Test Information Guide

Field 09: Mathematics
Sample Multiple-Choice Questions

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The following reference material will be available to you during the test:

Formulas PDF opens in new window.

Candidates taking the Mathematics test (field 09) will be provided with an on-screen scientific calculator with functions that include the following: addition, subtraction, multiplication, division, square root, percent, sine, cosine, tangent, exponents, and logarithms. You may NOT bring your own calculator to the test.

Number Sense and Operations

Objective 0002
Understand the properties of real and complex numbers and the real and complex number systems.
  1. associative
  2. distributive
  3. commutative
  4. transitive
Answer
Correct Response: A.

Correct Response: A.


Objective 0003
Understand the principles of number theory.
  1. 2
  2. 6
  3. 42
  4. 84
Answer
Correct Response: B.

Correct Response: B.


Patterns, Relations, and Algebra

Objective 0005
Understand the properties of functions and relations.

3. Which of the following graphs represents a one-to-one function?


  1. Graph with a straight horizontal line below the x axis.


  2. Graph with a parabola with the vertex at the origin opened up to the right



Answer
Correct Response: C.

Correct Response: C.


Objective 0008
Understand the properties and applications of quadratic relations and functions.

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

Square P Q R S whose corners have been cut off to form a regular octagon.  Each side of the square is one centimeter long. Each side of the octagon is x.

The four corners of a square PQRS have been cut off to form a regular octagon, as shown in the diagram above. If each side of the square is 1 cm long, which of the following equations should be solved to find the length of each side of the octagon, x?

  1. x2 + 2x 1 = 0
  2. x2 4x + 2 = 0
  3. 3x2 + 2x 1 = 0
  4. 7x2 8x + 2 = 0
Answer
Correct Response: A.

Correct Response: A.


Objective 0010
Understand the properties and applications of exponential and logarithmic functions and relations.

5. If logx10 = 0.9603, which of the following is the best approximation of x?

  1. 7
  2. 9
  3. 11
  4. 13
Answer
Correct Response: C.

Correct Response: C.


Geometry and Measurement

Objective 0013
Prove theorems within the axiomatic structure of Euclidean geometry.

6. Use the geometric proof below to answer the question that follows.

Which of the following statements and reasons would be most appropriate in step 5 of this proof?

  1. Statement, Angle QPR is congruent to angle QPS.
	Reason, Line PQ is perpendicular to line RS.

  2. Statement, P is the center of the circle.
	Reason, Definition of a circle.

  3. Statement, Angle PSQ is congruent to angle PRQ.
	Reason, Properties of isosceles triangle.

  4. Statement, Line PQ is congruent to line PQ.
	Reason, Reflexive property of congruence.
Answer
Correct Response: D.

Correct Response: D.


Objective 0015
Understand the principles and properties of coordinate and transformational geometry and characteristics of non-Euclidean geometries.

7. The center of a town is located at (0, 0) on an x-y coordinate system with each grid unit measured in miles. A radio tower is located at the point (15, 20). The radio signal is strong enough to reach homes within a 40-mile radius. Which of the following inequalities represents all ground locations within 40 miles of the radio tower?

  1. (x 15)2 + (y + 20)2 ≤ 40
  2. (x + 15)2 + (y 20)2 ≤ 40
  3. (x 15)2 + (y + 20)2 ≤ 1600
  4. (x + 15)2 + (y 20)2 ≤ 1600
Answer
Correct Response: C.

Correct Response: C.


Data Analysis, Statistics, and Probability

Objective 0016
Understand the principles and concepts of descriptive statistics and their application to the problem-solving process.

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

The graph shows the distribution of the age of 50 cars in a parking lot. Rounded to the nearest whole number, the mean, μ, is 6 years and the standard deviation, σ, is 3 years. How many cars have an age within one standard deviation of the mean?

  1. 17
  2. 20
  3. 33
  4. 41
Answer
Correct Response: C.

Correct Response: C.


Trigonometry, Calculus, and Discrete Mathematics

Objective 0019
Understand the properties of trigonometric functions and identities.

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

The graph of which of the following equations is shown in the figure above?

  1. y = one half cos (2x)
  2. y = 2 cos open parenthesis x over two close parenthesis
  3. y = one half sin (2x)
  4. y = 2 sin open parenthesis x over two close parenthesis
Answer
Correct Response: C.

Correct Response: C.


Objective 0022
Understand integral calculus.

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

The graph above approximates an airplane's velocity, v, in miles per hour, during a four-hour-and-thirty-minute flight. The plane left the ground at a velocity of 100 mph and took 30 minutes to reach its cruising speed of 600 mph. One hour before landing it began to descend and landed at a velocity of 100 mph. Which of the following is the best estimate of the total distance in miles that the airplane flew while in the air?

  1. 1875
  2. 2175
  3. 2250
  4. 2325
Answer
Correct Response: D.

Correct Response: D.