# Test Information Guide

## Field 47: Mathematics (Middle School) Sample Multiple-Choice Questions

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

Formulas

Calculators will NOT be provided for the Mathematics (Middle School) test.

### Number Sense and Operations

##### Objective 0002Understand principles and operations related to integers, fractions, decimals, percents, ratios, and proportions.

1. Use the sequence of steps below to answer the question that follows.

The sequence of steps above could be used to answer which of the following questions?

1. How can a decimal be converted to a fraction reduced to lowest terms?
2. Where should the decimal point be placed in the product of two decimals?
3. Why is it necessary to invert and multiply when solving problems involving fractions?
4. How is scientific notation used to multiply decimals?
Correct Response: B.

Correct Response: B.

##### Objective 0003Understand and solve problems involving integers, fractions, decimals, percents, ratios, and proportions.

2. Which of the following situations represents 2 ÷ ?

1. A 2-acre lot needs to be plowed. If four workers split the plowing evenly, how many acres will each person plow?
2. One side of a one-fourth-square-foot rectangle is 2 feet. How long is the other side?
3. Alix sawed off one fourth of a 2-yard log. How many yards did Alix saw off?
4. Terry picked 2 pounds of berries and put them into one-quarter-pound containers. How many containers of berries did Terry fill?
Correct Response: D.

Correct Response: D.

### Patterns, Relations, and Algebra

##### Objective 0007Understand properties of functions and relations.

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

Which of the following graphs represents the function described in the above diagram?

Correct Response: B.

Correct Response: B.

##### Objective 0008Understand properties and applications of linear relations and functions.

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

The graph shown above represents the relationship between the length of a geyser's eruption, ℓ, and the time until the next eruption, t. Which of the following linear equations best models the data?

1. t + 12ℓ = 33
2. 2t – 3ℓ = –66
3. 12ℓ – t = –33
4. 3ℓ + 2t = 66
Correct Response: C.

Correct Response: C.

##### Objective 0009Understand properties and applications of quadratic relations and functions.

5. In solving the quadratic equation x2 + 14x – 4 = –30 by completing the square, the first step is to add 4 to both sides of the equation. The second step is to:

1. add 49 to both sides of the equation.
2. factor x from the binomial x2 + 14x.
3. factor the number 2 from 14, –4, and 30.
4. take the square root of both sides of the equation.
Correct Response: A.

Correct Response: A.

### Geometry and Measurement

##### Objective 0012Understand the principles of Euclidean geometry and use them to prove theorems.

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?

Correct Response: D.

Correct Response: D.

##### Objective 0014Solve problems involving three-dimensional shapes.

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

Square corners, 5 units on a side, are removed from a 15-unit-by-25-unit rectangular piece of cardboard. The sides of the cardboard are then folded to form an open box. Which of the following is the volume, in cubic units, of the box?

1. 375
2. 625
3. 1000
4. 1125
Correct Response: A.

Correct Response: A.

### Data Analysis, Statistics, and Probability

##### Objective 0016Understand descriptive statistics and the methods used in collecting, organizing, reporting, and analyzing data.

8. Which of the following situations best represents a random sampling?

1. Ask every tenth person coming out of a health spa how many times a week they exercise to determine how often people in the town exercise.
2. Survey students in advanced biology classes to determine the average amount of time students in a certain school study each week.
3. Find the heights of all boys in a senior gym class to determine the average height of all boys in the school.
4. Count the number of chocolate chips in every fifth cookie to determine the average number of chocolate chips per cookie in a bag of cookies.
Correct Response: D.

Correct Response: D.

##### Objective 0017Understand the fundamental principles of probability.

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

A point is randomly selected within the rectangle shown in the diagram above. What is the probability that the y-coordinate of the point is less than or equal to 2?

Correct Response: C.

Correct Response: C.

### Trigonometry, Calculus, and Discrete Mathematics

##### Objective 0019Understand the conceptual basis of calculus.

10. The graph of the function f(x) = 2x2 – 6x + 4 has its minimum value at the point (, –). Which of the following statements must be true?

1. The derivative of f(x) is zero when x is equal to .
2. The value of f(x) approaches a limit of zero as x approaches .
3. The graph of f(x) shifts from a concave downward shape to a concave upward shape.
4. The slope of the line tangent to f(x) at x = is equal to –.