• 60 questions

IAAT Practice Test

Sixty algebra readiness questions, fifteen in each of the four parts of the Iowa Algebra Aptitude Test.

What is 3/4 + 5/8?

Pick an answer, then press Check answer. Then you see Correct or Not quite, with the reason. Keys: A to D pick, Enter checks.

Print covers the next 60 questions. Share this set copies a link to the same questions in the same order.

Exam mode: 60 questions, 40 minutes.

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Unofficial practice questions, not affiliated with Riverside Insights or the University of Iowa. Bank checked October 7, 2026.

The real test: Iowa Algebra Aptitude Test

Questions
60
Time limit
40 minutes
Parts
Pre-Algebraic Number Skills and Concepts; Interpreting Mathematical Information; Representing Relationships; Using Symbols.
Sections
Four sections of 15 questions: 1 to 15, 16 to 30, 31 to 45 and 46 to 60.
Question kind
Multiple choice. The report guide describes each question as a stem, a correct answer and three distractors.
How it is given
On paper (Fifth Edition) or online (6th Edition), in two forms.
Scores
Raw score, standard score, national percentile rank, normal curve equivalent and stanine.
Levels
By national percentile rank in the report guide: Exceeds Standards 84 to 99, Meets Standards 70 to 83, Not Yet Meets Standards 1 to 69.

Checked October 7, 2026 against the Iowa Algebra Aptitude Test page, brochure and Item Response Report guide of Riverside Insights. Rules change, so confirm with the agency itself before your test.

The publisher's page for the test

Next step More arithmetic practiceGrade 8 math practice

All 60 questions

Part 1: Pre-Algebraic Number Skills and Concepts 15

  • A bag holds 3 red, 4 blue and 5 green marbles. What fraction of the marbles are blue? Riverside Insights, Iowa Algebra Aptitude Test brochure, Part 1: Pre-Algebraic Number Skills and Concepts
  • A hiker walks 3 miles in 45 minutes. At that rate, how far does the hiker walk in 2 hours? Riverside Insights, Iowa Algebra Aptitude Test brochure, Part 1: Pre-Algebraic Number Skills and Concepts
  • A shade of green uses 3 cans of blue paint for every 4 cans of yellow. How many cans of yellow go with 12 cans of blue? Riverside Insights, Iowa Algebra Aptitude Test brochure, Part 1: Pre-Algebraic Number Skills and Concepts
  • What is (−6) × (−3) − 20? Riverside Insights, Iowa Algebra Aptitude Test brochure, Part 1: Pre-Algebraic Number Skills and Concepts
  • What is 2.4 × 0.35? Riverside Insights, Iowa Algebra Aptitude Test brochure, Part 1: Pre-Algebraic Number Skills and Concepts
  • What is 2³ × 3²? Riverside Insights, Iowa Algebra Aptitude Test brochure, Part 1: Pre-Algebraic Number Skills and Concepts
  • What is 3/4 + 5/8? Riverside Insights, Iowa Algebra Aptitude Test brochure, Part 1: Pre-Algebraic Number Skills and Concepts
  • What is 5/6 ÷ 2/3? Riverside Insights, Iowa Algebra Aptitude Test brochure, Part 1: Pre-Algebraic Number Skills and Concepts
Show all 60 questions (52 more)

Part 1: Pre-Algebraic Number Skills and Concepts, continued

  • What is 45% of 80? Riverside Insights, Iowa Algebra Aptitude Test brochure, Part 1: Pre-Algebraic Number Skills and Concepts
  • What is the least common multiple of 12 and 18? Riverside Insights, Iowa Algebra Aptitude Test brochure, Part 1: Pre-Algebraic Number Skills and Concepts
  • What is −7 + 12 − (−4)? Riverside Insights, Iowa Algebra Aptitude Test brochure, Part 1: Pre-Algebraic Number Skills and Concepts
  • Which is the best estimate of 49.7 × 20.2? Riverside Insights, Iowa Algebra Aptitude Test brochure, Part 1: Pre-Algebraic Number Skills and Concepts
  • Which number is between −1/2 and −1/4 on the number line? Riverside Insights, Iowa Algebra Aptitude Test brochure, Part 1: Pre-Algebraic Number Skills and Concepts
  • Which of these four numbers has the greatest value? Riverside Insights, Iowa Algebra Aptitude Test brochure, Part 1: Pre-Algebraic Number Skills and Concepts
  • Which statement about the sum of two odd whole numbers is always true? Riverside Insights, Iowa Algebra Aptitude Test brochure, Part 1: Pre-Algebraic Number Skills and Concepts

