7th Grade IAR Math FREE Sample Practice Questions

One of the main points that 7th-grade students should pay attention to is that after reviewing the contents of the Illinois Assessment of Readiness (IAR) math test, they should use the sample practice questions to become more proficient. Using these sample practice questions plays an important role in increasing their confidence on the day of the IAR math test.

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If you are one of the 7th-grade students who do not know where to find IAR math sample test practice questions, we will guide you in this article. In fact, in this article, we have collected the best sample practice questions to pave the way for your success in the 7th-grade IAR math test.

To pass the IAR 2026 math test, just use our sample practice questions. These questions have all the implications you need for the test.

Also, be sure to follow some of the related links at the bottom of this post to get a better understanding of what kind of math questions 7th-grade students should practice.

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Common Core Math Exercise Book for Grade 7 Student Workbook and Two Realistic Common Core Math Tests

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10 Sample 7th Grade IAR Math Practice Questions

1- A chemical solution contains \(4\%\) alcohol. If there are \(24 ml\) of alcohol, what is the volume of the solution?

A. \(240 ml\)

B. \(480 ml\)

C. \(600 ml\)

D. \(1200 ml\)

2- The price of a laptop is decreased by \(10\%\) to \($360\). What is its original price?

A. \(320\)

B. \(380\)

C. \(400\)

D. \(450\)

3- What is the median of these numbers? \(4, 9, 13, 8, 15, 18, 5\)

A. \(8\)

B. \(9\)

C. \(13\)

D. \(15\)

4- Three times the price of a laptop is equal to five times the price of a computer. If the price of the laptop is \($200\) more than a computer, what is the price of the computer?

A. \(300\)

B. \(500\)

C. \(800\)

D. \(1500\)

5- What is the perimeter of a square that has an area of \(595.36\) feet?

6- Jason is \(9\) miles ahead of Joe running at \(5.5\) miles per hour and Joe is running at the speed of \(7\) miles per hour. How long does it take Joe to catch Jason?

A. \(3\) hours

B. \(4\) hours

C. \(6\) hours

D. \(8\) hours

7- \(55\) students took an exam and \(11\) of them failed. What percent of the students passed the exam?

A. \(20 \%\)

B. \(40 \%\)

C. \(60 \%\)

D. \(80 \%\)

8- Jason needs an \(75\%\) average in his writing class to pass. On his first \(4\) exams, he earned scores of \(68\%, 72\%, 85\%,\) and \(90\%\). What is the minimum score Jason can earn on his fifth and final test to pass?

9- A bank is offering \(3.5\%\) simple interest on a savings account. If you deposit \($12,000\), how much interest will you earn in two years?

A. \($420\)

B. \($840\)

C. \($4200\)

D. \($8400\)

10- \(5\) less than twice a positive integer is \(83\). What is the integer?

A. \(39\)

B. \(41\)

C. \(42\)

D. \(44\)

Best 7th Grade IAR Math Workbook Resource

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Answers:

2- C
Let \(x\) be the original price.
If the price of a laptop is decreased by \(10\%\) to \($360\), then:
\(90 \%\) of\( x=360 ⇒ 0.90x=360 ⇒ x=360÷0.90=400\)

3- B
Write the numbers in order:
\(4, 5, 8, 9, 13, 15, 18\)
Since we have \(7\) numbers (\(7\) is odd), then the median is the number in the middle, which is \(9\).

4- A
Let L be the price of a laptop and C be the price of a computer.
\(3\)(L) \(=5\)(C) \(\space\) and \(\space\) L \(= $200 +\) C
Therefore, \(3($200 +\) C\()=5\)C \(⇒ $600 + 3\)C \(= 5\)C \(⇒\) C\(=$300\)

5- 97.6
Use the area of the square formula.
\(S = a^2 ⇒ 595.36 = a^2 ⇒ a = 24.4\)
Use the perimeter of the square formula.
\(P = 4a ⇒ P=4(24.4) ⇒ P = 97.6\)

6- C
The distance between Jason and Joe is \(9\) miles. Jason running at \(5.5\) miles per hour and Joe is running at the speed of 7 miles per hour. Therefore, every hour the distance is \(1.5\) miles less.
\(9 ÷ 1.5 = 6\)

7- D
The failing rate is \(11\) out of \(55 = \frac{11}{55}\).
Change the fraction to percent:
\(\frac{11}{55} ×100\%=20\%\)
\(20\) percent of students failed. Therefore, \(80\) percent of students passed the exam.

8- 60
Jason needs an \(75\%\) average to pass five exams. Therefore, the sum of \(5\) exams must be at least \(5 × 75 = 375\)
The sum of \(4\) exams is:
\(68 + 72 + 85 + 90 = 315\)
The minimum score Jason can earn on his fifth and final test to pass is:
\(375 – 315 = 60\)

9- B
Use simple interest formula:
\(I=prt\)
(I = interest, p = principal, r = rate, t = time)
\(I=(12000)(0.035)(2)=840\)

10- D
Let \(x\) be the integer. Then:
\(2x – 5 = 83\)
Add \(5\) both sides: \(2x = 88\)
Divide both sides by \(2: x = 44\)

Looking for the best resource to help you succeed on the IAR Grade 7 Math test?

The Best Books to Ace 7th Grade IAR Math Test

Frequently Asked Questions

What is the IAR test?

The Illinois Assessment of Readiness (IAR) is Illinois\’s annual state test in math and English language arts for grades 3 through 8. It replaced the older PARCC test and follows the Illinois Learning Standards (closely aligned to Common Core).

Which math topics dominate the 7th grade IAR?

Proportional relationships (constant of proportionality, percent applications), rational-number operations, two-step equations and inequalities, geometry (scale drawings, circles, prisms), and basic probability.

How long is the IAR math test?

About two hours split across two sessions. The first session is non-calculator; later sessions allow the embedded online calculator.

Are calculators allowed on the IAR?

On part of the test. The opening session prohibits calculators. The remaining sessions allow the basic scientific calculator built into the testing platform. Practice in both modes so the switch is not a distraction.

What types of questions appear?

Three main types: standard multiple-choice (pick one), multi-select (pick all that apply), and technology-enhanced items (drag-and-drop, fill in a table, plot a point, select from a drop-down). Each type rewards careful reading of directions.

Does the IAR have multi-part questions?

Yes. Many items have multiple parts (Part A, Part B, etc.). Each part is scored independently. Always answer every part — leaving Part B blank because you weren\’t sure about Part A loses points unnecessarily.

Are there time limits on individual sessions?

Each session has a recommended time, but most schools give students additional time as needed within the session window. The test is more about thoughtful answers than racing the clock.

How is the IAR scored?

Performance is reported on a 5-level scale. Levels 4 (Meeting) and 5 (Exceeding) indicate the student is on track for the next grade; levels 1-3 indicate the student would benefit from additional support.

What is the best last-week-before-test routine?

Light review only — re-read the short lessons that felt shaky, work a few examples slowly, and stop early the night before to rest. Cramming new content the final week tends to backfire.

Are sample questions enough to prepare?

They are a good start, but full-length practice tests in test conditions matter more. Sample questions teach the format; full tests teach the pacing, the fatigue management, and the rhythm of the actual assessment.

Related Lessons You May Like

• How to add and subtract integers
• How to solve proportional ratios
• How to solve percent of change
• How to solve one-step equations
• How to solve multi-step word problems

If you want a workbook that lines up with these questions one chapter at a time, Mastering Grade 7 Math covers every Grade 7 standard with patient explanations and lots of practice. For extra word-problem reps, Mastering Grade 7 Math Word Problems is a strong companion.