10 Most Common 6th Grade IAR Math Questions

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 the 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 \(x\)?

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

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

C. \( x=A+13\)

D. \( x=A-13\)

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Answers:

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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Frequently Asked Questions

What is the 6th grade IAR math test?

The Illinois Assessment of Readiness (IAR) is Illinois’s state test for English language arts and math in grades 3–8. The 6th-grade math portion aligns to the Illinois Learning Standards (essentially the Common Core for Grade 6 math) and is administered each spring.

Which math topics show up most on 6th grade IAR?

Ratios and rates, dividing fractions by fractions, multi-digit decimal operations, GCF and LCM, an introduction to negative numbers and the coordinate plane, one-step equations and inequalities, area of triangles and special quadrilaterals, volume of prisms with fractional edges, surface area, and basic statistics (mean, median, range).

How long is the 6th grade IAR math test?

About two hours, split across two sessions. The first session is calculator-prohibited; the remaining sessions allow the basic scientific calculator embedded in the testing platform. Scratch paper is available throughout.

Are calculators allowed on 6th grade IAR math?

On part of the test. The first session is non-calculator. Later sessions allow the embedded online calculator. Practice both ways so the calculator switch doesn’t become a distraction.

What does a passing score look like on the IAR?

IAR reports a performance level from 1 to 5 rather than a pass/fail cutoff. Levels 4 (\”meeting\”) and 5 (\”exceeding\”) indicate grade-level proficiency or above.

How do I divide one fraction by another?

Multiply by the reciprocal: \( \dfrac{a}{b} \div \dfrac{c}{d} = \dfrac{a}{b} \times \dfrac{d}{c} \). For example, \( \dfrac{3}{4} \div \dfrac{2}{5} = \dfrac{3}{4} \times \dfrac{5}{2} = \dfrac{15}{8} \). Simplify the result if you can.

How is a unit rate different from a ratio?

A ratio compares any two quantities; a unit rate is a ratio whose second quantity is 1. If a car covers 120 miles in 3 hours, the ratio is 120:3 — the unit rate is 40 miles per 1 hour, or 40 mph. Unit rates make ratios easy to compare.

How do I find the area of a triangle?

Use \( A = \frac{1}{2} b h \), where \( b \) is the base and \( h \) is the height perpendicular to that base. A triangle with base 8 and height 5 has area \( \frac{1}{2}(8)(5) = 20 \). The height must be perpendicular to the chosen base — students often confuse a slanted side with the height.

How does the coordinate plane show up?

Students plot points in all four quadrants, find distances along horizontal or vertical lines using absolute value, and identify the coordinates of a point’s reflection across the x- or y-axis. Pay attention to signs — that’s the source of most coordinate-plane mistakes.

How can my 6th grader prepare for IAR math?

Take at least one full-length, mixed-topic practice set; review every miss with the underlying concept named out loud (not just \”I forgot\”); and pace the review across weeks rather than the last weekend. Small, consistent practice beats one long cram session.

Related Lessons You May Like

• How to find the percent of a number
• How to add and subtract fractions with unlike denominators
• How to multiply and divide decimals
• How to solve ratio word problems
• How to solve multi-step word problems

If you want a workbook that pairs with these questions topic by topic, Mastering Grade 6 Math walks through every sixth-grade standard with worked examples and short practice sets. For extra word-problem reps, Mastering Grade 6 Math Word Problems drills the same skills inside real-world scenarios.