Test Information Guide

Field 68: Elementary Mathematics
Sample Multiple-Choice Questions

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Number Systems and Operations

Objective 0001
Apply number theory, structures of numeration systems, and arithmetic properties to the real number system.

1. When w is divided by x, the quotient is y, and the remainder is z. Which of the following equations is always true?

  1. w minus x equals y
  2. w minus x equals z
  3. the product of x and y equals w plus z
  4. the product of x and y equals w minus z
Answer
Correct Response: D.
Objective 0001
Apply number theory, structures of numeration systems, and arithmetic properties to the real number system.

2. Which of the following representations best illustrates how addends could be displayed to introduce the operation of multiplication?

  1. Four dice are shown aligned in a row. The dice display the numbers 1, 2, 4, and 5 when viewed from left to right.
  2. Four dice are shown aligned in a row. The dice display the numbers 2, 4, 1, and 5 when viewed from left to right.
  3. Four dice are shown aligned in a row. The dice display the numbers 3, 3, 3, and 3 when viewed from left to right.
  4. Four dice are shown aligned in a row. The dice display the numbers 2, 2, 4 and 4 when viewed from left to right.
Answer
Correct Response: C.
Objective 0002
Demonstrate knowledge of the principles and operations related to whole numbers, decimals, and percents.

3. The sum of 5 numbers is estimated by rounding each number to the nearest hundred before adding. What is the maximum possible difference between the estimated sum and the true sum of the numbers?

  1. 50
  2. 150
  3. 250
  4. 500
Answer
Correct Response: C.
Objective 0003
Understand principles and operations related to integers and fractions.

4. The depth of paper in a school's paper recycling container was 14and five-eighths inches. Each week for the next 3 weeks, the depth of paper grew by 5and three-quarters inches. If the depth of the container is 3 feet, what was the depth of the remaining space in the container at the end of the 3 weeks?

  1. 3and one-half inches
  2. 4and one-eighths inches
  3. 4and three-eighths inches
  4. 5and one-quarter inches
Answer
Correct Response: B.

Algebraic Thinking and Relations

Objective 0005
Understand how to manipulate and simplify algebraic expressions and translate problems into algebraic expressions, equations, and inequalities.

5. A cylindrical pool begins filling with an initial water depth of one-half foot. It takes 3 hours for the water depth to reach 1and one-half feet. The water depth must be at least 5 feet to reach the filter intake but no more than 6 feet to avoid overflowing. Which of the following inequalities shows the solution where h represents the possible number of hours of filling time to satisfy these conditions?

  1. 4and one-half is less than or equal to h is less than or equal to 5and one-half
  2. 5and one-half is less than or equal to h is less than or equal to 6and one-half
  3. 13and one-half is less than or equal to h is less than or equal to 16and one-half
  4. 16and one-half is less than or equal to h is less than or equal to 19and one-half
Answer
Correct Response: C.
Objective 0007
Analyze properties and applications of linear relations and functions.

6. Machine A works at a constant rate and produces 260 bars of soap in 2 hours. Machine B works at a constant rate and produces 440 bars of soap in 5 hours. Working simultaneously, how many bars of soap do the two machines produce in 3 hours?

  1. 300
  2. 327
  3. 600
  4. 654
Answer
Correct Response: D.

Geometry

Objective 0008
Analyze the characteristics and properties of two- and three-dimensional figures.

7. Use the diagram below to answer the question that follows.

a net of a three-dimensional figure

A net of a three-dimensional figure is shown. A square is at its center. A long rectangle is adjacent to the square's top edge, and the rectangle's top edge is labeled "3 inches." A right triangle is adjacent to the left edge of the central square. The hypotenuse, labeled 5 inches, attaches to the upper-left vertex of the square. The shortest leg of the triangle shares an edge with the square. Another right triangle with the same appearance is adjacent to the right side of the square. A second rectangle is adjacent to the square's bottom edge, but it is shorter than the top rectangle. The entire perimeter of the square is shared with the shapes that surround it.

The diagram shows a net of a three-dimensional figure. The net has a square in the center. What is the volume of the three-dimensional figure?

  1. 18 cubic inches
  2. 30 cubic inches
  3. 36 cubic inches
  4. 48 cubic inches
Answer
Correct Response: A.
Objective 0009
Understand the principles and properties of coordinate and transformational geometry.

8. Use the graph below to answer the question that follows.

a circle on a graph

A circle is shown in the coordinate plane. It is centered at 5, 3 and has a radius of 2 units.

The circle shown is reflected over the y-axis and then rotated counterclockwise 90° around the origin. Which of the following coordinate pairs represents the closest point that the transformed circle comes to the x-axis?

  1. (–5, –1)
  2. (–3, –3)
  3. (3, 3)
  4. (5, 1)
Answer
Correct Response: B.

Measurement, Data, and Probability

Objective 0011
Understand the fundamental principles of probability.

9. Four balls numbered 1, 2, 3, and 4 are in a bag. One ball is randomly chosen from the bag, and then another ball is randomly chosen without replacing the first ball. When the probability of selecting a specific order of two numbered balls is expressed as a fraction, which of the following numbers would be its denominator?

  1. 6
  2. 10
  3. 12
  4. 24
Answer
Correct Response: C.
Objective 0012
Understand descriptive statistics and the methods used in collecting, organizing, reporting, and analyzing data.

10. Use the box plot below to answer the question that follows.

a box and whisker plot that displays data about the number of apples per tree

A box and whisker plot that displays data about the number of apples per tree is shown. The 5-number summary is described by the values 400, 550, 600, 650, and 800.

The box plot summarizes the data for apples produced per tree on an orchard in one season. Which of the following statements about the data is true?

  1. Twenty-five percent of the trees produced at least 550 apples each.
  2. Fifty percent of the trees produced fewer than 650 apples each.
  3. Seventy-five percent of the trees produced at least 550 apples each.
  4. Seventy-five percent of the trees produced at least 650 apples each.
Answer
Correct Response: C.