RELEASE ITEMS by Indicator - GOAL 3

 

From: http://www.mdk12.org/instruction/clg/algebra_data_analysis/goal3.html

 

Contents:

Expectation 3.1.1 - design/collect investigation using stat methods to analyze and communicate

Expectation 3.1.2 - use measures of central tendency and/or variability to make informed conclusions

Expectation 3.1.3 - calculate theoretical probability or use simulations or statistical inference from data to estimate the probability of an event

Expectation 3.2.1 - will make informed decisions and predictions based upon the results of simulations and data from research

Expectation 3.2.2 - misuse of statistics

 

EXPECTATION 3.1.1

 

Goal 3 Data Analysis And Probability

 

Expectation 3.1 The student will collect, organize, analyze, and present data.

 

Indicator 3.1.1 The student will design and/or conduct an investigation that uses statistical methods to analyze data and communicate results.

 

Assessment Limits:

The student will design investigations stating how data will be collected and justify the method.

Types of investigations may include: simple random sampling, representative sampling, and probability simulations.

Probability simulations may include the use of spinners, number cubes, or random number generators.

In simple random sampling each member of the population is equally likely to be chosen and the members of the sample are chosen independently of each other. Sample size will be given for these investigations.

  1. Brief Constructed Response (BCR) Item - Released in 2001

The administration of Central High School has decided to add a new sport for next year's ninth-grade girls. They are considering adding either soccer, tennis, or track. The administration needs to design an investigation in which 30 ninth-grade girls are surveyed to decide which new sport next year's ninth-grade girls would prefer.

Complete the following in the answer box below:

  • Based on simple random sample principles, explain at least two of the key elements that should be part of the administration's design.

/share/clg/xml/public_release/mathematics/2001_311_alg29.xml
  1. Brief Constructed Response (BCR) Item - Released in 2002

Apples from an orchard need to be sampled to see if they are sweet enough for juice. The orchard has 25,000 apple trees. Each tree has at least 1,000 apples.

Alfred suggests, “Randomly choose one tree and test 500 apples from that tree.”

Betsy suggests, “Randomly choose 1,000 trees and test one apple from each tree.”

Complete the following in the answer box below:

  • Whose suggestion gives a sample that is more representative of the apples in the orchard? Use mathematics to justify your answer.

/share/clg/xml/public_release/mathematics/2002_311_alg22.xml
  1. Brief Constructed Response (BCR) Item - Released in 2003

The Knitwear Company wants to know what sock colors teenagers will buy. The company is considering the three options below for collecting data.

Option 1:     

Spend five days in the sock department of a randomly selected store and ask every person who enters what color socks they buy.

Option 2:     

Spend one day in the sock departments of five randomly selected stores in randomly selected cities and ask every teenager who enters what color socks they buy.

Option 3:     

Spend one day in eight randomly selected shopping centers and ask ten randomly selected teenagers at each shopping center what color socks they buy.

Complete the following in the answer box below:

  • Which option gives the company the most representative sample of sock colors that teenagers will buy?
  • Use mathematics to justify why the other two options do not give the company the most representative sample.

/share/clg/xml/public_release/mathematics/2003_311_alg06.xml
  1. Selected Response Item - Released in 2005

Steve is a member of the baseball team. He averages 2 hits for every 5 times at bat. Steve might get a hit his next time at bat. Which of these methods could not be used to simulate this situation?
  1. Flip a fair coin once. Let heads represent a hit and let tails represent not getting a hit.
  2. Use a random number generator. Let 1 and 5 represent a hit and let 2, 3, and 4 represent not getting a hit.
  3. Spin a spinner with 10 equally-sized sections. Let 4 sections represent getting a hit and let 6 sections represent not getting a hit.
  4. Draw a marble from a bag that contains 8 red and 12 blue marbles. Let a red marble represent getting a hit and let a blue marble represent not getting a hit.

/share/clg/xml/public_release/mathematics/2005_311_alg27.xml

Correct Answer:
A
  1. Brief Constructed Response (BCR) Item - Released in 2005

A high school principal is meeting with the PTA to discuss the amount of time students spend doing homework each day. He asked a teacher to gather data for the parents. The teacher is going to survey 25 students from a student body of 1,000 students. Consider the methods of sampling shown below.

Method 1: randomly select 25 students from honors classes

Method 2: select 25 members of the girls' varsity softball team at random

Method 3: use a random number generator to generate 25 random numbers and use these to select 25 students from a numerical list of the students

Method 4: randomly select 25 classrooms and ask the teacher in each classroom to select a student

Complete the following in the answer box below:

  • Which of the above methods of sampling would give the most representative random sample of the student population? Use mathematics to justify your answer. Include in your justification why you chose that method and why you did not choose each of the other three methods.
     

