Full-Length 7th Grade IAR Math Practice Test

1- The score of Mia was \(3\) times that of Ava, and the score of Emma was one and a half times that of Ava. If the score of Mia was \(90\), what is the score of Emma?

A. \(30\)

B. \(40\)

C. \(45\)

D. \(60\)

2- In the figure below, the two triangles are similar. What is the value of \(x\)?

A. \(2\)

B. \(4\)

C. \(6\)

D. \(8\)

3- If \(40\%\) of a class are girls, and \(25\%\) of girls play tennis, what fraction of the class plays tennis?

A. \(\frac{1}{8}\)

B. \(\frac{1}{10}\)

C. \(\frac{1}{20}\)

D. \(\frac{1}{25}\)

4- A boat sails \(30\) miles south and then \(40\) miles east. How far is the boat from its start point?

A. \(30\) miles

B. \(40\) miles

C. \(50\) miles

D. \(60\) miles

5- You can buy \(12\) cans of green beans at a supermarket for \($7.40\). How much does it cost to buy \(30\) cans of green beans?

A. \($18.50\)

B. \($24.20\)

C. \($26.00\)

D. \($34.00\)

6- What is the volume of the following square pyramid?

A. \(460 \space m^3\)

B. \(520 \space m^3\)

C. \(750 \space m^3\)

D. \(960 \space m^3\)

7- At a party, \(6\) soft drinks are required for every \(8\) guest. If there are \(240\) guests, how many soft drinks are required?

A. \(38\)

B. \(146\)

C. \(180\)

D. \(200\)

8- Since last year, the price of gasoline has increased from \($1.4\) per gallon to \($1.75\) per gallon. The new price is what percent of the original price?

A. \(20\%\)

B. \(25\%\)

C. \(30\%\)

D. \(35\%\)

9- \([8×(-14)+15]-(10)+[4×6]÷3=?\)

10- Simplify \(5x^2 y(2xy^3)^4=?\)

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A. \(40x^3 y^{12}\)

B. \(16x^5 y^{24}\)

C. \(40x^6 y^{12}\)

D. \(80x^6 y^{13}\)

11- Jason is \(14\) miles ahead of Joe running at \(6\) miles per hour and Joe is running at the speed of \(8\) miles per hour. How long does it take Joe to catch Jason?

A. \(3\) hours

B. \(5\) hours

C. \(7\) hours

D. \(9\) hours

12- \(9\) less than five times a positive integer is \(101\). What is the integer?

A. \(22\)

B. \(26\)

C. \(32\)

D. \(44\)

13- Last week \(18,000\) fans. This week \(2.5\) times as many bought tickets, but one-fifth of them canceled their tickets. How many are attending this week?

A. \(20,000\)

B. \(22,000\)

C. \(32,000\)

D. \(36,000\)

14- What is the median of these numbers? \(25,12,13,18,22,36,22\)

A. \(12\)

B. \(20\)

C. \(22\)

D. \(26\)

15- Sophia purchased a sofa for \($615.00\). The sofa is regularly priced at \($820\). What was the percent discount Sophia received on the sofa?

A. \(8\%\)

B. \(12\%\)

C. \(18\%\)

D. \(25\%\)

16- Robert is preparing to run a marathon. He runs \(4\frac{1}{3}\) miles on Saturday and two times that many on Monday and Wednesday. Robert wants to run a total of \(35\) miles this week. How many more miles does he need to run?

17- What is the area of the shaded region?

A. \(10π \space cm^2\)

B. \(20π \space cm^2\)

C. \(25π \space cm^2\)

D. \(30π \space cm^2\)

18- Right triangle \(ABC\) has two shorter legs of lengths \(12\space cm\space (AB)\) and \(5\space cm\space (AC)\). What is the length of the third side \((BC)\)?

