IAR - Illinois Assessment of Readiness Math Concepts and Reasoning Questions and Answers

Question 1

A firefighter leans a 25-foot ladder against a building. The base of the ladder is 7 feet from the building's wall. How high up the wall does the ladder reach?

Accepted Answer

24 feet

Answer

18 feet

Answer

26 feet

Answer

32 feet

Question 2

The following dataset represents the number of minutes 7 students spent on homework: {45, 50, 52, 55, 60, 65, 150}. Which of the following statements is true about the measures of central tendency for this dataset?

Accepted Answer

The mean is greater than the median.

Answer

The median is greater than the mean.

Answer

The mean and median are equal.

Answer

The mode is the most accurate measure of center.

Question 3

A movie theater sold 200 tickets for a total of $2,050. Adult tickets cost $12 each and child tickets cost $8 each. If 'a' represents the number of adult tickets and 'c' represents the number of child tickets, which system of equations correctly models this situation?

Accepted Answer

a + c = 200; 12a + 8c = 2050

Answer

a + c = 2050; 12a + 8c = 200

Answer

a - c = 200; 12a + 8c = 2050

Answer

12a + 8c = 200; a + c = 2050

Question 4

A map has a scale where 1 inch represents 25 miles. If the distance between two cities on the map is 5.2 inches, what is the actual distance between them?

Accepted Answer

130 miles

Answer

4.81 miles

Answer

30.2 miles

Answer

125.5 miles

Question 5

The expression 5000(1 + 0.03/4)^(4t) is used to calculate the value of an investment after 't' years. Which of the following best describes the meaning of the value 0.03/4 in this context?

Accepted Answer

The interest rate applied during each compounding period.

Answer

The number of times the interest is compounded per year.

Answer

The total interest earned after t years.

Answer

The annual interest rate.

Question 6

A cylindrical water tank has a radius of 5 feet and a height of 12 feet. What is the approximate volume of water the tank can hold? (Use π ≈ 3.14)

Accepted Answer

942 cubic feet

Answer

188.4 cubic feet

Answer

376.8 cubic feet

Answer

3,768 cubic feet

A firefighter leans a 25-foot ladder against a building.The base of the ladder is 7 feet from the building's wall.How high up the wall does the ladder reach?

A firefighter leans a 25-foot ladder against a building.
The base of the ladder is 7 feet from the building's wall.
How high up the wall does the ladder reach?