/share/clg/xml/public_release/mathematics/2005_311_alg35.xml
  1. Selected Response Item - Released in 2003

A teacher conducts a random survey to determine how many students use the school library on a regular basis. Which of these methods would provide the teacher with a simple random sample?
  1. Choose every 3rd student that enters the library on Monday.
  2. Select 50 students from the list of students who have perfect attendance.
  3. Choose the name of every 10th student in her grade book until 30 names are selected.
  4. Number every student in the school and then generate random numbers to select 50 students.

/share/clg/xml/public_release/mathematics/2003_311_alg23.xml

Correct Answer:
D
  1. Brief Constructed Response (BCR) Item - Released in 2006

A cereal company awards a prize to anyone who collects all 5 different game pieces. Each game piece has an equal chance of being placed in a box of cereal. Each box of cereal contains only 1 game piece.

Complete the following in the Answer Book:

  • Design a simulation of at least 30 trials that can be used to estimate how many boxes of cereal a person needs to buy to collect all 5 different game pieces. Describe how to collect and interpret the data so that you have confidence in the estimation.

/share/clg/xml/public_release/mathematics/2006_311_alg06.xml
  1. Selected Response Item - Released in 2006

Inés wants to conduct a survey to determine how many customers see the advertisement for her store. Which of these methods provides Inés with the most representative sample of her customers?

  1. Survey customers who live near her store.
  2. Survey customers who shop at her store on weekends.
  3. Survey customers who shop at her store early in the morning.
  4. Survey customers who shop at her store at different times throughout the week.

/share/clg/xml/public_release/mathematics/2006_311_alg30.xml

Correct Answer:
D

 

 

 

EXPECTATION 3.1.2

 

Goal 3 Data Analysis And Probability

 

Expectation 3.1 The student will collect, organize, analyze, and present data.

 

Indicator 3.1.2 The student will use the measures of central tendency and/or variability to make informed conclusions.

 

Assessment Limits:

o                                            Measures of central tendency include mean, median, and mode.

o                                            Measures of variability include range, interquartile range, and quartiles.

o                                            Data may be displayed in a variety of representations which may include: frequency tables, box and whisker plots, and other displays.

Selected Response Item - Released in 2001

Each year Ms. Fong, a physics teacher, has her students build bridges out of toothpicks. Last year Ms. Fong recorded the number of toothpicks that 20 of her students used. Her list is shown below.

Ms. Fong will use the mode of this data set to determine the number of toothpicks needed for each student this year. How many toothpicks will be needed for each student?
  1. 147
  2. 150
  3. 157
  4. 200

/share/clg/xml/public_release/mathematics/2001_312_alg17.xml

Correct Answer:
C

Selected Response Item - Released in 2001

A businesswoman calculates that the median cost of her five business trips last month was $600. Which of these statements is correct?
  1. She spent a total of $3,000 on business trips last month.
  2. She spent $600 on most of the business trips last month.
  3. She spent $600 or more on at least half of the business trips last month.
  4. She spent $600 more on her most expensive business trip than she did on her least expensive trip.

/share/clg/xml/public_release/mathematics/2001_312_alg27.xml

Correct Answer:
C

Selected Response Item - Released in 2001

The box-and-whisker plot below summarizes the test scores of an algebra class.

Based on the box-and-whisker plot, which of these must be true?
  1. The median score is 70.
  2. The lower quartile score is 50.
  3. Half of the scores are between 60 and 75.
  4. The interquartile range is half of the range.

/share/clg/xml/public_release/mathematics/2001_312_alg31.xml

Correct Answer:
D

Brief Constructed Response (BCR) Item - Released in 2001

The table below shows the salaries of the teachers at Polk High School.

Complete the following in the answer box:

  • What are the median and mean of this salary data? Use mathematics to explain how you determined your answers. Use words, symbols, or both in your explanation.
     
  • A journalist who believes that teachers earn too much money is going to write an article based on this data. Which measure of central tendency (mean or median) should the journalist use to convince the public to agree with her opinion? Use mathematics to justify your answer.

/share/clg/xml/public_release/mathematics/2001_312_alg40.xml

Selected Response Item - Released in 2002

The growing season is defined as the average number of days between the last frost in the spring and the first frost of the fall. The table below shows the average growing season for nine major U.S. cities.

