Preparing for the 8th-Grade Illinois Assessment of Readiness (IAR) Math Test can always be difficult or challenging. If you are an 8th-grade student who wants to get a good score on the IAR Math Test, do not miss the 8th Grade IAR Math Practice Test Questions! Using the 10 practice questions of the IAR exam along with the step-by-step solutions to each question is a great way to review the math topics of the IAR exam.

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**10 Sample 8th Grade IAR Math Practice Questions**

1- Five years ago, Amy was three times as old as Mike was. If Mike is \(10\) years old now, how old is Amy?

A. \(4\)

B. \(8\)

C. \(12\)

D. \(20\)

2- What is the length of \(AB\) in the following figure if \(AE=4, CD=6\) and \(AC=12\)?

A. \(3.8\)

B. \(4.8\)

C. \(7.2\)

D. \(24\)

3- If a gas tank can hold \(25\) gallons, how many gallons does it contain when it is \(\frac{2}{5}\) full?

A. \(50\)

B. \(125\)

C. \(62.5\)

D. \(10\)

4- In the \(xy\)-plane, the point \((4,3)\) and \((3,2)\) are on line \(A\). Which of the following equations of lines is parallel to line \(A\)?

A. \(y=3x \)

B. \(y=\frac{x}{2}\)

C. \(y=2x \)

D. \(y=x \)

5- If \(x\) is directly proportional to the square of \(y\), and \(y=2\) when \(x=12\), then when \(x=75 y=\) ?

A. \(\frac{1}{5}\)

B. \(1\)

C. \(5\)

D. \(12\)

6- Jack earns \($616\) for his first \(44\) hours of work in a week and is then paid \(1.5\) times his regular hourly rate for any additional hours. This week, Jack needs \($826\) to pay his rent, bills, and other expenses. How many hours must he work to make enough money this week?

A. \(40\)

B. \(48\)

C. \(53\)

D. \(54\)

7-

If a is the mean (average) of the number of cities in each pollution type category, b is the mode, and c is the median of the number of cities in each pollution type category, then which of the following must be true?

A. \(a<b<c\)

B. \(b<a<c\)

C. \(a=c\)

D. \(b<c=a\)

8-

What percent of cities are in the type of pollution \(A, C,\) and \(D\) respectively?

A. \(60\%, 40\%, 90\%\)

B. \(30\%, 40\%, 90\%\)

C. \(30\%, 40\%, 60\%\)

D. \(40\%, 60\%, 90\%\)

9-

How many cities should be added to the type of pollution \(B\) until the ratio of cities in a type of pollution \(B\) to cities in the type of pollution \(E\) will be \(0.625\)?

A. \(2\)

B. \(3\)

C. \(4\)

D. \(5\)

10- In the following right triangle, if the sides \(AB\) and \(AC\) become twice longer, what will be the ratio of the perimeter of the triangle to its area?

A. \(\frac{1}{2}\)

B. \(2\)

C. \(\frac{1}{3}\)

D. \(3\)

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## Answers:

1- **D**

Five years ago, Amy was three times as old as Mike. Mike is \(10\) years now. Therefore, \(5\) years ago Mike was \(5\) years.

Five years ago, Amy was: \( A=3×5=15 \)

Now Amy is \(20\) years old: \(15 + 5 = 20\)

2- **B**

Two triangles \(∆BAE\) and \(∆BCD\) are similar. Then:

\(\frac{AE}{CD}=\frac{AB}{BC}=\frac{4}{6}=\frac{x}{12-x}\)

\(→48-4x=6x→10x=48→x=4.8\)

3-** D**

\(\frac{2}{5}×25=\frac{50}{5}=10\)

4- **D**The slop of line \(A\) is:

\(m = \frac{y_2-y_1}{x_2-x_1}=\frac{3-2}{4-3}=1\)

Parallel lines have the same slope and only choice \(D (y=x)\) has slope of \(1\).

5- **C**

\(x\) is directly proportional to the square of \(y\). Then:

\(x=cy^2\)

\(12=c(2)^2→12=4c→c=\frac{12}{4}=3\)

The relationship between \(x\) and \(y\) is:

\(x=3y^2\)

\(x=75\)

\(75=3y^2→y^2=\frac{75}{3}=25→y=5\)

6- **D**

the amount of money that jack earns for one hour: \(\frac{$616}{44}=$14\)

The number of additional hours that he works to make enough money is: \(\frac{$826-$616}{1.5×$14}=10\)

The number of total hours is: \(44+10=54\)

7- **C**

Let’s find the mean (average), mode, and median of the number of cities for each type of pollution.

Number of cities for each type of pollution: \(6, 3, 4, 9, 8\)

\(mean\:\ (average) = \frac{sum \space of \space terms}{number \space of \space terms}=\frac{6+3+4+9+8}{5}=6\)

Median is the number in the middle. To find median, first list numbers in order from smallest to largest.

\(3, 4, 6, 8, 9\)

Median of the data is \(6\).

Mode is the number that appears most often in a set of numbers. Therefore, there is no mode in the set of numbers.

\(Median = Mean, then, a=b\)

8- **A**

Percent of cities in the type of pollution A: \(\frac{6}{10} × 100=60\%\)

Percent of cities in the type of pollution C: \( \frac{4}{10} × 100 = 40\%\)

Percent of cities in the type of pollution D: \( \frac{9}{10}× 100 = 90\%\)

9- **A**

Let the number of cities should be added to type of pollutions \(B\) be \(x\). Then:

\(\frac{x + 3}{8}=0.625→x+3=8×0.625→x+3=5→x=2\)

10- **A**

\(AB=12\) And \(AC=5\)

\(BC=\sqrt{(12^2+5^2 )} = \sqrt{(144+25)} = \sqrt{169}=13\)

\(Perimeter =5+12+13=30 \)

\(Area =\frac{5×12}{2}=5×6=30\)

In this case, the ratio of the perimeter of the triangle to its area is:

\(\frac{30}{30}= 1\)

If the sides \(AB\) and \(AC\) become twice longer, then:

\(AB=24\) And \(AC=10\)

\(BC=\sqrt{(24^2+10^2 )} = \sqrt{(576+100)} = \sqrt{676} = 26\)

Perimeter \(=26+24+10=60\)

\(Area =\frac{10×24}{2}=10×12=120\)

In this case the ratio of the perimeter of the triangle to its area is:

\(\frac{60}{120}=\frac{1}{2}\)

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