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.

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

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 \(2: x = 44\)

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The Best Books to Ace 7th Grade IAR Math Test

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Frequently Asked Questions

Is there an IAR 7th grade math practice test?

Yes. The Illinois State Board of Education offers free grade 7 IAR practice tests on its website, built on the same online system used on test day. Work through the 10 sample questions here first to spot weak topics such as proportions or negative numbers, then take the official practice test in one sitting to get used to the pacing and on-screen tools.

Is there an IAR 7th grade math reference sheet?

Yes. Illinois provides a grade 7 math reference sheet for the IAR, and it is available during the test. It lists common measurement conversions and geometry formulas, such as those for circles and the volume of prisms. Download it from the ISBE practice materials and use it while you practice, so you know where each formula sits before test day.

What is covered in 7th grade math?

Seventh grade math focuses on ratios and proportional relationships, operations with positive and negative numbers, and solving two-step equations and inequalities like 3x − 5 = 16. Students also work with scale drawings, circle area and circumference, surface area and volume, and simple probability. Percent problems such as tax, tips and discounts show up often on the IAR.

What are the Illinois 7th grade math standards?

Illinois uses the Illinois Learning Standards for math, which are based on the Common Core. For grade 7 they fall into five domains: Ratios and Proportional Relationships, The Number System, Expressions and Equations, Geometry, and Statistics and Probability. The full list is on the ISBE website, and every sample question here is tied to one of these domains.

Can 7th graders take Algebra 1?

Some can. Many Illinois districts offer an accelerated path where strong students take Algebra 1 in 7th or 8th grade, usually based on test scores and teacher recommendation. Students on that path still need a firm grip on 7th grade skills like proportions and integer operations, since Algebra 1 builds right on them. Ask your school about its placement rules.

How do you pass 7th grade math?

Keep up with daily homework, and fix gaps early, especially with negative numbers and fractions, since later units depend on them. Practice a few mixed problems each week instead of cramming, show your steps so you can find mistakes, and ask your teacher as soon as a topic feels shaky. Checking your answers against worked solutions, like the ones here, helps a lot.

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.