If the circled number 156 is changed to 256, how would the mean, median, and mode of this data change?
  1. increase mean, median, and mode
  2. decrease mean, median, and mode
  3. increase mean, median, eliminate mode
  4. increase mean and mode, decrease median

/share/clg/xml/public_release/mathematics/2002_312_alg23.xml

Correct Answer:
C

Brief Constructed Response (BCR) Item - Released in 2002

The table below shows the number of medals won by 24 countries during the 1998 Winter Olympic Games.

Complete the following in the answer box below:

  • Use the data from the table to create a box-and-whisker plot on the box below.
  • What was the least number of medals won by a country in the top 25% of the final medal standings? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.

/share/clg/xml/public_release/mathematics/2002_312_alg31.xml

Brief Constructed Response (BCR) Item - Released in 2005

A cereal company awards a prize to anyone who collects all 5 different game pieces. Each game piece has an equal chance of being placed in a box of cereal. Each box of cereal contains 1 game piece. A class of 20 students conducted a simulation to see how many boxes of cereal must be purchased to collect all 5 different game pieces. Their results are shown in the table below.

Complete the following in the answer box below:

  • What are the mean, median, and mode of the data?
     
  • A box of cereal costs $2.80. Based on the simulation results, how much money must a consumer spend to collect all 5 different game pieces? Use measures of central tendency to justify your answer.
     
  • One student in the class suggested that the data point of 26 should be ignored. Will ignoring this data point have a greater influence on the mean or the median? Use mathematics to justify your answer.
     

/share/clg/xml/public_release/mathematics/2005_312_alg06.xml

Selected Response Item - Released in 2005

While studying a school's top 10 college entrance exam scores, a guidance counselor found the mean score to be 1,472. In looking at the calculations, the counselor realized he had made a mistake. One of the student's scores was 10 points greater than the counselor used in his calculations. What is the correct mean score?
  1. 1,462
  2. 1,472
  3. 1,473
  4. 1,482

/share/clg/xml/public_release/mathematics/2005_312_alg31.xml

Correct Answer:
C

Selected Response Item - Released in 2005

Four teachers gave a test to their classes. A summary of the test results is shown below.

Which teacher's class has the widest spread in the middle 50% of the test scores?
  1. Mrs. Lee
  2. Mr. Green
  3. Mrs. Smith
  4. Mr. Wang

/share/clg/xml/public_release/mathematics/2005_312_alg34.xml

Correct Answer:
A

Selected Response Item - Released in 2001

The table below shows the average daily temperatures, in degrees Fahrenheit (°F), for four selected cities. The average daily temperatures are given for the months of January and July.

According to the information in the table, which city experiences the greatest range of temperatures between January and July?
  1. Baltimore
  2. Mexico City
  3. Tokyo
  4. Toronto

/share/clg/xml/public_release/mathematics/2001_312_alg11.xml

Correct Answer:
D

Selected Response Item - Released in 2003

The table below shows the percentages of high school students who took a college entrance examination in 1997 in 7 states.

Which of these states' percentages is at the third quartile?
  1. Maryland
  2. Massachusetts
  3. New Jersey
  4. Pennsylvania

/share/clg/xml/public_release/mathematics/2003_312_alg05.xml

Correct Answer:
D

Selected Response Item - Released in 2003

The table below shows the number of points scored by the winner of the men's ski jumping competition during the Olympics from 1980 to 1994.

After the 1998 Olympics, the mean number of points scored by all winners since 1980 was 241.9. Which of these might have been the winning number of points in 1998?
  1. 217.5
  2. 234.6
  3. 243.1
  4. 248.4

/share/clg/xml/public_release/mathematics/2003_312_alg22.xml

Correct Answer:
B

Selected Response Item - Released in 2004

Paul earned scores of 76, 78, and 86 on his first three science tests. What score does he need on his fourth test to earn a mean score of 82?
  1. 78
  2. 80
  3. 84
  4. 88

/share/clg/xml/public_release/mathematics/2004_312_alg03.xml

Correct Answer:
D

Brief Constructed Response (BCR) Item - Released in 2004

Matt caught 6 fish and recorded each of their weights as shown in the table below.

Complete the following in the answer box below:

  • Find the mean and the median of the data.
     
  • Which measure of central tendency, mean or median, should Matt use to best represent the typical weight of the fish he caught? Use mathematics to justify your answer.
     

/share/clg/xml/public_release/mathematics/2004_312_alg05.xml

Selected Response Item - Released in 2004

A credit card company investigates any purchase that is larger than the third quartile of a customer's last 12 purchases. Mike's last 12 purchases are shown below.

