]> ETS :: Praxis TAAG :: Middle School Mathematics (0069)
E T S Praxis Series

Middle School Mathematics (0069)

Skip Navigation

Download Free Viewers

Sample Test Questions

Viewing the mathematical equations on this page requires certain system requirements.

Current section: Multiple Choice > Questions

Skip Section Navigation

The sample questions that follow illustrate the kinds of questions in the test. They are not, however, representative of the entire scope of the test in either content or difficulty. Answers with explanations follow the questions.

Directions:  Each of the questions or statements below is followed by four suggested answers or completions. Select the one that is best in each case.


  1. x y
    –4 –2
    –3 –32
    –2 –1
    –1 –12
    0 0

    Which of the following is true about the data in the table above?

    1. As x decreases, y increases.
    2. As x increases, y does not change.
    3. As x increases, y decreases.
    4. As x increases, y increases.

  2. The average number of passengers who use a certain airport each year is 350 thousand. A newspaper reported the number as 350 million. The number reported in the newspaper was how many times the actual number?

    1. 10
    2. 100
    3. 1,000
    4. 10,000

  3. If there are exactly 5 times as many children as adults at a show, which of the following CANNOT be the number of people at the show?

    1. 102
    2. 80
    3. 36
    4. 30

  4. The original price of a certain car was 25 percent greater than its cost to the dealer. The actual selling price was 25 percent less than the original price. If c is the cost of the car to the dealer and p is the selling price, which of the following represents p in terms of c?

    1. p = 1.00c
    2. p = 1.25c
    3. p = 0.25(0.75c)
    4. p = 0.75(1.25c)

  5. Question 5 includes an illustration that shows intersecting vertical and horizontal lines. Each line includes 14 hash marks along its length. The intersection of the lines occurs at the 8th hash mark of the horizontal line (starting from the left) and the 9th hash mark of the vertical line (starting from the top). The vertical line is the y-axis. The horizontal line is the x-axis. In the upper-left portion of the diagram is a right triangle, labeled A, B, and C at each of its points. Vertically, the triangle runs along the y-axis from the 2nd hash mark to the 6th hash mark. Horizontally, the triangle runs along the x-axis from the 5th hash mark to the 7th hash mark. A square that is 1 hash mark by 1 hash mark is located inside the triangle at bottom-right.

    Which figure below results if right triangle ABC above is flipped (reflected) across the y-axis and then turned (rotated) clockwise about point C' by 90 degrees?

    The four possible answers to Question 5 are all diagrams that have intersecting vertical and horizontal lines and hash marks identical to the lines described in the question. In answer A, the triangle has been flipped into the upper-right portion of the diagram. Vertically, the triangle runs along the y-axis from the 6th to 8th hash marks. Horizontally, the triangle runs along the x-axis from the 9th to 13th hash marks. The 1 by 1 square is at the top-left of the triangle.


  6. Question 6 contains a rectangular block that is 9 centimeters high, 12 centimeters wide, and 8 centimeters deep. The block contains smaller equally sized blocks within it. The side of the rectangle that is 9 by 12 centimeters contains three rows of smaller blocks. The side of the rectangle that is 8 by 9 centimeters contains two rows of smaller blocks.

    The large rectangular block pictured above was made by stacking smaller blocks, all of which are the same size. What are the dimensions in centimeters of each of the smaller blocks?

    1. 3 × 2 × 3
    2. 3 × 3 × 3
    3. 3 × 4 × 3
    4. 4 × 4 × 3

  7. Question 7 contains an illustration that shows two parallel horizontal lines intersected by a diagonal line. The top horizontal line is labeled l. The bottom line is labeled p. The diagonal line begins above the top line near the left edge of the line. It ends at below the bottom line near the right edge. The smaller exterior angle where the diagonal line intersects the top horizontal line is labeled x degrees. The larger exterior angle where the diagonal line intersects the bottom horizontal line is labeled y degrees.

    In the figure above, line l and line p are parallel and y = 3x. What is the value of x ?

    1. 30
    2. 45
    3. 60
    4. 75

  8. Question 8 contains two diagrams, each showing a square inscribed in a circle. The square and circle in diagram A appear to be about half the size of the square and circle in diagram B. In both drawings, the corners of the square touch the edges of the circles. In diagram A, a diagonal line shows the radius of the circle is 1. In diagram B, a diagonal line shows the radius of the circle is 2.

