Extended Constructed Response (ECR) Item - Released in 2004 |
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Students in a nutrition class decide to sell orange juice at their school's next sports
event. To determine the price, the students record prices of orange juice from
various stores in their city. The table below shows the price of different-sized
bottles of juice.
Complete the following in the answer box below:
- Write an equation for a line of best fit. (If you choose to draw a graph, use the
grid provided in the Answer Book.)
- What is the slope of your equation? What does the slope mean in the context of
this problem?
- The students are selling 8-ounce bottles of orange juice. According to your line
of best fit, what is the price of an 8-ounce bottle of juice? Use mathematics to
explain how you determined your answer. Use words, symbols, or both in your
explanation.
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/share/clg/xml/public_release/mathematics/2004_322_alg27.xml |
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Brief Constructed Response (BCR) Item - Released in 2001 |
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Wind makes the air feel colder than the actual temperature. This is called wind
chill. The graph below shows the wind-chill temperatures for various wind
speeds when the actual air temperature is 8° Celsius. A curve of best fit has
been drawn.
Complete the following in the answer box below:
- For what wind speed is the wind-chill temperature 0° Celsius? Use
mathematics to explain how you determined your answer. Use words,
symbols, or both in your explanation. You may need to provide additional calculations on a separate sheet of paper.
- Use the graph to explain how the wind-chill temperature changes in
comparison to the wind speed. Include an estimate of when the effect of
the wind levels off.
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/share/clg/xml/public_release/mathematics/2001_322_alg10.xml |
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Selected Response Item - Released in 2001 |
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The scatter plot below shows the relationship between the number of bags of popcorn that are sold and the price per bag.
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- Graph A
- Graph B
- Graph C
- Graph D
/share/clg/xml/public_release/mathematics/2001_322_alg13.xml |
Correct Answer:
B
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Brief Constructed Response (BCR) Item - Released in 2001 |
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The table below shows the distances, in miles, and the lowest-priced airfares,
in dollars, of flights from Baltimore to various destinations.
The data from the table is graphed on the scatter plot below.
Complete the following in the answer box below:
- Write an equation for a line of best fit that can represent the relationship between the distance (d) traveled and the lowest-priced airfare (f).
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Graph the equation for your line of best fit on a scatter plot.
- According to your equation, what is the cost of a plane ticket to Orlando, which is 790 miles from Baltimore? Use mathematics to justify your answer.
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/share/clg/xml/public_release/mathematics/2001_322_alg30.xml |
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Selected Response Item - Released in 2005 |
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The graph below models the relationship between light intensity and the distance from a light source.
Which of these is the best estimate of the intensity, in milliwatts per square centimeter, of light 2 meters from the source?
- 0.015
- 0.181
- 1.520
- 1.720
/share/clg/xml/public_release/mathematics/2005_322_alg29.xml |
Correct Answer:
A
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Selected Response Item - Released in 2002 |
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| The table below shows the consumption of bottled water per person for the years 1980 through 1995.
Which of these lines best models the data? |
/share/clg/xml/public_release/mathematics/2002_322_alg11.xml |
Correct Answer:
B
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Brief Constructed Response (BCR) Item - Released in 2002 |
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| The table below shows the sales for a greeting card company for the years 1990 through 1998.
Complete the following in the answer box below:
- Write an equation for the line of best fit for this data. Let x represent the years since 1900 and y represent the sales, in thousands of dollars.
(If you choose to draw a graph, you should do so on a separate sheet of graph paper.)
- According to your equation, what were the sales in 1999? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.
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/share/clg/xml/public_release/mathematics/2002_322_alg12.xml |
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Extended Constructed Response (ECR) Item - Released in 2002 |
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| The scatter plot below shows the average family size for the years 1972 through 1996. A curve of best fit has been drawn.
Complete the following in the answer box below:
- Describe the changes in family size that are indicated by the graph for the years 1972 through 1996.
- According to the curve of best fit, what is the average family size in 1998? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.
- Would it be reasonable to use this curve of best fit to predict the average family size for 2010? Use mathematics to justify your answer.
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/share/clg/xml/public_release/mathematics/2002_322_alg36.xml |
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Brief Constructed Response (BCR) Item - Released in 2005 |
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A tire company wants to determine how quickly the tread on its tires wears down with average use. Let x represent the number of months the tire was used. Let y represent the thickness of the tire tread, in millimeters. An equation for a line of best fit is shown below.
Complete the following in the Answer Book:
- What is the slope of this line of best fit? What does the slope mean in the context of this problem?
- What is the y-intercept of this line of best fit? What does the y-intercept mean in the context of this problem?
- Tina will need to replace her new tires when they have 5 millimeters of tire tread left. According to the line of best fit, for how many months can Tina drive before she needs to replace her tires? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.
