NumicornNumicornLearn, solve, progress

Illinois State Assessments · IAR Math

Illinois IAR Math Practice Test

Build Illinois mathematics readiness with five focused 10-question practice sets covering number, algebra, geometry, measurement, data, probability, and problem solving.

Illinois IAR Math practice sets

This Illinois IAR Math Practice Test page provides five short practice sets with 10 original multiple-choice questions each. The sets cover number and operations, expressions and equations, geometry and measurement, data and probability, and integrated multi-step problem solving.

IAR Math skills

The Illinois State Board of Education describes IAR mathematics as an assessment for Grades 3–8 that requires students to reason about quantities and relationships in real-world situations. These supplemental sets practice computation, fractions and decimals, algebraic thinking, geometry, measurement, statistics, probability, and mathematical reasoning.

How to use this page

Complete one 10-question set at a time. Show your work, check units and labels, then review the explanation after each response.

This is supplemental State Test Practice, State Assessment Practice, and Standardized Test Practice. It does not replace current Illinois State Board of Education guidance, official materials, accommodations, tool policies, or testing procedures.

For broader grade-level study paths, explore Elementary School Tests, Middle School Tests, and High School Tests.

Select a test

5 Tests
1. Test2. Test3. Test4. Test5. Test

3. Test

Illinois IAR Math Practice Questions

A 10-question Illinois IAR Math practice set on geometry and measurement, with answers and explanations.

Read each problem, graph, table, or model carefully, choose one answer, and review the explanation after responding.

10 Questions
0/10 Questions0 %
Correct 0
Incorrect 0
Unanswered 10
1. QuestionMultiple choice

What is the area of a rectangle that is 8 units long and 6 units wide?

Please select an answer first.

Correct answer: A

The correct answer is 48 square units.

  1. Read the IAR math task: Identify the quantities, operation, representation, or relationship the problem asks you to use.
  2. Show the reasoning: Area equals length times width: 8 × 6 = 48 square units.
  3. Check the result: Confirm that the answer is reasonable and that units, labels, and conditions are included.

Area equals length times width: 8 × 6 = 48 square units.

2. QuestionMultiple choice

A square has side length 11 centimeters. What is its perimeter?

Please select an answer first.

Correct answer: B

The correct answer is 44 centimeters.

  1. Read the IAR math task: Identify the quantities, operation, representation, or relationship the problem asks you to use.
  2. Show the reasoning: A square has four equal sides, so 4 × 11 = 44 centimeters.
  3. Check the result: Confirm that the answer is reasonable and that units, labels, and conditions are included.

A square has four equal sides, so 4 × 11 = 44 centimeters.

3. QuestionMultiple choice

What is the volume of a rectangular prism measuring 4 units by 3 units by 5 units?

Please select an answer first.

Correct answer: C

The correct answer is 60 cubic units.

  1. Read the IAR math task: Identify the quantities, operation, representation, or relationship the problem asks you to use.
  2. Show the reasoning: Volume equals 4 × 3 × 5 = 60 cubic units.
  3. Check the result: Confirm that the answer is reasonable and that units, labels, and conditions are included.

Volume equals 4 × 3 × 5 = 60 cubic units.

4. QuestionMultiple choice

A right angle measures how many degrees?

Please select an answer first.

Correct answer: D

The correct answer is 90 degrees.

  1. Read the IAR math task: Identify the quantities, operation, representation, or relationship the problem asks you to use.
  2. Show the reasoning: A right angle is defined as 90 degrees.
  3. Check the result: Confirm that the answer is reasonable and that units, labels, and conditions are included.

A right angle is defined as 90 degrees.

5. QuestionMultiple choice

A triangle has angles of 35 degrees and 75 degrees. What is the third angle?

Please select an answer first.

Correct answer: A

The correct answer is 70 degrees.

  1. Read the IAR math task: Identify the quantities, operation, representation, or relationship the problem asks you to use.
  2. Show the reasoning: Triangle angles total 180 degrees, so 180 − 35 − 75 = 70 degrees.
  3. Check the result: Confirm that the answer is reasonable and that units, labels, and conditions are included.

