Selected Response Item - Released in 2004 |
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| The table below lists the names most frequently given to boys born in Hollister
City during the year 2000.
Mary concludes that 20% of the boys born in Hollister City during 2000 were named Timothy. Why is Mary's conclusion incorrect? |
- Mary did not consider the top five names for girls.
- Mary did not consider the entire population of the United States.
- Mary did not consider the names most frequently given to boys in other years.
- Mary did not consider that there were other names given to boys born in the
year 2000.
/share/clg/xml/public_release/mathematics/2004_323_alg07.xml |
Correct Answer:
D
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Selected Response Item - Released in 2001 |
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| Ms. Madison, a dance teacher, wants to know if students would go to an
after-school dance. According to simple random sampling principles, which
of these is the best method to survey students about the dance? |
- Ask 50 girls to complete a survey.
- Ask 50 students who attended the last dance.
- Ask 50 randomly selected students from her classes.
- Ask 50 randomly selected students from the school.
/share/clg/xml/public_release/mathematics/2001_323_alg41.xml |
Correct Answer:
D
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Extended Constructed Response (ECR) Item - Released in 2001 |
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A movie producer is considering two different endings for a movie. To decide
which ending is better, the producer randomly selected two groups of people to
watch each ending. There were 200 people in each group. The two groups rated
the movie endings on a scale of 1 to 100. The box-and-whisker plots below show
a summary of their results.
Complete the following in the answer box:
- Which ending had a higher median rating? Use mathematics to justify
your answer.
- Which ending had a wider range of ratings? Use mathematics to justify
your answer.
- Based on the data shown in the box-and-whisker plots, the movie producer
decided that the first ending was better than the second ending. Is this a
valid conclusion to make from the data given? Use mathematics to justify
your answer.
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/share/clg/xml/public_release/mathematics/2001_323_alg49.xml |
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Selected Response Item - Released in 2005 |
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Wendy asked 40 students on the school football team if they have ever injured themselves playing sports. Fifteen football team members responded "Yes." Wendy concluded that 375 of the 1,000 students in her school have injured themselves playing sports. Which of these explains why her conclusion is invalid?
- computation is incorrect
- sample size is too large
- sample is biased
- sample is random
/share/clg/xml/public_release/mathematics/2005_323_alg17.xml |
Correct Answer:
C
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Extended Constructed Response (ECR) Item - Released in 2005 |
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Paul asked 50 randomly selected eleventh-grade students to choose their favorite candidate for class president. The survey results are shown in the table below.
Complete the following in the Answer Book:
- There are 300 eleventh-grade students at Paul's school. Based on the survey results, how many votes will Marie expect to receive? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.
- Using the survey results, Paul claims that Bertha will receive 2 more votes than Nick in the election. Is Paul correct? Use mathematics to justify your answer.
- Loren asked the same question in another survey. She asked 50 randomly selected eleventh-grade chorus students to choose their favorite candidate for class president. Will you expect Loren's survey or Paul's survey to give more reliable results? Use mathematics to justify your answer.
/share/clg/xml/public_release/mathematics/2005_323_alg30.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_323_alg36.xml |
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Extended Constructed Response (ECR) Item - Released in 2003 |
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Juan conducted two different surveys about student transportation to school. For Survey A, he stood at the entrance of the school at 7:30 a.m. and surveyed the first 80 students. For Survey B, he used a random number generator to select 80 students in the school to survey. His results are shown in the tables below.
Complete the following in the answer box below:
- Use principles of simple random sampling to justify why Juan should have more confidence in the results of Survey B.
- Use principles of simple random sampling to justify why Juan should have less confidence in the results of Survey A.
- According to the data collected from Survey B, of the 400 total students in the school, how many students should Juan expect to ride a bike? 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_323_alg21.xml |
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Selected Response Item - Released in 2003 |
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| Monique found that 90% of the students in her computer applications class have computers at home. She then predicted that since there are 800 students in her school, about 720 of them have computers in their homes. Which of these best describes the reason that her prediction is not valid? |
- use of opinion to influence a prediction
- incorrect arithmetic computation
- inappropriate use of mean
- biased sampling
/share/clg/xml/public_release/mathematics/2003_323_alg34.xml |
Correct Answer:
D
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Extended Constructed Response (ECR) Item - Released in 2004 |
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A city bus company requires exact change or a token to ride a bus. The company
conducted a random survey of 100 passengers to determine how they paid their bus
fare. The survey results are shown in the table below.
Complete the following in the answer box below:
- Last week 2,000 passengers rode the bus. Based on this survey, how many of
these passengers would be expected to use exact change to pay the bus fare? Use
mathematics to explain how you determined your answer. Use words, symbols,
or both in your explanation.
- Mr. Blake, a bus driver for the city bus company, reported that 44 passengers
who rode on his bus one morning paid using a token. Based on this survey,
estimate how many passengers rode on his bus that morning. Use mathematics
to explain how you determined your answer. Use words, symbols, or both in
your explanation.
- Should a different city use these survey results to predict the number of bus
passengers that would be expected to use exact change to ride the bus in their
city? Use mathematics to justify your answer.
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/share/clg/xml/public_release/mathematics/2004_323_alg11.xml |
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Selected Response Item - Released in 2002 |
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| The graphs below show the number of residents in Town A and Town B from the years 1982 to 1988. The two towns have comparable populations. The mayor of Town B uses the graphs to claim that there was a larger increase in the number of residents in Town B than in Town A from the years 1982 to 1988.
 
According to the information given, which of these explains why the graphs are misleading?
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- The time periods are different.
- The types of data are different.
- The vertical scales are different.
- The population of the towns are different.
/share/clg/xml/public_release/mathematics/2002_323_alg19.xml |
Correct Answer:
C
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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_323_alg24.xml |
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Selected Response Item - Released in 2006 |
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The 12th-grade class is conducting a survey to determine music preferences for the spring dance. The class decides to survey the first 150 students that enter the school on Monday. Which of these best describes why this type of sampling may give biased results?
- The sample size is too small.
- Students are randomly selected.
- Not all students have the same chance to be surveyed.
- Every other student entering the school should be surveyed.
/share/clg/xml/public_release/mathematics/2006_323_alg05.xml |
Correct Answer:
C
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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_323_alg12.xml |
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Selected Response Item - Released in 2007 |
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Fred wants to determine the mean hourly wage of the working students at his school. He asks thirty of his friends their hourly wage and calculates the sample mean to be $6. Which of these statements must be true?
- The sample was selected randomly.
- Bias was present in the selection process.
- The sample was representative of the population.
- The mean hourly wage of the working students at Fred's school was $6.
/share/clg/xml/public_release/mathematics/2007_323_alg19.xml |
Correct Answer:
B
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