/share/clg/xml/public_release/mathematics/2005_322_alg16.xml |
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Selected Response Item - Released in 2003 |
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| The graph below shows the population growth for the United States since 1800. A curve of best fit has been drawn.
According to the curve of best fit, in what year will the population be 300 million? |
- 2000
- 2024
- 2031
- 2050
/share/clg/xml/public_release/mathematics/2003_322_alg24.xml |
Correct Answer:
B
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Brief Constructed Response (BCR) Item - Released in 2003 |
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Mike wants to know how many calories he can burn while jogging. The number of calories burned depends on the length of time Mike jogs. The table below shows the number of calories Mike burns while jogging.
Complete the following in the answer box below, and/or on a piece of paper.
- Write an equation for a line of best fit. (If you choose to draw a graph, use the grid provided in the Answer Book.)
- What is the slope of your line of best fit? What does the slope mean in the context of this problem?
- Mike jogged for 60 minutes. According to your line of best fit, how many calories did he burn? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.
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/share/clg/xml/public_release/mathematics/2003_322_alg30.xml |
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Selected Response Item - Released in 2004 |
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| The graph below relates the length
and weight of fish found in Lake
Opinicon.
Using the curve of best fit, what
would be the expected weight of a
fish that is 14.5 inches long?
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- 1.5 pounds
- 1.7 pounds
- 1.8 pounds
- 1.9 pounds
/share/clg/xml/public_release/mathematics/2004_322_alg18.xml |
Correct Answer:
B
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Selected Response Item - Released in 2006 |
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The graph below shows the percentage of television-owning households with cable television. The line of best fit is drawn.
Using the line of best fit, what percentage of television-owning households can be expected to have cable television in the year 2000?
- 69%
- 71%
- 72%
- 73%
/share/clg/xml/public_release/mathematics/2006_322_alg03.xml |
Correct Answer:
C
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Brief Constructed Response (BCR) Item - Released in 2006 |
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Erin used the equation below to model the price (y) of postage stamps,
in cents, between 1950 and 1995. In Erin's model, x represents the number of
years since 1950.
y = 0.014x² + 0.09x + 1.28
The graph below models the price of postage stamps, in cents, between
1950 and 1995.
Complete the following in the Answer Book:
- According to the model, when was the price of a postage stamp 29¢? Use
mathematics to explain how you determined your answer. Use words, symbols,
or both in your explanation.
- According to the model, what was the cost of postage stamps in 1970? Express your answer to the nearest cent. Use mathematics to explain how you
determined your answer. Use words, symbols, or both in your explanation.
/share/clg/xml/public_release/mathematics/2006_322_alg16.xml |
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Extended Constructed Response (ECR) Item - Released in 2006 |
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The table below shows the relationship between the average temperature in March
and the date in April when the cherry trees bloom in Washington, D.C.
Complete the following in the Answer Book:
(If you choose to draw a graph to help write the equation, use the grid provided in
the Answer Book.)
- Write an equation of a line of best fit for the data.
- According to your equation, what would be the date in April of the bloom if the average March temperature were 3.5°C? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.
- Suppose the average March temperature is 14°C. Is it appropriate to use your equation to predict the date in April when the cherry trees will bloom in Washington, D.C.? Use mathematics to justify your answer.
/share/clg/xml/public_release/mathematics/2006_322_alg24.xml |
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Brief Constructed Response (BCR) Item - Released in 2007 |
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The graph below shows the height of a ball in one-second intervals. The curve of best fit has been drawn.
Complete the following in the Answer Book:
- According to the curve of best fit, what is the height of the ball at 4.5 seconds? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.
- According to the curve of best fit, when will the ball be at a height of 100 feet? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.
/share/clg/xml/public_release/mathematics/2007_322_alg06.xml |
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Extended Constructed Response (ECR) Item - Released in 2007 |
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The table below shows the age and the value of a computer.
Complete the following in the Answer Book:
- Write an equation for a line of best fit. (If you choose to draw a graph to help you write the equation, use the grid provided in the Answer Book.)
- What is the slope of your equation? What does the slope represent in the context of this problem?
- What is the age of the computer when its value is $300? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.
- Will your equation remain a good model to predict the value of a computer when it is 6 years old? Use mathematics to justify your answer.
/share/clg/xml/public_release/mathematics/2007_322_alg12.xml |
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Selected Response Item - Released in 2007 |
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The scatter plot below shows the relationship between the age and value of Judy’s car. A curve of best fit has been drawn.
According to the curve of best fit, how much would Judy’s car have decreased in value when the car is 6 years old?
- $4,000
- $6,000
- $16,000
- $20,000
/share/clg/xml/public_release/mathematics/2007_322_alg21.xml |
Correct Answer:
C
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