Triangle angles total 180 degrees, so 180 − 35 − 75 = 70 degrees.

6. QuestionMultiple choice

A map uses a scale of 1 inch for 5 miles. How many miles are represented by 7 inches?

Please select an answer first.

Correct answer: B

The correct answer is 35 miles.

  1. Read the IAR math task: Identify the quantities, operation, representation, or relationship the problem asks you to use.
  2. Show the reasoning: Multiply 7 inches by 5 miles per inch to get 35 miles.
  3. Check the result: Confirm that the answer is reasonable and that units, labels, and conditions are included.

Multiply 7 inches by 5 miles per inch to get 35 miles.

7. QuestionMultiple choice

A circle has radius 4 units. Using pi as 3.14, what is its circumference approximately?

Please select an answer first.

Correct answer: C

The correct answer is 25.12 units.

  1. Read the IAR math task: Identify the quantities, operation, representation, or relationship the problem asks you to use.
  2. Show the reasoning: Circumference is approximately 2 × 3.14 × 4 = 25.12 units.
  3. Check the result: Confirm that the answer is reasonable and that units, labels, and conditions are included.

Circumference is approximately 2 × 3.14 × 4 = 25.12 units.

8. QuestionMultiple choice

Point A is at (3, 2). It moves 5 units left and 4 units up. What are the new coordinates?

Please select an answer first.

Correct answer: D

The correct answer is (-2, 6).

  1. Read the IAR math task: Identify the quantities, operation, representation, or relationship the problem asks you to use.
  2. Show the reasoning: Subtract 5 from the x-coordinate and add 4 to the y-coordinate.
  3. Check the result: Confirm that the answer is reasonable and that units, labels, and conditions are included.

Subtract 5 from the x-coordinate and add 4 to the y-coordinate.

9. QuestionMultiple choice

A line segment from (2, 4) to (2, 13) is how long?

Please select an answer first.

Correct answer: A

The correct answer is 9 units.

  1. Read the IAR math task: Identify the quantities, operation, representation, or relationship the problem asks you to use.
  2. Show the reasoning: The x-coordinate stays the same, so subtract the y-values: 13 − 4 = 9.
  3. Check the result: Confirm that the answer is reasonable and that units, labels, and conditions are included.

The x-coordinate stays the same, so subtract the y-values: 13 − 4 = 9.

10. QuestionMultiple choice

A rectangular garden has a perimeter of 34 meters and a length of 12 meters. What is its width?

Please select an answer first.

Correct answer: B

The correct answer is 5 meters.

  1. Read the IAR math task: Identify the quantities, operation, representation, or relationship the problem asks you to use.
  2. Show the reasoning: 2(12 + w) = 34, so 12 + w = 17 and w = 5.
  3. Check the result: Confirm that the answer is reasonable and that units, labels, and conditions are included.

2(12 + w) = 34, so 12 + w = 17 and w = 5.

Previous testNext test

Choose your next study path

Illinois State Test Practice

Review integrated Illinois IAR and ISA-style reading, math, science, data, and evidence questions.

Illinois IAR ELA Practice Test

Practice Illinois IAR reading, vocabulary, language, evidence, revision, and writing skills.

Elementary School Tests

Build foundational reading, math, science, and social studies skills for Grades 1–5.

Middle School Tests

Review grade-level ELA, math, science, and social studies skills for Grades 6–8.

High School Tests

Explore course and assessment preparation for Grades 9–12.

Pomodoro Timer

Use focused study intervals to work through your next practice set.

Frequently asked questions about Illinois IAR Math Practice

Which grades are covered by Illinois IAR Math?

The Illinois State Board of Education states that IAR mathematics is available in Grades 3–8. Check the official IAR page for current assessment information.

Which math skills are included?

The practice sets include number and operations, fractions and decimals, expressions and equations, geometry, measurement, data, statistics, probability, and multi-step reasoning.

Are these official IAR questions?

No. These are original supplemental practice questions. Check the official Illinois State Board of Education IAR page for current practice items, tool policies, accommodations, and testing procedures.