# Study Guide

## Sample Selected-Response Questions

Field 99: Adult Education: Mathematics

### Practice Questions

#### Subarea I–Number Sense and Algebraic Thinking

##### Objective 0001: Demonstrate knowledge of number properties and number operations, and apply quantitative reasoning and problem-solving skills.

1. A student earns 15 dollars per hour plus a 5.5% commission on sales at a part-time job. The past month, after working 18 hours, the student earned a total of 350 dollars. To the nearest dollar, what was the amount of the student's sales that month?

- 440 dollars
- 636 dollars
- 1,455 dollars
- 1,925 dollars

- Enter to expand or collapse answer. Answer expanded
**Correct Response: C.**

##### Objective 0001: Demonstrate knowledge of number properties and number operations, and apply quantitative reasoning and problem-solving skills.

2. Rangers at a lake in a wildlife preserve have to estimate the size of a Canadian goose population. The rangers trapped 40 geese and fitted them with neckbands. A week later, the rangers returned and counted 220 geese, of which 15 had neckbands. What is the approximate size of the goose population at this preserve?

- 245
- 303
- 415
- 587

- Enter to expand or collapse answer. Answer expanded
**Correct Response: D.**

##### Objective 0002: Demonstrate knowledge of fundamental principles and applications of algebra to model and solve problems.

3. A salesperson's automobile averages 30 miles per gallon in the city and 42 miles per gallon on the highway. Using a total of 12 gallons of gasoline, the salesperson drove 474 miles. Approximately how many miles were driven on the highway?

- 105 miles
- 277 miles
- 285 miles
- 399 miles

- Enter to expand or collapse answer. Answer expanded
**Correct Response: D.**

##### Objective 0002: Demonstrate knowledge of fundamental principles and applications of algebra to model and solve problems.

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

The diagram shows a rectangle which measures ten inches wide by eight inches tall. This rectangle is enclosed within a larger rectangle. There are Xs between arrows pointing in opposite directions indicating the space between each side of the interior rectangle and each side of the exterior rectangle.

An 8 inch by 10 inch picture is to be framed by an oak border of uniform width. To keep a low weight for the frame, the total area of the border cannot exceed 120 square inches. Which equation can be used to find the maximum width of the border?

- x squared plus nine x minus ten equals zero
- x squared plus nine x minus thirty equals zero
- x squared plus eighteen x minus forty equals zero
- x squared plus eighteen x minus hundred twenty equals zero

- Enter to expand or collapse answer. Answer expanded
**Correct Response: B.**

#### Subarea II–Geometry & Measurement and Data Analysis, Statistics & Probability

##### Objective 0003: Demonstrate knowledge of fundamental principles and applications of geometry and measurement.

5. A homeowner is building an aluminum ramp for a power wheelchair to a porch that is 2 feet off the ground. The aluminum material cost 58 dollars per square foot. Using the maximum slope for power wheelchairs of 1.5 to 12 and a surface width of 42 inches, approximately how much will the surface of the ramp cost?

- 3676 dollars
- 3273 dollars
- 3654 dollars
- 3248 dollars

- Enter to expand or collapse answer. Answer expanded
**Correct Response: B.**

##### Objective 0004: Demonstrate knowledge of fundamental principles and applications of data analysis, statistics, and probability.

6. **Use the graph below to answer the question that follows.**

The vertical axis is labeled frequency and lists values from zero to ten in increments of one. The horizontal axis is labeled highway mileage left paren m p g right paren and begins with an axis break followed by values from 24 to 51 listed in increments of three. The values of the bars are as follows:

24 to 27 m p g, frequency 1

27 to 30 m p g, frequency 7

30 to 33 m p g, frequency 4

33 to 36 m p g, frequency 5

36 to 39 m p g, frequency 1

39 to 42 m p g, frequency 0

42 to 45 m p g, frequency 0

45 to 48 m p g, frequency 0

48 to 51 m p g, frequency 1

The histogram shows the highway miles per gallon of different vehicles. What is the best estimate of the median number of miles per gallon for the data shown?

- 27 mpg
- 28 mpg
- 32 mpg
- 37 mpg

- Enter to expand or collapse answer. Answer expanded
**Correct Response: C.**