# Study Guide

## Test of Academic Proficiency

Sample Multiple-Choice Questions

### Field 403: Mathematics

Each multiple-choice question has four answer choices. Read each question and its answer choices carefully and choose the ONE best answer.

During the test you should try to answer all questions. Even if you are unsure of an answer, it is better to guess than not to answer a question at all. You will NOT be penalized for choosing an incorrect response.

**Standard 0014**

Solve problems involving integers, fractions, decimals, and units of measurement.

1. During a bike-a-thon, a local company pledges to donate $1.25 for every $4.00 pledged by the public. If the public pledges a total of $156.00 dollars per mile, how much will the company donate per mile?

- $2.75
- $48.75
- $195.00
- $499.20

- Answer
**Correct Response: B.**

**Standard 0014**

Solve problems involving integers, fractions, decimals, and units of measurement.

2. The nutritional label on a snack food indicates that one serving of the snack provides 20% of the daily adult requirement of protein. If one serving weighs 1 ounces, how many ounces of the snack food would provide 100% of the daily requirement of protein?

- 3 ounces
- 8 ounces
- 11.43 ounces
- 21 ounces

- Answer
**Correct Response: B.**

**Standard 0015**

Apply mathematical reasoning skills to analyze patterns and solve problems.

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

If the sequence above continues in the same pattern, how
many small triangles would be needed to make the figure that would
occur in **Step 5**?

- 16
- 25
- 36
- 49

- Answer
**Correct Response: B.**

**Standard 0015**

Apply mathematical reasoning skills to analyze patterns and solve problems.

4. When a student is questioned about his school, he replies that there are at least as many freshmen as there are juniors and at least as many juniors as there are sophomores. If the student is correct, which of the following statements must be true?

- There are just as many sophomores as there are freshmen.
- There are at least as many sophomores as there are freshmen.
- There are at least as many freshmen as there are sophomores.
- There are more freshmen than there are sophomores.

- Answer
**Correct Response: C.**

**Standard 0016**

Solve problems involving algebra and geometry.

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

The graph shows data collected by measuring the height, *h*, in
centimeters, of a burning candle at different times, *t*, in minutes.
Which of the following equations best represents the line drawn
through the data points?

*h*= –2*t*+ 10*h*= –*t*+ 10*h*= 2*t*+ 20*h*= 10*t*+ 20

- Answer
**Correct Response: B.**

**Standard 0016**

Solve problems involving algebra and geometry.

6. If 6*b* + 20 = *a*, and 4*b* + 30 = *a*, then *b* =

- –5
- –1
- 1
- 5

- Answer
**Correct Response: D.**

**Standard 0016**

Solve problems involving algebra and geometry.

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

The diagram above (not to scale) shows how an elementary student who is 4 feet tall estimates the height of a lamppost. The student stands 30 feet from the base of the lamppost and measures her shadow from the light as 6 feet long. Approximately how high is the lamppost?

- 20 feet
- 24 feet
- 36 feet
- 45 feet

- Answer
**Correct Response: B.**

**Standard 0016**

Solve problems involving algebra and geometry.

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

A metal worker is building a wire frame (represented by the dotted and solid lines in the diagram above) for a cubic box that is to have a volume of 27 cubic feet. What is the total length of wire the metal worker will need?

- 27 feet
- 36 feet
- 54 feet
- 81 feet

- Answer
**Correct Response: B.**

**Standard 0017**

Understand concepts and procedures related to data analysis and statistics.

9. **Use the pie charts below to answer the question that follows.**

The first pie chart represents a company's total expenditures, and the second pie chart shows a breakdown of the company's advertising expenditures. What percentage of the company's total expenditures is spent on radio advertising?

- 6.3%
- 11.7%
- 18.0%
- 35.0%

- Answer
**Correct Response: A.**

**Standard 0017**

Understand concepts and procedures related to data analysis and statistics.

10. Scientists have stocked Wilson's pond with a species of fish. The scientists note that the
population has steadily decreased over a period of time until the population is approximately half the
number of fish originally stocked. If the number of fish is plotted on the *y*-axis and the amount of time on
the *x*-axis, which of the following graphs represents the population of fish in the pond with respect to time?

- Answer
**Correct Response: A.**

**Standard 0017**

Understand concepts and procedures related to data analysis and statistics.

11. **Use the distribution curves below to answer the question that follows.**

The distribution curves above show data on the gas mileage for two different brands of car. Which of the following correctly analyzes the information presented in these distributions?

- The mean gas mileage of Brand A is greater than the mean gas mileage of Brand B.
- Data was collected for more cars of Brand A than of Brand B.
- Brand A cars have smaller variability in gas mileage than Brand B cars.
- Brand A cars get poorer gas mileage than Brand B cars.

- Answer
**Correct Response: C.**

**Standard 0018**

Solve applied problems using a combination of mathematical skills
(including word problems involving one and two variables).

12. **Use the diagram and the information below to answer the question that follows.**

A company has a right cylindrical storage tank for storing natural gas. The tank measures 20 feet wide by 60 feet high.

The company estimates that it will cost $2.00 per square foot to paint the tank. Which of the following expressions could be used to determine the total cost to paint the top and the side of the tank?

- (1200π + 100π)(2.00)
- (1200π + 200π)(2.00)

- Answer
**Correct Response: A.**

**Standard 0018**

Solve applied problems using a combination of mathematical skills
(including word problems involving one and two variables).

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

The diagram shows the dimensions of a triangular field next to a school. To estimate the number of wildflowers growing in the field, students counted a total of 36 flowers in a randomly selected 3-feet-by-4-feet rectangular section. Assuming the section is a representative sample of the entire field, approximately how many flowers are in the entire field?

- 17,500
- 35,000
- 90,000
- 180,000

- Answer
**Correct Response: C.**