What is the largest purchase Mike could make next without having his purchase investigated?
  1. $26.25
  2. $28.84
  3. $38.75
  4. $43.25

/share/clg/xml/public_release/mathematics/2004_312_alg26.xml

Correct Answer:
C

Selected Response Item - Released in 2002

An athletic director asked 4 groups of students, “What is the most that you would pay for an athletic event?” The responses are shown below.

Which group's answers showed the least variability?
  1. Group 1
  2. Group 2
  3. Group 3
  4. Group 4

/share/clg/xml/public_release/mathematics/2002_312_alg25.xml

Correct Answer:
D

Brief Constructed Response (BCR) Item - Released in 2003

Amar compared the ages of the U.S. presidents who served between 1789 and 1845 at their first inaugurations to the ages of the presidents who served between 1945 and 2000 at their first inaugurations, as shown below.

Complete the following in the answer box below:

  • What are the mean and median for each group of U.S. presidents?
     
  • Amar wanted to use this data to show that the ages of the U.S. presidents at their first inaugurations have decreased between 1789 and 2000. How could Amar use this data to support his conclusion?
     
  • Do you think the data provides Amar with support strong enough to make his conclusion valid? Use mathematics to justify your answer.
     

/share/clg/xml/public_release/mathematics/2003_312_alg17.xml

Selected Response Item - Released in 2006

Christine has a mean score of 18 points per game in her first four basketball games of the season. How many points must she score in her next game to raise her mean score to 20 points per game?

  1. 20
  2. 22
  3. 25
  4. 28

/share/clg/xml/public_release/mathematics/2006_312_alg07.xml

Correct Answer:
D

Brief Constructed Response (BCR) Item - Released in 2006

The student government wants to determine if students get better grades in morning or afternoon classes. They randomly surveyed 20 students that take math class in the morning and 20 students that take math class in the afternoon. The survey results are shown in the stem-and-leaf plots below.

Complete the following in the Answer Book:

  • What are the mean, median, and mode for each class?
  • Based on the data, do students get better grades in the morning classes? Use measures of central tendency to justify your answer.

/share/clg/xml/public_release/mathematics/2006_312_alg28.xml

Selected Response Item - Released in 2006

Look at the bowling scores in the table below.

Which of these is the range of the bowling scores?

  1. 10
  2. 26
  3. 34
  4. 54

/share/clg/xml/public_release/mathematics/2006_312_alg32.xml

Correct Answer:
D

 

 

 

EXPECTATION 3.1.3

 

Goal 3 Data Analysis And Probability

 

Expectation 3.1 The student will collect, organize, analyze, and present data.

 

Indicator 3.1.3 The student will calculate theoretical probability or use simulations or statistical inference from data to estimate the probability of an event.

 

Assessment Limits:

o                                            This indicator does not include finding probabilities of dependent events.

Selected Response Item - Released in 2001

A spinner has spaces labeled X, Y, and Z. The spinner was spun 20 times. The results are shown in the table below.

According to this data, what is the experimental probability that the spinner will land on Y?




/share/clg/xml/public_release/mathematics/2001_313_alg16.xml

Correct Answer:
A

Student Produced Response (SPR) Item - Released in 2002

Use the answer box below to complete the following.

Mrs. Penner has 7 keys for her school on her key ring. All of the keys are different but look alike. One of these keys is for the bathroom and two are for her classroom. If she picks one key at random, what is the probability that the key is not for the bathroom or her classroom?

/share/clg/xml/public_release/mathematics/2002_313_alg15.xml

Correct Answer:
0.57-0.6

Student Produced Response (SPR) Item - Released in 2002

Use the answer box below to complete the following.

Hank tosses 4 coins at the same time. He repeats this action 10 times. The results are shown below, where H represents heads and T represents tails.

Based on this data, what is the probability that at least one out of the group of 4 coins tossed will land with tails up?

/share/clg/xml/public_release/mathematics/2002_313_alg16.xml

Correct Answer:
0.9

Selected Response Item - Released in 2002

Pedro designed a board game with a spinner that is divided into 4 equal sections: 1, 2, 3, and “Lose a Turn.” He wanted to determine how many times a player would spin “Lose a Turn” in 10 spins. He conducted a simulation where one trial consisted of 10 spins. The table below shows his results for 50 trials.

Based on the simulation, what is the probability that a player will spin “Lose a Turn” 3 or more times in 10 spins?




/share/clg/xml/public_release/mathematics/2002_313_alg21.xml

Correct Answer:
C

Student Produced Response (SPR) Item - Released in 2005

Use the answer box below to complete the following.

