General Knowledge
For Testing until 12/31/2023
Mathematics Subtest
Test Format and Sample Questions
The Mathematics Subtest consists of approximately 35 multiple-choice questions and is 100 minutes long.
Each of the questions will contain four response options. You will choose the best response out of the available options, and indicate A, B, C, or D. For the Mathematics Subtest, an on-screen 4-function calculator and a mathematics reference sheet will be provided.
The table below presents types of questions on the exam and directs you to examples of these formats among the sample items that follow.
Table of Question Formats
Type of Question | Sample Question |
---|---|
Scenario Examine a situation, problem, or case study. Then answer a question, make a diagnosis, or recommend a course of action by selecting the best response option. |
Question 2 |
Word Problem Apply mathematical principles to solve a real-world problem. |
Question 7 |
Direct Question Choose the response option that best answers the question. |
Question 18 |
Command Select the best response option. |
Question 19 |
Graphics Choose the option that best answers a question involving a number line, a geometric figure, graphs of lines or curves, a table, or a chart. |
Question 34 |
Sample Questions
The following questions represent both the form and content of questions on the examination. These questions will acquaint you with the general format of the examination; however, these sample questions do not cover all of the competencies and skills that are tested and will only approximate the degree of examination difficulty.
Question 1
Mathematics Subtest
Competency 1—Knowledge of number sense, concepts, and operations
Which of the following symbols should be placed in the box to form a true statement?
- Enter to expand or collapse answer.Answer expanded
- Correct Response: C.
Question 2
Mathematics Subtest
Competency 1—Knowledge of number sense, concepts, and operations
The regular price of a computer is 1200 dollars and the regular price of a printer is 300 dollas. An electronics store has a promotion that offers a 40 percent discount on the printer when the computer is purchased at the regular price. What is the total cost of the computer and the printer at the promotional price?
- Enter to expand or collapse answer.Answer expanded
- Correct Response: B.
Question 3
Mathematics Subtest
Competency 1—Knowledge of number sense, concepts, and operations
Which of the following symbols should be placed in the box to form a true statement?
- Enter to expand or collapse answer.Answer expanded
- Correct Response: C.
Question 4
Mathematics Subtest
Competency 1—Knowledge of number sense, concepts, and operations
Students in a mathematics class are allowed to drop their lowest quiz grade. If a student earns the following grades, which grade will be dropped?
six eights, two thirds, 73 percent, six tenth
- Enter to expand or collapse answer.Answer expanded
- Correct Response: D.
Question 5
Mathematics Subtest
Competency 1—Knowledge of number sense, concepts, and operations
An electronics store has a current inventory of 50 stereo systems. The lowest priced stereo system in the store sells for 800 dollars, and the highest priced stereo system sells for 3000 dollars. Which of the following is the maximum amount of 3000 dollar systems on hand if the current inventory totals 111,000 dollars?
- Enter to expand or collapse answer.Answer expanded
- Correct Response: B.
Question 6
Mathematics Subtest
Competency 1—Knowledge of number sense, concepts, and operations
Simplify.
left paren 15 minus 3 right paren divided by left paren 2 plus 1 right paren times left paren 8 minus 6 right paren
- Enter to expand or collapse answer.Answer expanded
- Correct Response: C.
Question 7
Mathematics Subtest
Competency 2—Knowledge of geometry and measurement
A building 51 feet tall casts a shadow 48 feet long. Simultaneously, a nearby statue casts a shadow of 16 feet. How tall is the statue?
- Enter to expand or collapse answer.Answer expanded
- Correct Response: A.
Question 8
Mathematics Subtest
Competency 2—Knowledge of geometry and measurement
A rectangular animal pen will be built using 200 meters of fencing. If one side of the rectangle is 60 meters, find the area of the pen.
- Enter to expand or collapse answer.Answer expanded
- Correct Response: C.
Question 9
Mathematics Subtest
Competency 2—Knowledge of geometry and measurement
Which of the following geometric figures must have perpendicular diagonals?
- Enter to expand or collapse answer.Answer expanded
- Correct Response: D.
Question 10
Mathematics Subtest
Competency 2—Knowledge of geometry and measurement
Select the geometric figure that possesses all of the following characteristics:
- quadrilateral
- diagonals that bisect each other
- at least one right angle
- Enter to expand or collapse answer.Answer expanded
- Correct Response: A.
