# 6th Grade IAR Math FREE Sample Practice Questions

Need sample practice questions to prepare your student for the 6th-grade IAR math test? So it’s better to know that you are in the right place now!

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.

These sample practice questions cover the most important concepts in the IAR 2022 test, so by focusing on these sample practice questions, the success of 6th-grade students will be a definite thing!

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

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## 10 Sample 6th Grade IAR Math Practice Questions

1- If the area of the following trapezoid is equal to $$A$$, which equation represents $$x$$?
$$\img {https://appmanager.effortlessmath.com/public/images/questions/131313444444444444444444444444444.JPG }$$

A. $$x = \frac{13}{A}$$

B. $$x = \frac{A}{13}$$

C. $$x=A+13$$

D. $$x=A-13$$

2- By what factor did the number below change from the first to the fourth number?
$$8, 104, 1352, 17576$$

A. $$13$$

B. $$96$$

C. $$1456$$

D. $$17568$$

3- $$170$$ is equal to …

A. $$-20-(3×10)+(6×40)$$

B. $$((\frac{15}{8})×72 )+ (\frac{125}{5})$$

C. $$((\frac{30}{4} + \frac{15}{2})×8) – \frac{11}{2} + \frac{222}{4}$$

D. $$\frac{481}{6} + \frac{121}{3}+50$$

4- The distance between the two cities is $$3,768$$ feet. What 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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1- B
The area of the trapezoid is: area$$= \frac{(base \space 1+base \space 2)}{2}×$$height$$= (\frac{10 + 16}{2})x = A$$
$$→13x = A→x = \frac{A}{13}$$

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. $$((\frac{30}{4} + \frac{15}{2})×8) – \frac{11}{2} + \frac{222}{4} = ((\frac{30 + 30}{4})×8)- \frac{11}{2}+ \frac{111}{2}=(\frac{60}{4})×8) + \frac{100}{2}= 120 + 50 = 170$$
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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Original price was: $18.99.Current price is:$13.99.
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