The Game Land Company developed a new trivia game. The spinner below is used to determine what kind of question is asked. The spinner is divided into 4 equal sections. One of the sections is divided in half.

What is the probability that a circle question is asked?

/share/clg/xml/public_release/mathematics/2005_313_alg13.xml

Correct Answer:
.37 .375 .38 .4

Selected Response Item - Released in 2005

A company manufactures CD players. The quality control department checks 600 CD players and discovers that 12 of them are defective. What is the probability that a CD player is not defective?
  1. 0.12
  2. 0.50
  3. 0.72
  4. 0.98

/share/clg/xml/public_release/mathematics/2005_313_alg20.xml

Correct Answer:
D

Selected Response Item - Released in 2001

The table below shows information about the students in Ms. Murphy's algebra class.

What is the probability that a randomly selected male student does not ride the bus to school?




/share/clg/xml/public_release/mathematics/2001_313_alg36.xml

Correct Answer:
D

Student Produced Response (SPR) Item - Released in 2001

Use the answer box below to complete the following:

A recent survey of Americans who work outside the home found that 10% take public transportation, 80% drive to work, and 10% use other forms of transportation.

Meghan used a random number generator to simulate the various methods that a group of five people may use to get to work. For her simulation, Meghan assigned digits to the various methods of transportation as shown in the table below.

She ran the simulation 10 times, and the results are shown below.

Based on Meghan's simulation, what is the probability that all 5 people in the group drive to work?

/share/clg/xml/public_release/mathematics/2001_313_alg39.xml

Correct Answer:
0.3

Selected Response Item - Released in 2001

In a simulation designed to represent families with two children, two coins are tossed to model the gender of each child. The results of 50 trials are shown in the table below.

Based on the results in the table, what is the probability that a family with two children have at least one boy?
  1. 0.30
  2. 0.44
  3. 0.58
  4. 0.74

/share/clg/xml/public_release/mathematics/2001_313_alg47.xml

Correct Answer:
D

Selected Response Item - Released in 2003

The words "mathematics" and "algebra" are written on cards with one letter on each card. If one card is drawn at random, what is the probability that the card will have an "a" on it?
  1.  2
     9
  2.  2 
    11
  3.  1 
    12
  4.  4 
    19

/share/clg/xml/public_release/mathematics/2003_313_alg10.xml

Correct Answer:
A

Student Produced Response (SPR) Item - Released in 2003

Use the answer box below to complete the following.

Valerie surveyed 50 people about their choice of pizza crusts. Her results are shown in the table below.

If an adult is selected at random, what is the probability that the adult prefers thin crust?

/share/clg/xml/public_release/mathematics/2003_313_alg16.xml

Correct Answer:
0.56

Student Produced Response (SPR) Item - Released in 2003

Use the answer box below to complete the following.

The spinner below is divided into 8 equal sections.

If the arrow lands on a number, what is the probability that it will land on a 1 or a 4 ?

/share/clg/xml/public_release/mathematics/2003_313_alg38.xml

Correct Answer:
.25

Student Produced Response (SPR) Item - Released in 2004

Use the answer box below to complete the following.

A bag contains 5 red apples, 7 yellow apples, and 8 green apples. Brett picks an apple from the bag without looking. What is the probability that Brett will pick a green apple?

/share/clg/xml/public_release/mathematics/2004_313_alg13.xml

Correct Answer:
0.4

Student Produced Response (SPR) Item - Released in 2004

Use the answer box below to complete the following.

The senior class sold school spirit items. The table below shows the number of items sold on the first day of a two-day sale.

Based on sales from the first day, what is the probability that the first person on the second day of the sale will buy a hat?

/share/clg/xml/public_release/mathematics/2004_313_alg15.xml

Correct Answer:
.2 .24 .244 .2444

Selected Response Item - Released in 2004

Customers at Harvey's Store can win appliances at the grand opening. The table below shows the type and the number of appliances.

Toby is the first customer to win an appliance. What is the probability that Toby will win an iron or a toaster?
  1.  4 
    16
  2.  5 
    16
  3.  9 
    16
  4. 11
    16

/share/clg/xml/public_release/mathematics/2004_313_alg23.xml

Correct Answer:
C

Selected Response Item - Released in 2002

The bar graph below shows the results of spinning a spinner 1,000 times. The spinner has 5 colored sections.

Which of these spinners most likely produced the above bar graph?




/share/clg/xml/public_release/mathematics/2002_313_alg30.xml

Correct Answer:
C

Student Produced Response (SPR) Item - Released in 2005

Use the answer box below to complete the following.

