A classroom has 4 tables with 6 chairs at each table. 3 chairs are empty. How many chairs are filled?Answer: 21. Source: Illinois Learning Standards for Mathematics, standard 3.OA.8
A coach shares 32 cones equally among 4 teams. Which expression shows how many cones each team gets?Answer: 32 ÷ 4. Source: Illinois Learning Standards for Mathematics, standard 3.OA.2
A pattern follows the rule "add 4": 4, 8, 12, 16. What is the next number?Answer: 20. Source: Illinois Learning Standards for Mathematics, standard 3.OA.9
Show all 40 questions (37 more)
Operations and algebraic thinking, continued
A shelf holds 8 rows of jars with 7 jars in each row. How many jars are on the shelf?Answer: 56. Source: Illinois Learning Standards for Mathematics, standard 3.OA.3
Lena buys 3 packs of pencils with 8 pencils in each pack. She already had 12 pencils. How many pencils does she have now?Answer: 36. Source: Illinois Learning Standards for Mathematics, standard 3.OA.8
Maya has 45 stickers. She puts 5 stickers on each page of her album. How many pages does she fill?Answer: 9. Source: Illinois Learning Standards for Mathematics, standard 3.OA.3
What is 2 × 5 × 4?Answer: 40. Source: Illinois Learning Standards for Mathematics, standard 3.OA.5
What is 7 × 9?Answer: 63. Source: Illinois Learning Standards for Mathematics, standard 3.OA.7
What is 36 ÷ 4?Answer: 9. Source: Illinois Learning Standards for Mathematics, standard 3.OA.7
What number makes this equation true? 7 × ? = 42Answer: 6. Source: Illinois Learning Standards for Mathematics, standard 3.OA.4
What number makes this equation true? ? ÷ 6 = 7Answer: 42. Source: Illinois Learning Standards for Mathematics, standard 3.OA.4
Which expression has the same value as 6 × 9?Answer: (6 × 5) + (6 × 4). Source: Illinois Learning Standards for Mathematics, standard 3.OA.5
Which multiplication fact helps you find 48 ÷ 8?Answer: 8 × 6 = 48. Source: Illinois Learning Standards for Mathematics, standard 3.OA.6
Which situation can be shown by 4 × 6?Answer: 4 bags with 6 apples in each bag. Source: Illinois Learning Standards for Mathematics, standard 3.OA.1
Number and operations in base ten 4
A school has 415 students. 268 of them ride the bus. How many do not ride the bus?Answer: 147. Source: Illinois Learning Standards for Mathematics, standard 3.NBT.2
What is 6 × 40?Answer: 240. Source: Illinois Learning Standards for Mathematics, standard 3.NBT.3
What is 348 + 275?Answer: 623. Source: Illinois Learning Standards for Mathematics, standard 3.NBT.2
What is 702 − 386?Answer: 316. Source: Illinois Learning Standards for Mathematics, standard 3.NBT.2
Number and operations: fractions 9
A number line from 0 to 1 is split into 4 equal parts. Which fraction names the point at the end of the third part, counting from 0?Answer: 3/4. Source: Illinois Learning Standards for Mathematics, standard 3.NF.2
A pizza is cut into 8 equal slices. Dan eats 3 slices. What fraction of the pizza does Dan eat?Answer: 3/8. Source: Illinois Learning Standards for Mathematics, standard 3.NF.1
A ribbon is cut into 6 equal parts. What fraction of the ribbon is 1 part?Answer: 1/6. Source: Illinois Learning Standards for Mathematics, standard 3.NF.1
On a number line, the space from 0 to 1 is split into 3 equal parts. How long is each part?Answer: 1/3. Source: Illinois Learning Standards for Mathematics, standard 3.NF.2
Two same-size sandwiches are cut into equal pieces. Ana eats 1/3 of hers. Ben eats 1/6 of his. Who eats more?Answer: Ana, because thirds are larger than sixths. Source: Illinois Learning Standards for Mathematics, standard 3.NF.3d
Which fraction is equal to the whole number 3?Answer: 6/2. Source: Illinois Learning Standards for Mathematics, standard 3.NF.3c
