# 10 Most Common 6th Grade IAR Math Questions

Because 6th-grade students’ scores on the Illinois Assessment of Readiness (IAR) math test affect their fate, we also decided to compile 10 Most Common 6th Grade IAR Math Questions for 6th-Grade IAR Math and provide them to 6th-grade students. These questions are very similar to the main test questions and this helps a lot in 6th-grade students mastering the concepts of the 6th-grade IAR Math Test.

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 your students need to practice.

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**10 Sample 6th Grade IAR Math Practice Questions**

1- What is the equation of a line that passes through points \((0, 4)\) and \((2, 8)\)?

A. \(y = x\)

B. \(y = x + 4\)

C. \(y = 2x + 4\)

D. \(y = 2x – 4\)

2- What is the volume of a box with the following dimensions?

Height \(= 6 cm\) , Width \(= 7 cm\), Length \(= 9 cm\)

A. \(63 \space cm^3\)

B. \(126\space cm^3\)

C. \(189\space cm^3\)

D. \(378\space cm^3\)

3- Anita’s trick–or–treat bag contains \(14\) pieces of chocolate, \(15\) suckers, \(16\) pieces of gum, and \(20\) pieces of licorice. If she randomly pulls a piece of candy from her bag, what is the probability of her pulling out a piece of sucker?

A. \(\frac{1}{13}\)

B. \(\frac{3}{13}\)

C. \(\frac{14}{65}\)

D. \(\frac{16}{65}\)

4-

In the following rectangle, which statement is false?

A. AD is parallel to BC

B. The measure of the sum of all the angles equals \(360^\circ\).

C. Length of AB equal to length DC.

D. AB is perpendicular to AC.

5- The area of a rectangular yard is \(90\) square meters. What is its width if its length is \(15\) meters?

A. \(10\) meters

B. \(8\) meters

C. \(6\) meters

D. \(4\) meters

6- Which statement about \(4\) multiplied by \(\frac{3}{5}\) must be true?

A. The product is between \(1\) and \(2\)

B. The product is greater than \(3\)

C. The product is equal to \(\frac{75}{31}\)

D. The product is between \(2\) and \(2.5\)

7- Which of the following lists shows the fractions in order from least to greatest?

\(\frac{3}{4}, \frac{2}{7}, \frac{3}{8} , \frac{5}{11}\)

A. \(\frac{3}{8}, \frac{2}{7}, \frac{3}{4}, \frac{5}{11}\)

B. \(\frac{2}{7}, \frac{5}{11}, \frac{3}{8}, \frac{3}{4}\)

C. \(\frac{2}{7}, \frac{3}{8}, \frac{5}{11}, \frac{3}{4}\)

D. \(\frac{3}{8}, \frac{2}{7}, \frac{5}{11}, \frac{3}{4}\)

8- A car costing \($300\) is discounted \(10\%\). Which of the following expressions can be used to find the selling price of the car?

A. \((300)(0.4)\)

B. \(300-(300×0.1)\)

C. \((300)(0.1)\)

D. \( 300-(300×0.9)\)

9- What is the missing price factor of number \(420\)?

\(420=2^2×3^1×…\)

A. \(2^2×3^1×5^1×7^1\)

B. \(2^2×3^1×7^1×9^1\)

C. \(1^2×2^3×2^1×3^1\)

D. \(3^2×5^1×7^1×9^1\)

10- If the area of the following trapezoid is equal to \(A\), which equation represents \(x\)?

A. \(x = \frac{13}{A}\)

B. \(x = \frac{A}{13}\)

C. \( x=A+13\)

D. \( x=A-13\)

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### Common Core Math Exercise Book for Grade 6 Student Workbook and Two Realistic Common Core Math Tests

## Answers:

1- **C **

The slope of the line is:

\(\frac{y_2-y_1}{x_2-x_1 }= \frac{8 – 4}{2 – 0}=\frac{4}{2}=2\)

The equation of a line can be written as:

\( y-y_0=m(x – x_0 )→y-4 = 2(x – 0)→y-4 = 2x→y = 2x + 4\)

2- **D**

Volume of a \(box = length × width × height = 6 × 7 × 9 = 378\)

3- **B**

\(Probability = \frac{number \space of \space desired \space outcomes}{number \space of \space total \space outcomes}=\frac{15}{14+15+16+20}= \frac{15}{65}=\frac{3}{13}\)

4- **D**

In any rectangle, sides are not perpendicular to diagonals.

5- **C**

Let \(y\) be the width of the rectangle. Then; \(15×y=90→y=\frac{90}{15}=6\)

6- **D**

\( 4×\frac{3}{5}=\frac{12}{5}=2.4 \)

\( 2.4>2\)

\( 2.4<3\)

\( \frac{75}{31}=2.419≠2.4\)

\(2<2.4<2.5 \) This is the answer!

7- **C**

Let’s compare each fraction:

\(\frac{2}{7}< \frac{3}{8}< \frac{5}{11} < \frac{3}{4}\)

Only choice C provides the right order.

8- **B **

To find the discount, multiply the number (\(100\%\)\(-\) rate of discount)

Therefore; \(300(100\%-10\%)=300(1-0.1)=300-(300×0.1)\)

9- **A**

\(420=2^2×3^1×5^1×7^1\)

10- **B**

The area of the trapezoid is: area= \(\frac{(base 1+base 2)}{2}×height= (\frac{10 + 16}{2})x = A\)

\( →13x = A→x = \frac{A}{13}\)

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### Common Core Math Exercise Book for Grade 6 Student Workbook and Two Realistic Common Core Math Tests

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