Judy asked 140 students at her high school their opinion of the school mascot. The survey results are shown below.

If a female student is selected at random, what is the probability that she likes the mascot?

/share/clg/xml/public_release/mathematics/2005_313_alg15.xml

Correct Answer:
Range 0.6 to 0.6143

Student Produced Response (SPR) Item - Released in 2006

A reporter surveyed 300 randomly selected people of all ages about their opinion of a new song. The results are shown in the table below.

What is the probability that a person who had no opinion of the new song was older than 46?

/share/clg/xml/public_release/mathematics/2006_313_alg14.xml

Correct Answer:
0.186

Student Produced Response (SPR) Item - Released in 2006

Paloma conducts a survey to determine the type of candy that students prefer. The survey results are shown in the table below.

Based on the survey results, what is the probability that a randomly selected student prefers Fruit Bursts?

/share/clg/xml/public_release/mathematics/2006_313_alg25.xml

Correct Answer:
0.2

Selected Response Item - Released in 2006

The spinner below has 8 equal sections.

What is the probability of spinning a number less than 3?

  1. 1
    4
  2. 3
    4
  3. 1
    8
  4. 3
    8

/share/clg/xml/public_release/mathematics/2006_313_alg33.xml

Correct Answer:
A

 

 

EXPECTATION 3.2.1

 

Goal 3 Data Analysis And Probability

 

Expectation 3.2 The student will apply the basic concepts of statistics and probability to predict possible outcomes of real-world situations.

 

Indicator 3.2.1 The student will make informed decisions and predictions based upon the results of simulations and data from research.

Selected Response Item - Released in 2001

A quality control engineer for the Have Fun Toys Company tested 800 video game cartridges and found 3 defective cartridges. The company plans to produce 500,000 video game cartridges this year. Based on the findings, how many video game cartridges can be expected to be defective?
  1. 16
  2. 20
  3. 1,875
  4. 2,000

/share/clg/xml/public_release/mathematics/2001_321_alg48.xml

Correct Answer:
C

Extended Constructed Response (ECR) Item - Released in 2001

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.

/share/clg/xml/public_release/mathematics/2001_321_alg49.xml

Selected Response Item - Released in 2002

Sue is scheduled to take a biology test at school today. To perform well on the test, she knows it is best to eat a breakfast with a high ratio of carbohydrates to serving size.

Which of these foods has the highest ratio of carbohydrates to serving size?
  1. Bagel
  2. Milkshake
  3. Raisins
  4. Wheat cereal

/share/clg/xml/public_release/mathematics/2002_321_alg20.xml

Correct Answer:
D

Selected Response Item - Released in 2002

The spinner shown below is spun 20 times.

The results of the spins are shown below.

Based on these results, how many times would 2 be expected to appear in 60 spins?
  1. 8
  2. 15
  3. 24
  4. 28

/share/clg/xml/public_release/mathematics/2002_321_alg24.xml

Correct Answer:
C

Selected Response Item - Released in 2005

Karen spun a spinner 50 times and recorded her results in the table below. The spinner had five numbered sections.

Based on the results in the table, how many times should Karen expect the spinner to land on section 3 or 4 if she spins the spinner 300 times?
  1. 60
  2. 72
  3. 108
  4. 132

/share/clg/xml/public_release/mathematics/2005_321_alg11.xml

Correct Answer:
D

Extended Constructed Response (ECR) Item - Released in 2005

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 box below:

  • 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_321_alg30.xml

Selected Response Item - Released in 2005

A student at West High School conducted a random survey of 200 tenth-grade students to determine their favorite season. The survey results are shown in the table below.

There are 500 tenth-grade students in the school. Based on the survey results, how many of these tenth-grade students would be expected to choose Spring as their favorite season?
  1. 105
  2. 125
  3. 130
  4. 160

/share/clg/xml/public_release/mathematics/2005_321_alg32.xml

Correct Answer:
D

Selected Response Item - Released in 2001

A television producer wants to broadcast a new program for young children. The table below shows information on the average daily television viewing time for two age groups of children.

Based on the data in the table, which time period would be the best choice for the new television program for 2- to 5-year-olds?
  1. 7 to 10 a.m.
  2. 10 a.m. to 1 p.m.
  3. 4 to 7 p.m.
  4. 7 to 10 p.m.

/share/clg/xml/public_release/mathematics/2001_321_alg12.xml

Correct Answer:
A

Selected Response Item - Released in 2003

Mr. Shin wants to order notebooks for the school store. Notebooks come in four colors: red, blue, green, and black. He randomly surveyed 50 students to determine which color notebook they would buy. The table below shows the results.