    A square is inscribed in each of the circles above. The radius of circle A is 1, and the radius of circle B is 2. What is the ratio of the area of the square inscribed in circle A to the area of the square inscribed in circle B?

    1. 1: 2
    2. 1:2
    3. 1:22
    4. 1:4

  9. Which of the following defines y as a function of x ?

    1. x – y2 = 4
    2. x2 + y2 = 4
    3. y = x2 + 2
    4. y < x + 1

  10. A taxi ride costs $2.50 for the first 14 mile or fraction thereof plus $0.50 for each additional 14 mile or fraction thereof. Which of the following graphs represents the total cost of a ride as a function of distance traveled?


    1. Each option is a step function where each step is one-fourth of a mile long, with an open circle on the left and closed circle on the right. Answer A shows the first step beginning with an open circle at 2 dollars and 50 cents for the first quarter-mile, with an increase of 50 cents for each quarter-mile thereafter, up to 5 dollars for 1 and one-half miles.


    2. Each option is a step function where each step is one-fourth of a mile long, with an open circle on the left and closed circle on the right. Answer B shows the first step beginning with an open circle at 3 dollars for the first quarter-mile, with an increase of 50 cents for each quarter-mile thereafter, up to 5 dollars for 1 and one-quarter miles.


    3. Each option is a step function where each step is one-fourth of a mile long, with an open circle on the left and closed circle on the right. Answer C shows the first step beginning with an open circle at 2 dollars and 50 cents for the first quarter-mile, with an increase of 50 cents for each quarter-mile thereafter, up to 5 dollars for 1 and one-half miles.


    4. Each option is a step function where each step is one-fourth of a mile long, with an open circle on the left and closed circle on the right. Answer D shows the first step beginning with an open circle at 3 dollars for the first quarter-mile, with an increase of 50 cents for each quarter-mile thereafter, up to 5 dollars for 1 and one-quarter miles.

  11. In a class of 29 children, each of 20 children has a dog and each of 15 has a cat. How many of the children have both a dog and a cat?

    1. None of the children necessarily has both.
    2. Exactly 5
    3. Exactly 6
    4. At least 6 and at most 15

  12. A pie chart shows five categories of trash. Paper is 40 percent of a country's trash. Metals is 9 percent, plastics is 8 percent, glass is 7 percent and 36 percent is a category called other.

    The graph above shows the distribution of the content, by weight, of a county's trash. If approximately 60 tons of the trash consists of paper, approximately how many tons of the trash consists of plastics?

    1. 24
    2. 20
    3. 15
    4. 12

Questions 13-14 refer to the following graph.

A bar graph is labeled NUMBER OF STUDENTS IN MEDICAL SCHOOLS IN THE UNITED STATES, 1950-1985 (in thousands). In 1950, the height of the bar is just below the line for 30. In 1955, the height of the bar is about 31. In 1960, the height is about 32. In 1965, the height is about 35. In 1970, the height is about 40. In 1975, the height is about 58. In 1980, the height is about 70. In 1985, the height is about 72.

  1. In how many of the years shown were there more than twice as many students in medical schools as there were in 1950?

    1. None
    2. One
    3. Two
    4. Three

  2. The number of students in medical schools increased by approximately what percent from 1970 to 1980?

    1. 75%
    2. 60%
    3. 50%
    4. 45%

  3. In order to estimate the population of snails in a certain woodland, a biologist captured and marked 84 snails that were then released back into the woodland. Fifteen days later the biologist captured 90 snails from the woodland, 12 of which bore the markings of the previously captured snails.

    If all of the marked snails were still active in the woodland when the second group of snails were captured, what should the biologist estimate the snail population to be, based on the probabilities suggested by this experiment?

    1. 630
    2. 1,010
    3. 1,040
    4. 1,080

  4. If a student takes a test consisting of 20 true-false questions and randomly guesses at all of the answers, what is the probability that all 20 guesses will be correct?

    1. 0
    2. (12)20
    3. 12(20)
    4. 12

  5. ROBIN'S TEST SCORES
    88, 86, 98, 92, 90, 86

    In an ordered set of numbers, the median is the middle number if there is a middle number; otherwise, the median is the average of the two middle numbers. If Robin had the test scores given in the table above, what was her median score?

    1. 89
    2. 90
    3. 92
    4. 95