Test Information Guide

Field 53: Elementary Mathematics
Sample Multiple-Choice Questions

Expand All | Collapse All

Number Sense, Operations, and Data Analysis

Objective 0001
Understand number theory, the structure of numeration systems, and the properties of the real number system.

1. Simplify the expression start fraction numerator start cubed root x sup four end cubed root times start fourth root y cubed end fourth root denominator start cubed root x end cubed root times square root of y cubed end fraction.

  1. x sup four baseline y sup one half
  2. x y sup negative nine over four
  3. x sup negative nine over four baseline y
  4. x y sup negative three fourths
Answer
Correct Response: D.

Correct Response: D.

Objective 0002
Understand principles and operations related to integers.

2. Use the algorithms below to answer the question that follows.

A significant difference between the standard multiplication algorithm and the expanded multiplication algorithm is that the expanded multiplication algorithm:

  1. can be used with both positive and negative integers.
  2. emphasizes the use of the distributive property.
  3. minimizes the need to memorize multiplication facts.
  4. makes knowledge of place value unnecessary.
Answer
Correct Response: B.

Correct Response: B.

Objective 0003
Understand principles and operations related to fractions.

3. Simplify the expression below.

   start fraction numerator five over eight plus three over four denominator seven over eight minus three over five end fraction

  1. one half
  2. 2one half
  3. 4
  4. 5
Answer
Correct Response: D.

Correct Response: D.

Objective 0006
Understand the fundamental principles of probability.

4. A student rolls two dice. One die has six faces, each face marked with 1, 2, 3, 4, 5, or 6 spots, and the other die has eight faces, each marked with 1, 2, 3, 4, 5, 6, 7, or 8 spots. How many outcomes are in the sample space for this experiment?

  1. 14
  2. 28
  3. 48
  4. 64
Answer
Correct Response: C.

Correct Response: C.

Patterns, Relations, and Algebra

Objective 0007
Understand patterns and the properties of functions and relations.

5. Use the information below to answer the question that follows.

A particular function is defined as follows: Take any integer greater than zero. If the integer is even, multiply it by 2. If the integer is odd, add 1 and then multiply the result by 2.

What is the domain of the function?

  1. the number 2
  2. the set of even integers
  3. the set of odd integers
  4. the set of positive integers
Answer
Correct Response: D.

Correct Response: D.

Objective 0009
Understand properties and applications of linear relations and functions.

6. Use the inequality below to answer the question that follows.

   negative six less then or equal to start fraction x over three end fraction minus three less then or equals to five

Which of the following best represents the solution of the inequality above?

  1. number line ranging from negative thirty to thirty with a solid circle at about negative three solid line to the right up to solid circle at nine

  2. number line ranging from negative thirty to thirty with a solid circle at about negative seven solid line to the right up to a solid circle at five

  3. number line ranging from negative thirty to thirty with a solid circle at negative fifteen solid line to the right up to a solid circle at seventeen

  4. number line ranging from negative thirty to thirty with a solid circle at about negative nine solid line to the right up to a solid circle at twenty four
Answer
Correct Response: D.

Correct Response: D.

Objective 0011
Understand properties and applications of quadratic, exponential, polynomial, and rational functions and relations.

7. A scientist determines that the amount of mold growing in a laboratory culture triples every 4 days. If there is originally 0.5 grams of mold in the culture, which of the following equations best models the amount of mold, M, at a given time t?

  1. M = 0.5(3)0.25t
  2. M = 0.5(3)4t
  3. M = 3t + 0.5
  4. M = t3 + 0.5
Answer
Correct Response: A.

Correct Response: A.

Geometry and Measurement

Objective 0013
Understand the principles of Euclidean geometry and use them to prove theorems.

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

   Two triangles. Triangle c a t where line c a is eight units and line c t is twelve units triangle d o g where line d g is sixteen units.

If ΔCAT ∼ ΔDOG, what is the measure of line D O?

  1. 9one third
  2. 10two thirds
  3. 24
  4. 32
Answer
Correct Response: B.

Correct Response: B.

Objective 0014
Apply Euclidean geometry to analyze the characteristics and properties of two- and three-dimensional shapes.

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

   Right trapezoidal prism whose base is eight units, its top base is six units, its height is six units the length of the prism is eighteen units

The diagram shows a right trapezoidal prism. What is the area of a horizontal cross section of the prism, 3 units above and parallel to the base of the prism?

  1. 42
  2. 108
  3. 126
  4. 144
Answer
Correct Response: C.

Correct Response: C.

Objective 0015
Understand the principles and properties of coordinate and transformational geometry and use them to prove theorems.

10. An equilateral triangle is constructed on a set of coordinate axes. If one vertex is at the origin and another is at the point (a, 0), which of the following would be the y-coordinate of the third vertex of the triangle?

  1. start fraction numerator start square root three end square root a denominator two end fraction

  2. three a over four

  3. start fraction numerator start square root three end square root a denominator four end fraction

  4. three a over two
Answer
Correct Response: A.

Correct Response: A.