Mr. Shin will order 400 notebooks. How many blue notebooks should he order?
  1. 22
  2. 88
  3. 176
  4. 200

/share/clg/xml/public_release/mathematics/2003_321_alg20.xml

Correct Answer:
C

Extended Constructed Response (ECR) Item - Released in 2003

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.
     

/share/clg/xml/public_release/mathematics/2003_321_alg21.xml

Extended Constructed Response (ECR) Item - Released in 2004

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.

/share/clg/xml/public_release/mathematics/2004_321_alg11.xml

Selected Response Item - Released in 2004

The mayor of a town conducted an opinion survey of 90 randomly selected voters. The mayor wants to determine if a new shopping mall should be built in town. The survey results are shown in the table below.

There are 1,440 voters in the town. How many voters would be expected to want the new shopping mall built?
  1. 160
  2. 320
  3. 860
  4. 960

/share/clg/xml/public_release/mathematics/2004_321_alg17.xml

Correct Answer:
D

Selected Response Item - Released in 2004

One hundred randomly selected students from Western High School were surveyed to determine whether they would like school to start one hour later. Of the students surveyed, 58 favored the change. Western High School has 1,200 students. According to the survey results, which of these is a reasonable prediction of the total number of students who would favor this change?
  1. 42
  2. 58
  3. 504
  4. 696

/share/clg/xml/public_release/mathematics/2004_321_alg20.xml

Correct Answer:
D

Selected Response Item - Released in 2003

A quality-control expert for a key manufacturer examined the keys produced by a particular machine. The table below shows the number of defective keys found in the 8 groups of 100 keys he examined.

How many defective keys would be expected in a group of 5,000 keys? Round the answer to the nearest whole number.
  1. 150
  2. 170
  3. 213
  4. 243

/share/clg/xml/public_release/mathematics/2003_321_alg29.xml

Correct Answer:
C

Selected Response Item - Released in 2006

The table below shows the possible scores for a game and the number of times each score occurred.

Using the information in the table, predict how many times a score of "7" would occur in 100 tries.

  1. 12
  2. 15
  3. 18
  4. 22

/share/clg/xml/public_release/mathematics/2006_321_alg09.xml

Correct Answer:
B

Selected Response Item - Released in 2006

A store owner surveyed customers to determine color preferences of bathroom tile. The results of the survey are shown below.

Which of these is the best conclusion based on the results of the survey?

  1. The store owner should only order white tile.
  2. The store owner should only order beige and pink tile.
  3. The store owner should order more cases of beige and white tile than any other color.
  4. The store owner should order more cases of yellow and teal tile than any other color.

/share/clg/xml/public_release/mathematics/2006_321_alg10.xml

Correct Answer:
C

 

 

EXPECTATION 3.2.2

Goal 3 Data Analysis And Probability

 

Expectation 3.2 The student will apply the basic concepts of statistics and probability to predict possible outcomes of real-world situations.

 

Indicator 3.2.2 The student will interpret data and/or make predictions by finding and using a line of best fit and by using a given curve of best fit.

 

Assessment Limits:

o                                            Items should include a definition of the data and what it represents.

o                                            Data will be given when a line of best fit is required.

o                                            Equation or graph will be given when a curve of best fit is required.

 

Extended Constructed Response (ECR) Item - Released in 2004

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.
 

/share/clg/xml/public_release/mathematics/2004_322_alg28.xml

Brief Constructed Response (BCR) Item - Released in 2001

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.

/share/clg/xml/public_release/mathematics/2001_322_alg10.xml

Selected Response Item - Released in 2001

The scatter plot below shows the relationship between the number of bags of popcorn that are sold and the price per bag.

Which of these graphs shows the line of best fit?

A.                 Graph A

B.                 Graph B

C.                 Graph C

D.                Graph D

/share/clg/xml/public_release/mathematics/2001_322_alg13.xml

Correct Answer:
B

Brief Constructed Response (BCR) Item - Released in 2001

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).
 

·                     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.

/share/clg/xml/public_release/mathematics/2001_322_alg30.xml

Selected Response Item - Released in 2005

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?

A.                 0.015

B.                 0.181

C.                 1.520

D.                1.720

/share/clg/xml/public_release/mathematics/2005_322_alg29.xml

Correct Answer:
A

Selected Response Item - Released in 2002

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?

A.                

B.                

C.                

D.               