A. \(13\space cm\)

B. \(14\space cm\)

C. \(15\space cm\)

D. \(16\space cm\)

19- four times the price of a laptop is equal to seven times the price of a computer. If the price of the laptop is \($240\) more than a computer, what is the price of the computer?

A. \($320\)

B. \($400\)

C. \($420\)

D. \($960\)

20- Jason needs an \(75\%\) average in his writing class to pass. On his first \(4\) exams, he earned scores of \(62\%\), \(73\%\), \(82\%\), and \(88\%\). What is the minimum score Jason can earn on his fifth and final test to pass?

21- The price of a laptop is decreased by \(15\%\) to \($425\). What is its original price?

A. \($475\)

B. \($500\)

C. \($575\)

D. \($600\)

22- A rope weighs \(450\) grams per meter in length. What is the weight in kilograms of \(12\) meters of this rope? (\(1\) kilograms \(= 1,000\) grams)

A. \(0.0540\) kilograms

B. \(0.540\) kilograms

C. \(5.4\) kilograms

D. \(54.00\) kilograms

23- If \(x=-3\), which equation is true?

A. \(x(2x-4)=-52\)

B. \(8(7-x)=14\)

C. \(x(3x-2)=79\)

D. \((4x-2)x=42\)

24- Joe scored \(24\) out of \(32\) marks in Algebra, \(28\) out of \(40\) marks in science, and \(72\) out of \(90\) marks in Mathematics. In which subject his percentage of marks is best?

A. Algebra

B. Science

C. Mathematics

D. Algebra and Science

25- The marked price of a computer is \(D\) dollar. Its price decreased by \(25\%\) in January and later increased by \(15\%\) in February. What is the final price percent of the computer in \(D\) dollars?

A. \(78.55\space D\)

B. \(82.25\space D\)

C. \(86.25\space D\)

D. \(90.50\space D\)

26- What is the median of these numbers? \(42,21,15,28,43,34,26\)

A. \(15\)

B. \(28\)

C. \(34\)

D. \(42\)

27- John traveled \(210\space km\) in \(7\) hours and Alice traveled \(160\space km\) in \(5\) hours. What is the ratio of the average speed of John to the average speed of Alice?

A. \(13∶ 12\)

B. \(22∶ 23\)

C. \(15∶ 16\)

D. \(15∶ 18\)

28- A \($56\) shirt now selling for \($42\) is discounted by what percent?

A. \(15\%\)

B. \(18\%\)

C. \(20\%\)

D. \(25\%\)

29- The area of a circle is \(121π\). What is the circumference of the circle?

A. \(7π\)

B. \(14π\)

C. \(22π\)

D. \(24π\)

30- In a bag of small balls, \(\frac{1}{2}\) are black, \(\frac{1}{5}\) are white, \(\frac{1}{10}\) are red and the remaining \(12\) blue. How many balls are white?

A. \(8\)

B. \(12\)

C. \(16\)

D. \(24\)

31- A pizza cut into \(10\) parts. William and his sister Ella ordered two pizzas. William ate \(\frac{4}{5}\) of his pizza and Ella ate \(\frac{1}{2}\) of her pizza. What part of the two pizzas was left?

A. \(\frac{7}{20}\)

B. \(\frac{2}{10}\)

C. \(\frac{1}{4}\)

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

32- \(50\) students took an exam and \(14\) of them failed. What percent of the students passed the exam?

A. \(20\%\)

B. \(48\%\)

C. \(64\%\)

D. \(72\%\)

33- \(6.2\) is what percent of \(50\)?

A. \(1.2\)

B. \(5.6\)

C. \(12.4\)

D. \(24.6\)

34- What is the perimeter of a square that has an area of \(196\) feet?

35- Which of the following points lies on the line \(6x-14=4y\)?

A. \((2,1)\)

B. \((2,-\frac{1}{2})\)

C. \((-3,4)\)

D. \((2,2)\)

36- An angle is equal to one-fourth of its supplement. What is the measure of that angle?