Question 11
Mathematics Subtest
Competency 2—Knowledge of geometry and measurement
Which of the following best describes the faces for the following figure?
The figure is a solid with 2 visible faces, one triangular and one rectangular. The triangular face has a base labeled A, a height labeled B, and two angles dimensioned as 45 degrees. The rectangular face has the triangle's hypotenuse as one edge. The opposite edge is labeled C, and the base is labeled A.
- Enter to expand or collapse answer.Answer expanded
- Correct Response: D.
Question 12
Mathematics Subtest
Competency 2—Knowledge of geometry and measurement
Which of the following is the best estimate for the height of a kitchen refrigerator?
- Enter to expand or collapse answer.Answer expanded
- Correct Response: C.
Question 13
Mathematics Subtest
Competency 2—Knowledge of geometry and measurement
Which of the following is the best estimate for the height of a mountain?
- Enter to expand or collapse answer.Answer expanded
- Correct Response: C.
Question 14
Mathematics Subtest
Competency 2—Knowledge of geometry and measurement
How many square yards of carpet are needed to completely cover a rectangular floor that measures 15 feet by 9 feet?
- Enter to expand or collapse answer.Answer expanded
- Correct Response: B.
Question 15
Mathematics Subtest
Competency 2—Knowledge of geometry and measurement
A 3-foot-wide wood deck will be built around a rectangular-shaped pool that measures 15 feet by 30 feet. The resulting shape is also rectangular. If the lumber costs 10 dollars per square yard, what is the cost of the wood for the deck?
- Enter to expand or collapse answer.Answer expanded
- Correct Response: C.
Question 16
Mathematics Subtest
Competency 2—Knowledge of geometry and measurement
A teacher covered the exterior of a rectangular prism-shaped box that measured 8 inches by 9 inches by 10 inches using one sheet of rectangular-shaped wrapping paper that measured 2 feet by 3 feet. There were no gaps or overlapping paper. How many square inches of wrapping paper were left over?
- Enter to expand or collapse answer.Answer expanded
- Correct Response: B.
Question 17
Mathematics Subtest
Competency 2—Knowledge of geometry and measurement
A building contractor needs to compute the volume of air contained in a building with a rectangular floor, as shown in the figure below. The building is 20 feet long, 4 yards wide, 9 and a half feet high on two sides and 15 feet high from the floor to the peak. What is the volume of air in the building in cubic feet?
The figure shows a line drawing of a simple rectangular building with a peaked roof. The rectangular base is dimensioned as 4 yards wide and 20 feet long. One side wall is dimensioned as 9 and a half feet high. The end wall is dimensioned as 15 feet from the base to the peak of the roof.
- Enter to expand or collapse answer.Answer expanded
- Correct Response: C.
Question 18
Mathematics Subtest
Competency 3—Knowledge of algebraic thinking and the coordinate plane
Which of the following is a solution of the inequality?
negative 3 less than 2 x plus 1 less than 5
- Enter to expand or collapse answer.Answer expanded
- Correct Response: B.
Question 19
Mathematics Subtest
Competency 3—Knowledge of algebraic thinking and the coordinate plane
Solve for x.
4 x minus 1 over 5 equals 2 x plus 1
- Enter to expand or collapse answer.Answer expanded
- Correct Response: B.
Question 20
Mathematics Subtest
Competency 3—Knowledge of algebraic thinking and the coordinate plane
Find an algebraic expression equivalent to
- Enter to expand or collapse answer.Answer expanded
- Correct Response: B.
Question 21
Mathematics Subtest
Competency 3—Knowledge of algebraic thinking and the coordinate plane
A student argues that 4 left paren x minus 5 right paren minus left paren 6 x plus 1 right paren equals negative 2 x minus 19 Identify the first step that contains an error.
- STEP 1, 4 left paren x minus 5 right paren minus left paren 6 x plus 1 right paren equals 4 x minus 20 minus left paren 6 x plus 1 right paren
- STEP 2, 4 x minus 20 minus left paren 6 x plus 1 right paren equals 4 x minus 20 minus 6 x plus 1
- STEP 3, 4 x minus 20 minus 6 x plus 1 equals 4 x minus 6 x minus 20 plus 1
- STEP 4, 4 x minus 6 x minus 20 plus 1 equals negative 2 x minus 19
- Enter to expand or collapse answer.Answer expanded
- Correct Response: B.
