7th Grade IAR Math Practice Test Questions

Have you fully reviewed the math content of the 7th-grade IAR exam? Now it’s time to test your math skills!
The questions in this article are a collection of 10 of the most common questions in the 7th-grade Illinois Assessment of Readiness (IAR) math test.

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These questions cover the most important math concepts of the 7th-grade IAR exam. Using these questions, 7th-grade students can assess themselves and realize how well they master the concepts of the 7th-grade IAR math test.

If you are a 7th-grade student and you want to take an important step in increasing your score, do not miss these 10 best questions!

Make sure to follow some of the related links at the bottom of this post to get a better idea of what kind of mathematics questions students need to 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 Prep 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, \(3($200 + C) =5C ⇒ $600 + 3C = 5C ⇒ C=$300\)

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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Frequently Asked Questions

How should we run a practice test at home?

Quiet room, timer, scratch paper, basic calculator for the allowed sections, and step away — no hints. Replicate the actual test conditions. Score the test the same day so the experience is fresh during review.

What is the most efficient way to review wrong answers?

For each wrong answer: rewrite the correct work step-by-step; name the specific concept involved; and write one sentence about what to do differently next time. Five carefully debriefed misses help more than fifty rushed problems.

How many full-length practice tests does a 7th grader need?

Two is usually plenty. The first establishes a baseline; the second confirms targeted improvements stuck. More than that often produces fatigue without much added benefit.

Should kids guess on IAR?

Yes — there is no penalty for wrong answers, and a blank counts the same as a wrong answer. Answer every part of every question, even if you have to estimate.

Which 7th-grade math topics give students the most trouble?

Three repeat offenders: sign mistakes in rational-number arithmetic, mixing up radius and diameter in circle problems, and rushing the setup of percent-of-change problems. Spending extra time on those three lifts most students\’ scores measurably.

How do I solve a two-step equation cleanly?

Undo operations in reverse order. For \( 4x + 9 = 25 \): subtract 9 (getting \( 4x = 16 \)), then divide by 4 (getting \( x = 4 \)). Always check by substituting back into the original.

How are technology-enhanced items handled?

Read the directions carefully — they often ask for more than a single answer (drag-and-drop, multi-select, fill in a chart). Always answer every component before clicking submit.

What is the area of a trapezoid?

Use \( A = \frac{1}{2}(b_1 + b_2) h \), where \( b_1 \) and \( b_2 \) are the parallel bases and \( h \) is the perpendicular height. Never confuse a slanted side for the height — the height must be perpendicular to both bases.

What is a fair pacing rule for a 7th grade IAR session?

About one minute per item is a reasonable rule of thumb. If a question runs past two minutes, flag it, move on, and return on a second pass with fresh eyes.

When do IAR scores come back?

Illinois generally releases individual student reports to schools in late summer or early fall after the spring test. Your school\’s testing coordinator has the current year\’s timeline.

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.