# Study Guide

## Sample Selected-Response QuestionsField 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?

1. 440 dollars
2. 636 dollars
3. 1,455 dollars
4. 1,925 dollars
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?

1. 245
2. 303
3. 415
4. 587
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?

1. 105 miles
2. 277 miles
3. 285 miles
4. 399 miles
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?

1. x squared plus nine x minus ten equals zero
2. x squared plus nine x minus thirty equals zero
3. x squared plus eighteen x minus forty equals zero
4. x squared plus eighteen x minus hundred twenty equals zero
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?

1. 3676 dollars
2. 3273 dollars
3. 3654 dollars
4. 3248 dollars
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?

1. 27 mpg
2. 28 mpg
3. 32 mpg
4. 37 mpg