A. \(28\)

B. \(36\)

C. \(45\)

D. \(60\)

37- A bank is offering \(3.5\%\) simple interest on a savings account. If you deposit \($16,000\), how much interest will you earn in three years?

A. \($1220\)

B. \($1,680\)

C. \($2,120\)

D. \($4,220\)

38- What is the probability of getting a sum of \(7\) when two dice are thrown?

A. \(\frac{1}{9}\)

B. \(\frac{1}{6}\)

C. \(\frac{16}{17}\)

D. \(\frac{17}{18}\)

39- How many possible outfit combinations come from three shirts, eight slacks, and seven ties? _____________

40- A chemical solution contains \(7\%\) alcohol. If there are \(35\space ml\) of alcohol, what is the volume of the solution?

A. \(240\space ml\)

B. \(500\space ml\)

C. \(600\space ml\)

D. \(700\space ml\)

Answers and Explanations

The Best Books to Ace the 7th Grade IAR Math Test

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For a workbook covering every 7th grade IAR standard, the 7th Grade IAR Math for Beginners walks through each topic at grade level with worked examples. For complete prep with multiple full-length practice tests, see the 7th Grade IAR Math Test Prep Bundle.

Frequently Asked Questions

What is the 7th grade IAR Math test?

The Illinois Assessment of Readiness (IAR) is the state standardized test for ELA and Math in grades 3-8. It replaced PARCC starting in 2019. Grade 7 IAR Math covers Illinois Learning Standards (which align to Common Core grade 7) and is administered each spring.

How many questions are on the 7th grade IAR Math?

The test is split across multiple sessions and includes about 40-50 items total. Item types include traditional multiple choice, multi-select, drag-and-drop, equation editor (type a numeric answer), and constructed response (show your work and explain).

Is a calculator allowed on the 7th grade IAR Math?

No. The grade 7 IAR Math does not allow calculators. The test design assumes students can compute rational numbers, percents, ratios, and simple algebraic expressions by hand at grade level.

What topics does the 7th grade IAR Math cover?

Ratios and proportional relationships (including percent and percent change), the number system (rational number arithmetic, including negatives), expressions and equations (linear, two-step inequalities), geometry (scale drawings, angles, area, volume, surface area), and statistics and probability (random sampling, comparing populations, simulations).

How is the IAR scored?

Scores report as a scaled score and a performance level from 1 (did not yet meet expectations) through 5 (exceeded expectations). Level 4 (met expectations) is the goal for grade-level proficiency. Reports break performance down by content area so teachers can identify class-wide gaps.

Does the IAR affect my child’s grade?

Usually not directly. Most Illinois districts treat the IAR as accountability data rather than a classroom grade. Some districts use IAR results for placement decisions or summer-school recommendations, so check your school’s specific policy.

How is the IAR administered?

Online through the state’s secure test platform, split across multiple sessions within the spring testing window. Paper-and-pencil format is available for accommodations or when online delivery isn’t feasible.

How can my child prepare for the 7th grade IAR?

Take a full-length practice test first to identify the weakest topics. Then spend 15-25 minutes a day for 4-6 weeks alternating between focused practice on weak skills and short mixed-topic sets. Review answer explanations carefully and watch for repeat mistake patterns.

How is the IAR different from MAP Growth?

IAR is the high-stakes state accountability test taken once each spring. MAP Growth is a formative benchmark assessment many Illinois districts give 2-3 times per year to track growth. Both reference Illinois Learning Standards, but they serve different purposes.

Where can I find more 7th grade IAR practice?

EffortlessMath has the 7th Grade IAR Math for Beginners workbook covering every Illinois Learning Standard, plus the 7th Grade IAR Math Test Prep Bundle with multiple full-length practice tests and detailed answer explanations.

Related EffortlessMath Lessons

If a topic on this page feels rusty, these short lessons go deeper:

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• How to find the slope of a line
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