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Sample Questions

What questions are used in the NAEP mathematics assessment?

Explore sample questions from the mathematics assessment, and see how the NAEP mathematics questions relate to student performance.

 

Test Yourself in Mathematics

Select one of the grade tabs below to try out 10 questions from the 2009 NAEP mathematics assessment. After answering all the questions, compare your score with that of students nationally.

Grade 4
Grade 8
Grade 12


 Grade 12 Sample Questions

Question 1 of 10:

Table called Temperatures on October 1st for Five Cities (in Fahrenheit degrees). City A has a high of 72 degrees and a low of 50 degrees. City B has a high of 90 degrees and a low of 75 degrees. City C has a high of 83 degrees and 72 degrees. City D has a high of 50 degrees and low of 37 degrees. City E has a high of 92 and a low of 72 degrees.

The table above shows the high and low temperatures on October 1st for five cities. Which city had the greatest temperature range?

  1. City A
  2. City B
  3. City C
  4. City D
  5. City E
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The correct answer is: A
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Question 2 of 10:

John is going to cover an attic floor with insulation. The floor measures 25 feet by 35 feet. If one roll of insulation will cover 64 square feet, how many rolls of insulation does John need?

  1. 1
  2. 2
  3. 8
  4. 14
  5. 110
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The correct answer is: D
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Question 3 of 10:

The first four terms in a sequence are shown below.

40, 8, 24, 16,...

Each term after the first two terms is found by taking one-half the sum of the two preceding terms. Which term is the first odd number in this sequence?

  1. The 5th term
  2. The 6th term
  3. The 7th term
  4. The 8th term
  5. The 9th term
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The correct answer is: C
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Question 4 of 10:

alt text hereCircle with center O and quadrilateral ABCD inscribed on the circle.
Angle C of the quadrilateral ABCD is the only right angle of the quadrilateral.

Quadrilateral ABCD is inscribed in circle O , and Angle C is a right angle, as shown above. Segment AB is not parallel to segment DC . Which of the following statements must be true?

  1. Angle A is congruent to angle B.
  2. Angle B is congruent to angle D.
  3. Angle B. is a right angle.
  4. Line segment AC. is a diameter of circle O.
  5. Line segment BD. is a diameter of circle O.
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The correct answer is: E

Question 5 of 10:

The manager of a company has to order new engines for its delivery trucks after the trucks have been driven 150,000 miles. One of the delivery trucks currently has 119,866 miles on it. This truck has the same delivery route each week and is driven an average of 40,000 miles each year. At this rate, the manager should expect this truck to reach 150,000 miles in approximately how many months?

  1. Less than 4 months
  2. Between 4 and 6 months
  3. Between 6 and 8 months
  4. Between 8 and 10 months
  5. More than 10 months
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The correct answer is: D
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Question 6 of 10:

Which of the following expressions is NOT equivalent to (a + b) (x + y) ?

  1. (a + b) x + (a + b) y
  2. a (x + y) + b (x + y)
  3. (b + a) (y + x)
  4. ax + by
  5. ax + bx + ay + by
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The correct answer is: D
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Question 7 of 10:

The principal of a high school would like to determine why there has been a large decline during the year in the number of students who buy food in the school’s cafeteria. To do this, 25 students from the school will be surveyed. Which method would be the most appropriate for selecting the 25 students to participate in the survey?

  1. Randomly select 25 students from the senior class.
  2. Randomly select 25 students from those taking physics.
  3. Randomly select 25 students from a list of all students at the school.
  4. Randomly select 25 students from a list of students who eat in the cafeteria.
  5. Give the survey to the first 25 students to arrive at school in the morning.
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The correct answer is: C
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Question 8 of 10:

A scatterplot of incomes (vertical axis) to age (horizontal axis). Income starts at 0 with 
$5,000 increments up to $70,000. Age starts at 0 with 10 year increments, up to 70. Cloud of data 
agglutinates southwest to northeast with lowest data point at approximately (25, 30,000) and highest 
data point at approximately (45, 65,000).

A random sample of graduates from a particular college program reported their ages and incomes in response to a survey. Each point on the scatterplot above represents the age and income of a different graduate.

Of the following equations, which best fits the data above?

  1. y = - 1,000x + 15,000
  2. y = - 1,000x 
  3. y = 1,000x + 15,000 
  4. y = 10,000x 
  5. y = 10,000x + 15,000
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The correct answer is: C
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Question 9 of 10:

Angie has a bag containing n apples. She gives 4 to her brother and keeps 5 for herself. She then divides the remaining apples equally among 3 friends. Which of the following expressions represents the number of apples each friend receives?

  1. (n/3)-4-5, that is, the quantity n is divided by 3, and from result, subtract 4. From new result subtract 5.
  2. (n-4-5)/3, that is, the quantity n minus 4 minus 5 is divided by 3.
  3. (4+5-n)/3, that is, the quantity 4 plus 5 minus n is divided by 3.
  4. ((n-4)/3)-5, that is, the quantity n minus 4 is divided by 3, and from result, subtract 5.
  5. ((n-5)/3)-4, that is, the quantity n minus 5 is divided by 3, and from result, subtract 4.
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The correct answer is: B
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Question 10 of 10:

Carlene told Kyle that a rectangular room measured 16 feet by 12 feet, to the nearest foot. This means that the length could measure between 15.5 feet and 16.5 feet and the width could measure between 11.5 feet and 12.5 feet.

Kyle performed the following calculations.

A table with 6 rows and 2 columns. First row reads: Dimensions (feet) AND Area (square feet). 
Second row reads: 15 by 11 AND 165. Third row reads: 15.5 by 11.5 AND 178.25. Fourth row reads: 16 by 12 AND 192.
Fifth row reads: 16.5 by 12.5 AND 206.25. Sixth row reads: 17 by 13 AND 221.

Of the following intervals, which is the smallest interval that contains all possible values of the area of the room?

  1. Between 191.5 and 192.5 square feet
  2. Between 191 and 193 square feet
  3. Between 179 and 206 square feet
  4. Between 178 and 207 square feet
  5. Between 165 and 221 square feet
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The correct answer is: D
Done

The chart below shows the percentage of questions that you answered correctly, as well as how students at each of the achievement levels performed on this set of questions. For instance, twelfth-grade students at Proficient had a percentage correct of 80% on average.

[Overall|55],[Below Basic|33],[Basic|61],[Proficient|80],[Advanced|91] Twelfth-grade percentage correct on selected mathematics questions: 2009

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SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2009 Mathematics Assessment.

View this set of questions in the NAEP Questions Tool to see student performance by participating states.