write a function to determine the number of microorganisms on Dish C for any
given day. Write the function of x, where x is the day number.
________________________________________________________________________________
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