Part 2: Interpreting Mathematical Information 15

  • A bar graph shows the books four students read in a month: Ana 6, Ben 9, Cal 3 and Dee 12. How many times as many books did Dee read as Cal? Riverside Insights, Iowa Algebra Aptitude Test brochure, Part 2: Interpreting Mathematical Information
  • A bar graph shows the books four students read in a month: Ana 6, Ben 9, Cal 3 and Dee 12. What fraction of all the books did Ben read? Riverside Insights, Iowa Algebra Aptitude Test brochure, Part 2: Interpreting Mathematical Information
  • A bar graph shows the books four students read in a month: Ana 6, Ben 9, Cal 3 and Dee 12. What is the mean number of books for the four students? Riverside Insights, Iowa Algebra Aptitude Test brochure, Part 2: Interpreting Mathematical Information
  • A graph shows the cost of renting a kayak. Its points are (1 hour, $9), (2 hours, $13), (3 hours, $17) and (4 hours, $21), and they lie on one straight line. How much more does 4 hours cost than 2 hours? Riverside Insights, Iowa Algebra Aptitude Test brochure, Part 2: Interpreting Mathematical Information
  • A graph shows the cost of renting a kayak. Its points are (1 hour, $9), (2 hours, $13), (3 hours, $17) and (4 hours, $21), and they lie on one straight line. If the line continues, what does 6 hours cost? Riverside Insights, Iowa Algebra Aptitude Test brochure, Part 2: Interpreting Mathematical Information
  • A graph shows the cost of renting a kayak. Its points are (1 hour, $9), (2 hours, $13), (3 hours, $17) and (4 hours, $21), and they lie on one straight line. If the line is extended back to 0 hours, what cost does it show? Riverside Insights, Iowa Algebra Aptitude Test brochure, Part 2: Interpreting Mathematical Information
  • The digit sum of a whole number is the sum of its digits. For example, the digit sum of 407 is 4 + 0 + 7 = 11. What is the digit sum of 3,582? Riverside Insights, Iowa Algebra Aptitude Test brochure, Part 2: Interpreting Mathematical Information
  • The digit sum of a whole number is the sum of its digits. For example, the digit sum of 407 is 4 + 0 + 7 = 11. What is the smallest three-digit number with a digit sum of 10? Riverside Insights, Iowa Algebra Aptitude Test brochure, Part 2: Interpreting Mathematical Information
  • The digit sum of a whole number is the sum of its digits. For example, the digit sum of 407 is 4 + 0 + 7 = 11. Which number has a digit sum of 9? Riverside Insights, Iowa Algebra Aptitude Test brochure, Part 2: Interpreting Mathematical Information
  • For any numbers a and b, the operation a ◊ b means 2a + b. If 6 ◊ n = 20, what is n? Riverside Insights, Iowa Algebra Aptitude Test brochure, Part 2: Interpreting Mathematical Information
  • For any numbers a and b, the operation a ◊ b means 2a + b. What is 3 ◊ 5? Riverside Insights, Iowa Algebra Aptitude Test brochure, Part 2: Interpreting Mathematical Information
  • For any numbers a and b, the operation a ◊ b means 2a + b. What is 4 ◊ (−2)? Riverside Insights, Iowa Algebra Aptitude Test brochure, Part 2: Interpreting Mathematical Information
  • The symbol ⌊x⌋ means the greatest whole number that is not more than x. For example, ⌊4.7⌋ = 4 and ⌊6⌋ = 6. For which value of x is ⌊x⌋ = 7? Riverside Insights, Iowa Algebra Aptitude Test brochure, Part 2: Interpreting Mathematical Information
  • The symbol ⌊x⌋ means the greatest whole number that is not more than x. For example, ⌊4.7⌋ = 4 and ⌊6⌋ = 6. What is ⌊9.2⌋ + ⌊3.9⌋? Riverside Insights, Iowa Algebra Aptitude Test brochure, Part 2: Interpreting Mathematical Information
  • The symbol ⌊x⌋ means the greatest whole number that is not more than x. For example, ⌊4.7⌋ = 4 and ⌊6⌋ = 6. What is ⌊17 ÷ 5⌋? Riverside Insights, Iowa Algebra Aptitude Test brochure, Part 2: Interpreting Mathematical Information