/share/clg/xml/public_release/mathematics/2002_322_alg11.xml

Correct Answer:
B

Brief Constructed Response (BCR) Item - Released in 2002

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.

/share/clg/xml/public_release/mathematics/2002_322_alg12.xml

Extended Constructed Response (ECR) Item - Released in 2002

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.

/share/clg/xml/public_release/mathematics/2002_322_alg36.xml

Brief Constructed Response (BCR) Item - Released in 2005

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 box below:

·                     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

Selected Response Item - Released in 2003

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?

A.                 2000

B.                 2024

C.                 2031

D.                2050

/share/clg/xml/public_release/mathematics/2003_322_alg24.xml

Correct Answer:
B

Brief Constructed Response (BCR) Item - Released in 2003

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.
 

/share/clg/xml/public_release/mathematics/2003_322_alg30.xml

Selected Response Item - Released in 2004

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?

A.                 1.5 pounds

B.                 1.7 pounds

C.                 1.8 pounds

D.                1.9 pounds

/share/clg/xml/public_release/mathematics/2004_322_alg18.xml

Correct Answer:
B

Selected Response Item - Released in 2006

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?

A.                 69%

B.                 71%

C.                 72%

D.                73%

/share/clg/xml/public_release/mathematics/2006_322_alg03.xml

Correct Answer:
C

Brief Constructed Response (BCR) Item - Released in 2006

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 = 0.014x˛ + 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

Extended Constructed Response (ECR) Item - Released in 2006

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

 

 

 

 

EXPECTATION 3.2.3

 

Goal 3 Data Analysis And Probability

 

Expectation 3.2 The student will apply the basic concepts of statistics and probability to predict possible outcomes of real-world situations.

 

Indicator 3.2.3 The student will communicate the use and misuse of statistics.

 

Assessment Limits:

o                                            Examples of “misuse of statistics” include the following:

o                                                                    misuse of scaling on a graph

o                                                                    misuse of measures of central tendency and variability to represent data,

o                                                                    using three-dimensional figures inappropriately

o                                                                    using data to sway interpretation to a predetermined conclusion

o                                                                    using incorrect sampling techniques

o                                                                    using data from simulations incorrectly

o                                                                    predicting well beyond the data set.

Selected Response Item - Released in 2004

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?
  1. Mary did not consider the top five names for girls.
  2. Mary did not consider the entire population of the United States.
  3. Mary did not consider the names most frequently given to boys in other years.
  4. 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

Selected Response Item - Released in 2001

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?
  1. Ask 50 girls to complete a survey.
  2. Ask 50 students who attended the last dance.
  3. Ask 50 randomly selected students from her classes.
  4. Ask 50 randomly selected students from the school.

/share/clg/xml/public_release/mathematics/2001_323_alg41.xml

Correct Answer:
D

Extended Constructed Response (ECR) Item - Released in 2001

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.

/share/clg/xml/public_release/mathematics/2001_323_alg49.xml

Selected Response Item - Released in 2005

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?
  1. computation is incorrect
  2. sample size is too large
  3. sample is biased
  4. sample is random

/share/clg/xml/public_release/mathematics/2005_323_alg17.xml

Correct Answer:
C

Extended Constructed Response (ECR) Item - Released in 2005

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 box below:

  • 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

Extended Constructed Response (ECR) Item - Released in 2002

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.

/share/clg/xml/public_release/mathematics/2002_323_alg36.xml

Extended Constructed Response (ECR) Item - Released in 2003

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.
     

/share/clg/xml/public_release/mathematics/2003_323_alg21.xml

Selected Response Item - Released in 2003

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?
  1. use of opinion to influence a prediction
  2. incorrect arithmetic computation
  3. inappropriate use of mean
  4. biased sampling

/share/clg/xml/public_release/mathematics/2003_323_alg34.xml

Correct Answer:
D

Extended Constructed Response (ECR) Item - Released in 2004

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.

/share/clg/xml/public_release/mathematics/2004_323_alg11.xml

Selected Response Item - Released in 2002

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?
  1. The time periods are different.
  2. The types of data are different.
  3. The vertical scales are different.
  4. The population of the towns are different.

/share/clg/xml/public_release/mathematics/2002_323_alg19.xml

Correct Answer:
C

Extended Constructed Response (ECR) Item - Released in 2006

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

Selected Response Item - Released in 2006

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?

  1. The sample size is too small.
  2. Students are randomly selected.
  3. Not all students have the same chance to be surveyed.
  4. Every other student entering the school should be surveyed.

/share/clg/xml/public_release/mathematics/2006_323_alg05.xml

Correct Answer:
C