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

This scenario forms a right triangle with the ladder as the hypotenuse (c=25 ft), the distance from the wall as one leg (a=7 ft), and the height on the wall as the other leg (b). Using the Pythagorean theorem, a² + b² = c², we can solve for b: 7² + b² = 25². This simplifies to 49 + b² = 625. Subtracting 49 from both sides gives b² = 576. Taking the square root of 576 gives b = 24 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 value 150 is an outlier, which significantly affects the mean but not the median. The median is the middle value of the ordered set, which is 55. The mean is the sum of the values (477) divided by the count (7), which is approximately 68.14. Because the outlier pulls the average up, the mean is greater than the median.

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

The problem can be modeled with two separate equations. The first equation represents the total number of tickets sold: the number of adult tickets (a) plus the number of child tickets (c) equals 200. The second equation represents the total revenue: the price per adult ticket times the number of adult tickets (12a) plus the price per child ticket times the number of child tickets (8c) equals the total revenue of $2,050.

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

This problem can be solved by setting up a proportion: (1 inch / 25 miles) = (5.2 inches / x miles). To find the unknown distance 'x', you can cross-multiply: 1 * x = 25 * 5.2. The calculation 25 * 5.2 equals 130. Therefore, the actual distance between the cities is 130 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

In the standard compound interest formula, A = P(1 + r/n)^(nt), 'r' is the annual interest rate and 'n' is the number of times the interest is compounded per year. Here, 0.03 is the annual rate (r) and 4 is the number of compounding periods (n). The term r/n, or 0.03/4, represents the interest rate that is applied for each compounding period (quarterly, in this case).

IAR Practice Test

IAR Practice Test

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