6th Grade IAR Math FREE Sample Practice Questions

We have compiled a collection of the most common sample practice questions for the Grade 6 Illinois Assessment of Readiness (IAR) math test for your convenience, and in this article, we have provided it to you. For additional educational resources, .

These sample practice questions cover the most important concepts in the IAR 2026 test, so by focusing on these sample practice questions, the success of 6th-grade students will be a definite thing! For additional educational resources, .

By avoiding unnecessary questions, our team helps test takers purposefully review test resources and summarize them in the remaining time as best they can. For additional educational resources, .

Also, make sure you follow the relevant links at the bottom of this post to help your student learn better about the 6th-grade IAR math test.

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is the distance between the two cities in yards?

A. \(1,256 yd\)

B. \(11,304 yd\)

C. \(45,216 yd\)

D. \(3,768 yd\)

5- Mr. Jones saves \($3,400\) out of his monthly family income of \($74,800\). What fractional part of his income does Mr. Jones save?

A. \(\frac{1}{22}\)

B. \(\frac{1}{11}\)

C. \(\frac{3}{25}\)

D. \(\frac{2}{15}\)

6- What is the lowest common multiple of \(12\) and \(20\)?

A. \(60\)

B. \(40\)

C. \(20\)

D. \(12\)

7- Based on the table below, which expression represents any value of \(f\) in terms of its corresponding value of \(x\)?
\( \img {https://appmanager.effortlessmath.com/public/images/questions/28282828288888888888888888888888888888888.JPG
} \)

A. \(f=2x-\frac{3}{10}\)

B. \(f=x+\frac{3}{10}\)

C. \(f=2x+2 \frac{2}{5}\)

D. \(2x+\frac{3}{10}\)

8- Solve: \(96 kg =\) … ?

A. \(96 mg\)

B. \(9,600 mg\)

C. \(960,000 mg\)

D. \(96,000,000 mg\)

9- Calculate the approximate area of the following circle. (the diameter is \(25\))
\( \img {https://appmanager.effortlessmath.com/public/images/questions/3030303000000000000000000000000000.JPG
} \)

A. \(78\)

B. \(491\)

C. \(157\)

D. \(1963\)

10- The following graph shows the mark of six students in mathematics. What is the mean (average) of the marks?
\( \img {https://appmanager.effortlessmath.com/public/images/questions/313131313131111111111111111111111111111111111111.JPG
} \)

A. \(13\)

B. \(13.5\)

C. \(14\)

D. \(1.5\)

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Answers:

2- A
\(\frac{104}{8}=13, \frac{1352}{104}=13, \frac{17576}{1352}=13\)
Therefore, the factor is \(13\)

3- C
Simplify each option provided.
A. \(-20-(3×10)+(6×40)=-20-30+240=190\)
B. \((\frac{15}{8})×72 + (\frac{125}{5}) =135+25=160\)
C. \(((\frac{30}{4} + \frac{15}{2})×8) – \frac{11}{2} + \frac{222}{4} = ((\frac{30 + 30}{4})×8)- \frac{11}{2}+ \frac{111}{2}=(\frac{60}{4})×8) + \frac{100}{2}= 120 + 50 = 170\)
this is the answer
D. \(\frac{481}{6} + \frac{121}{3}+50= \frac{481+242}{6}+50=120.5+50=170.5\)

4- A
\(1\) yard \(= 3\) feet
Therefore, \(3,768 \space ft × \frac{1 \space yd }{3 \space ft}=1,256 \space yd\)

5- A
\(3,400\) out of \(74,800\) equals to \(\frac{3,400}{74,800}=\frac{17}{374}=\frac{1}{22}\)

6- A
Prime factorizing of \(20=2×2×5\)
Prime factorizing of \(12=2×2×3\)
\(LCM\)\(=2×2×3×5=60\)

7- C
Plugin the value of \(x\) into the function \(f\). First, plug-in \(3.1\) for\( x\).
A. \(f=2x-\frac{3}{10}=2(3.1)-\frac{3}{10}=5.9≠8.6\)
B. \(f=x+\frac{3}{10}=3.1+\frac{3}{10}=3.4≠10.8\)
C. \(f=2x+2 \frac{2}{5}=2(3.1)+2 \frac{2}{5}=6.2+2.4=8.6\)
This is correct!
Plug in other values of \(x. (x=4.2)\)
\(f=2x+2\frac{2}{5} =2(4.2)+2.4=10.8 \)
This one is also correct.
\(x=5.9\)
\(f=2x+2 \frac{2}{5}=2(5.9)+2.4=14.2 \)
This one works too!
D. \(2x+\frac{3}{10}=2(3.1)+\frac{3}{10}=6.5≠8.6\)

8- D
\(1 kg\)\(= 1000\) \(g\) and \(1 g\) \(= 1000\) \(mg\)
\(96\) \(kg\)\(= 96 × 1000\) \(g\) \(= 96 × 1000 × 1000 = 96,000,000\) \(mg\)

9- B
The diameter of a circle is twice the radius. Radius of the circle is \(\frac{25}{2}\).
Area of a circle = \(πr^2=π(\frac{25}{2})^2=156.25π=156.25×3.14=490.625≅491\)

10- B
Average (mean) \(=\frac{sum \space of \space terms}{number \space of \space terms}= \frac{10+11+15+14+15+17+12.5}{7}=13.5\)

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