Part 3: Representing Relationships 15

  • A carton holds 12 eggs. Which equation relates the number of eggs, e, to the number of full cartons, c? Riverside Insights, Iowa Algebra Aptitude Test brochure, Part 3: Representing Relationships
  • A class has 27 students. The number of girls is 5 more than the number of boys, b. Which equation can be used to find b? Riverside Insights, Iowa Algebra Aptitude Test brochure, Part 3: Representing Relationships
  • A number n is multiplied by 6, then 9 is subtracted, and the result is 33. Which equation says this? Riverside Insights, Iowa Algebra Aptitude Test brochure, Part 3: Representing Relationships
  • A plant is 8 centimeters tall and grows 3 centimeters each week. After how many weeks is it 29 centimeters tall? Riverside Insights, Iowa Algebra Aptitude Test brochure, Part 3: Representing Relationships
  • A rectangle is w centimeters wide, and its length is 5 centimeters more than its width. Which expression is its perimeter in centimeters? Riverside Insights, Iowa Algebra Aptitude Test brochure, Part 3: Representing Relationships
  • A table pairs x with y: when x is 0, 1, 2 and 3, y is 7, 5, 3 and 1. Which rule gives y? Riverside Insights, Iowa Algebra Aptitude Test brochure, Part 3: Representing Relationships
  • A table pairs x with y: when x is 1, 2, 3 and 4, y is 1, 4, 9 and 16. Which rule gives y? Riverside Insights, Iowa Algebra Aptitude Test brochure, Part 3: Representing Relationships
  • A table pairs x with y: when x is 1, 2, 3 and 4, y is 5, 8, 11 and 14. Which rule gives y? Riverside Insights, Iowa Algebra Aptitude Test brochure, Part 3: Representing Relationships
  • A table pairs x with y: when x is 2, 4, 6 and 8, y is 1, 2, 3 and 4. Which rule gives y? Riverside Insights, Iowa Algebra Aptitude Test brochure, Part 3: Representing Relationships
  • A table pairs x with y: when x is 3, 5, 7 and 9, y is 10, 16, 22 and 28. If the rule continues, what is y when x is 12? Riverside Insights, Iowa Algebra Aptitude Test brochure, Part 3: Representing Relationships
  • A table pairs x with y: when x is 10, 20 and 30, y is 4, 9 and 14. Which rule gives y? Riverside Insights, Iowa Algebra Aptitude Test brochure, Part 3: Representing Relationships
  • A taxi charges $4 to start a ride and $2 for each mile. Which equation gives the cost C, in dollars, of a ride of m miles? Riverside Insights, Iowa Algebra Aptitude Test brochure, Part 3: Representing Relationships
  • The first four numbers of a pattern are 6, 11, 16 and 21. Which expression gives the nth number? Riverside Insights, Iowa Algebra Aptitude Test brochure, Part 3: Representing Relationships
  • Mia has d dollars. Leo has 3 dollars less than twice Mia's amount. Which expression is Leo's amount in dollars? Riverside Insights, Iowa Algebra Aptitude Test brochure, Part 3: Representing Relationships
  • Sam is s years old, and Tia is 4 years older than Sam. Which expression is the sum of their ages? Riverside Insights, Iowa Algebra Aptitude Test brochure, Part 3: Representing Relationships