Question 22
Mathematics Subtest
Competency 3—Knowledge of algebraic thinking and the coordinate plane
Find an algebraic expression equivalent to y over x plus 3 over 2 y
- Enter to expand or collapse answer.Answer expanded
- Correct Response: D.
Question 23
Mathematics Subtest
Competency 3—Knowledge of algebraic thinking and the coordinate plane
A consumer makes a down payment of 250 dollars and plans to pay 60 dollars per month for a phone service. If m is the number of months, which of the following equations represents T, the total price paid?
- Enter to expand or collapse answer.Answer expanded
- Correct Response: B.
Question 24
Mathematics Subtest
Competency 3—Knowledge of algebraic thinking and the coordinate plane
Which is true for x in the equation?
negative 5 x minus 2 is less than or equal to negative 3 x minus 8
- Enter to expand or collapse answer.Answer expanded
- Correct Response: C.
Question 25
Mathematics Subtest
Competency 3—Knowledge of algebraic thinking and the coordinate plane
Which of the following inequalities is the solution to the inequality shown?
10 c plus 5 is less than 4 c minus 1
- Enter to expand or collapse answer.Answer expanded
- Correct Response: A.
Question 26
Mathematics Subtest
Competency 3—Knowledge of algebraic thinking and the coordinate plane
Which of the following inequalities is the solution to the inequality shown?
5 z minus 9 is less than or equal to 6 z plus 2
- Enter to expand or collapse answer.Answer expanded
- Correct Response: B.
Question 27
Mathematics Subtest
Competency 3—Knowledge of algebraic thinking and the coordinate plane
Which of the following equations can be used to find the number of gallons of a 50 percent, alchohol solution, x, that should be mixed with 10 gallons of a 35 percent solution in order to get a 40 percent solution?
- Enter to expand or collapse answer.Answer expanded
- Correct Response: C.
Question 28
Mathematics Subtest
Competency 3—Knowledge of algebraic thinking and the coordinate plane
Which of the following graphs represents a function?
- Enter to expand or collapse answer.Answer expanded
- Correct Response: B.
Question 29
Mathematics Subtest
Competency 3—Knowledge of algebraic thinking and the coordinate plane
Which of the following best describes why the following is a function?
For students in a class, assign their height.
- Enter to expand or collapse answer.Answer expanded
- Correct Response: B.
Question 30
Mathematics Subtest
Competency 3—Knowledge of algebraic thinking and the coordinate plane
Which of the following relations is a function?
Each response is a pair of vertical ovoids, side by side. The left ovoid is labeled Input, and the right ovoid is labeled Output. Each has a set of numbers arranged inside in a vertical column. Arrows indicate a mapping from the Input numbers to the Output numbers.
- Enter to expand or collapse answer.Answer expanded
- Correct Response: B.
Question 31
Mathematics Subtest
Competency 3—Knowledge of algebraic thinking and the coordinate plane
Which of the following input/output tables represents a function?
- Enter to expand or collapse answer.Answer expanded
- Correct Response: D.
Question 32
Mathematics Subtest
Competency 3—Knowledge of algebraic thinking and the coordinate plane
The equation of line A is given by 2 y minus x equals 6 Select the equation that could represent line B.
Two lines, labeled Line A and Line B, are plotted on an x, y graph. Line A extends from the upper right quadrant, through the upper left quadrant, into the lower left quadrant. Line B extends from the upper left quadrant, through the upper right quadrant, into the lower right quadrant.
- Enter to expand or collapse answer.Answer expanded
- Correct Response: C.
Question 33
Mathematics Subtest
Competency 4—Knowledge of probability, statistics, and data interpretation
The children in a family are ages 2, 2, 6, 12, 16, 19, and 20. What is the mean of the children's ages?
- Enter to expand or collapse answer.Answer expanded
- Correct Response: B.
Question 34
Mathematics Subtest
Competency 4—Knowledge of probability, statistics, and data interpretation
If the company would like to give the impression that its employees are highly paid, which salary statistics should it use?
Employee Salaries
employee salaries table Title Yearly salary President 120,000 dollars Office manager 40,000 Foreperson 60,000 Laborer 1 15,000 Laborer 2 15,000 Laborer 3 15,000 Laborer 4 15,000
- Enter to expand or collapse answer.Answer expanded
- Correct Response: D.
Question 35
Mathematics Subtest
Competency 4—Knowledge of probability, statistics, and data interpretation
Eight pumpkins were picked from a garden. Their weights were 8 pounds, 3 pounds, 7 pounds, 16 pounds, 8 pounds, 13 pounds, 12 pounds, and 1 pound. How much greater than the mean was the heaviest pumpkin?
- Enter to expand or collapse answer.Answer expanded
- Correct Response: B.
Question 36
Mathematics Subtest
Competency 4—Knowledge of probability, statistics, and data interpretation
A child has 26 pennies, 15 nickels, 21 dimes, and 18 quarters in a coin bank. When the child picks up the bank, a single coin falls out. What is the probability that the coin is a quarter?
- Enter to expand or collapse answer.Answer expanded
- Correct Response: B.
Question 37
Mathematics Subtest
Competency 4—Knowledge of probability, statistics, and data interpretation
A consultant uses the following graph to justify why air-conditioning costs were higher in 2014 than in 2015. What aspect of the graph makes it misleading?
The graph is a bar graph. The vertical axis is labeled Number of Days Temperature above 80°F, with values marked from 50 to 55 in increments of 1. The horizontal axis is labeled Year, with values marked 2011, 2014, and 2015. The 2011 bar has a value of 50. The 2014 bar has a value of 53. The 2015 bar has a value of 51.
- Enter to expand or collapse answer.Answer expanded
- Correct Response: B.
Question 38
Mathematics Subtest
Competency 4—Knowledge of probability, statistics, and data interpretation
What is the median of the numbers in the following data set?
14, 14, 12, 8, 14, 8, 14, 4
- Enter to expand or collapse answer.Answer expanded
- Correct Response: C.
Question 39
Mathematics Subtest
Competency 4—Knowledge of probability, statistics, and data interpretation
A basketball coach would like to know the total number of points the team scored in a 15-game season. Which of the following measures would provide the coach with the additional information needed to make this determination?
- Enter to expand or collapse answer.Answer expanded
- Correct Response: A.
Question 40
Mathematics Subtest
Competency 4—Knowledge of probability, statistics, and data interpretation
A teacher gives a test and notes that the mean is 79 points and the standard deviation is 2 points. Which of the following is the best interpretation of this result?
- Enter to expand or collapse answer.Answer expanded
- Correct Response: B.
Question 41
Mathematics Subtest
Competency 4—Knowledge of probability, statistics, and data interpretation
The owner of a roller-skating rink needs to purchase women's skates. After reading that the mean women's shoe size is a seven, the owner decides to purchase mostly women's size seven skates. Which of the following statements, if true, best supports the owner's decision?
- Enter to expand or collapse answer.Answer expanded
- Correct Response: C.
Question 42
Mathematics Subtest
Competency 4—Knowledge of probability, statistics, and data interpretation
A marketing company wants to determine consumer attitudes about a brand of soap in a particular city. Which of the following groups would make the best survey sample?
- Enter to expand or collapse answer.Answer expanded
- Correct Response: C.
Question 43
Mathematics Subtest
Competency 4—Knowledge of probability, statistics, and data interpretation
An ecologist takes a 0.05-milliliter drop of water from a stream and examines it under a microscope. The ecologist counts 25 examples of a particular microscopic organism. Using ratio and proportion, the ecologist infers that there are 0.5 million of these organisms per liter of water in the stream.
Which of the following is the most important assumption that the ecologist makes with this inference?
- Enter to expand or collapse answer.Answer expanded
- Correct Response: A.
Question 44
Mathematics Subtest
Competency 4—Knowledge of probability, statistics, and data interpretation
A company's human resources department is tracking the percentage of employees out sick and the relative humidity of the air in the building. Which of the following conclusions can best be inferred using the following data?
The data is plotted on a scatter graph. The vertical axis is labeled Employees Out Sick left paren percentage symbol right paren, with values marked from 0 to 25 in increments of 5. The horizontal axis is labeled Relative Humidity left paren percentage symbol right paren, with values marked from 0 to 100 in increments of 20. The data points cluster tightly in a band from the origin to the upper right extreme of the graph.
- Enter to expand or collapse answer.Answer expanded
- Correct Response: B.
Question 45
Mathematics Subtest
Competency 4—Knowledge of probability, statistics, and data interpretation
The mayor of a city announces that there were 50 percent fewer automobile accidents this year than last year. Which of the following is the most important additional piece of information needed to properly interpret these results?
- Enter to expand or collapse answer.Answer expanded
- Correct Response: A.