Part 4: Using Symbols 15

  • For which pair are the two expressions equal for every choice of nonzero numbers a and b? Riverside Insights, Iowa Algebra Aptitude Test brochure, Part 4: Using Symbols
  • If x = 3, which equation is true? Riverside Insights, Iowa Algebra Aptitude Test brochure, Part 4: Using Symbols
  • In algebra, what does 7n mean? Riverside Insights, Iowa Algebra Aptitude Test brochure, Part 4: Using Symbols
  • In the equation d = 50t, t increases by 2. By how much does d increase? Riverside Insights, Iowa Algebra Aptitude Test brochure, Part 4: Using Symbols
  • In the equation y = 20 − x, what happens to y as x gets larger? Riverside Insights, Iowa Algebra Aptitude Test brochure, Part 4: Using Symbols
  • The perimeter of a square is P = 4s, where s is the length of a side. If s is doubled, what happens to P? Riverside Insights, Iowa Algebra Aptitude Test brochure, Part 4: Using Symbols
  • The sum of three consecutive integers is 48. What is the smallest of the three? Riverside Insights, Iowa Algebra Aptitude Test brochure, Part 4: Using Symbols
  • Three consecutive integers start at n. Which expression is their sum? Riverside Insights, Iowa Algebra Aptitude Test brochure, Part 4: Using Symbols
  • What is the value of 3a − b when a = 4 and b = 5? Riverside Insights, Iowa Algebra Aptitude Test brochure, Part 4: Using Symbols
  • What is the value of 20 − 2 × (3 + 4)? Riverside Insights, Iowa Algebra Aptitude Test brochure, Part 4: Using Symbols
  • What value of x makes 4x + 6 = 30 true? Riverside Insights, Iowa Algebra Aptitude Test brochure, Part 4: Using Symbols
  • Which equation shows that addition is commutative? Riverside Insights, Iowa Algebra Aptitude Test brochure, Part 4: Using Symbols
  • Which expression is equal to 3(x + 4) for every value of x? Riverside Insights, Iowa Algebra Aptitude Test brochure, Part 4: Using Symbols
  • Which expression is equal to 5a + 2 − 3a + 6? Riverside Insights, Iowa Algebra Aptitude Test brochure, Part 4: Using Symbols
  • Which value of x makes 2x + 1 > 9 true? Riverside Insights, Iowa Algebra Aptitude Test brochure, Part 4: Using Symbols

How this list was compiled: Outline: Riverside Insights, the publisher of the Iowa Algebra Aptitude Test. Its page for the test, https://riversideinsights.com/k12-assessments/iaat, lists the four parts; its brochure, https://riversideinsights.com/hubfs/2022%20Site%20Redesign%20Collateral/IAAT/Iowa_Algebra_Aptitude_Test_Brochure.pdf, describes each part; its Item Response Report guide, https://riversideinsights.com/hubfs/Item%20Response%20Report-2026.pdf, gives the four sections of 15 questions. All read 2026-10-07. Licence: Own work. Questions, answer choices and explanations were written for this site. Nothing is copied or reworded from a form of the Iowa Algebra Aptitude Test, the sample items in the publisher's brochure or another practice test.

How it works

Unofficial practice for the Iowa Algebra Aptitude Test. The questions are ours, written from the four parts the publisher describes; none comes from a real form or its sample items. Not affiliated with Riverside Insights or the University of Iowa.

Read the full guide

What the IAAT covers

The publisher, Riverside Insights, lists four parts. Pre-Algebraic Number Skills and Concepts starts with computation and moves to problem solving. Interpreting Mathematical Information gives a graph or a new definition and asks about it. Representing Relationships asks for the rule behind a table or a situation. Using Symbols covers variables, equations, order of operations, commutativity and consecutive integers.

How this practice test is built

This full-length practice test runs the four parts in the real test's order. Every answer that is a calculation is worked out a second time from the numbers in the question. A graph is described in words, because the questions carry no pictures.

  • In a table question, test a rule on every pair. A wrong rule often fits the first pair.

Questions and answers

How many questions are on the IAAT?

60, in four sections of 15, by the publisher's report guide. Its brochure calls the test a 40-minute standardized assessment.

What is a good score on the IAAT?

The publisher's report guide shows three levels by national percentile rank: Exceeds Standards 84 to 99, Meets Standards 70 to 83 and Not Yet Meets Standards 1 to 69. It calls them recommended cut scores for Algebra I, used with other data.

Is there an IAAT practice test PDF?

After a round, Print puts the questions on paper, with the answer key if you tick it, and a browser's print window can save that as a PDF.

Is this an IAAT sample test?

No. It is unofficial practice written for this site. The publisher's own sample items are the four in its brochure, one for each part.

Can you take the IAAT online?

Yes. The publisher's brochure lists paper and pencil administration for the Fifth Edition and online administration for the 6th Edition. It also lists two forms, which it calls ideal for testing before and after.

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