Which fraction names the same amount as 1/2?Answer: 3/6. Source: Illinois Learning Standards for Mathematics, standard 3.NF.3b
Which fraction names the same amount as 1/4?Answer: 2/8. Source: Illinois Learning Standards for Mathematics, standard 3.NF.3b
Which of these comparisons is correct?Answer: 3/8 < 5/8. Source: Illinois Learning Standards for Mathematics, standard 3.NF.3d
Measurement and data 10
A bucket holds 9 liters of water. How many liters do 5 buckets hold?Answer: 45 liters. Source: Illinois Learning Standards for Mathematics, standard 3.MD.2
A garden is a rectangle 9 feet long and 6 feet wide. How much fence goes all the way around it?Answer: 30 feet. Source: Illinois Learning Standards for Mathematics, standard 3.MD.8
A melon has a mass of 850 grams. An apple has a mass of 170 grams. How much more mass does the melon have?Answer: 680 grams. Source: Illinois Learning Standards for Mathematics, standard 3.MD.2
A pencil is measured to the nearest quarter inch. Which length could be the measurement?Answer: 4 3/4 inches. Source: Illinois Learning Standards for Mathematics, standard 3.MD.4
A rectangle is covered by 15 unit squares with no gaps and no overlaps. What is its area?Answer: 15 square units. Source: Illinois Learning Standards for Mathematics, standard 3.MD.6
A rug is 7 feet long and 4 feet wide. What is its area?Answer: 28 square feet. Source: Illinois Learning Standards for Mathematics, standard 3.MD.7b
A show starts at 6:40 p.m. and lasts 35 minutes. What time does it end?Answer: 7:15 p.m. Source: Illinois Learning Standards for Mathematics, standard 3.MD.1
An L-shaped room is made of a rectangle 5 meters by 3 meters joined to a square 2 meters by 2 meters. What is the area of the room?Answer: 19 square meters. Source: Illinois Learning Standards for Mathematics, standard 3.MD.7d
On a picture graph, 1 star stands for 5 books. The row for Friday shows 6 stars. How many books does the row show?Answer: 30. Source: Illinois Learning Standards for Mathematics, standard 3.MD.3
Soccer practice starts at 3:15 p.m. and ends at 4:05 p.m. How long is practice?Answer: 50 minutes. Source: Illinois Learning Standards for Mathematics, standard 3.MD.1
Geometry 3
A circle is split into 4 equal parts. What fraction of the circle's area is each part?Answer: 1/4. Source: Illinois Learning Standards for Mathematics, standard 3.G.2
A shape has 4 sides and 4 right angles, and its sides are not all the same length. What is it?Answer: A rectangle that is not a square. Source: Illinois Learning Standards for Mathematics, standard 3.G.1
Which of these shapes is a quadrilateral?Answer: Rhombus. Source: Illinois Learning Standards for Mathematics, standard 3.G.1
How this list was compiled: Outline: the Illinois Assessment of Readiness Grade 3 Mathematics Blueprint of the Illinois State Board of Education, https://www.isbe.net/Documents/IAR-Grade-3-Math-Blueprint.pdf, linked from https://www.isbe.net/Pages/IAR.aspx, read 2026-10-07. Each question names the standard it practices in the Illinois Learning Standards for Mathematics, https://www.isbe.net/Documents/math-standards.pdf, read 2026-10-07. Every answer that is a number was worked out a second time from the numbers in the question. Licence: Own work. Questions, answer choices and explanations were written for this site. Nothing is copied or reworded from the Illinois Assessment of Readiness, a practice item or released item of the state, an example in the standards or another practice test.
Grade 4: all 40 questions with answers
Operations and algebraic thinking 7
A baker makes 6 trays of 24 rolls and sells 130 rolls. How many rolls are left?Answer: 14. Source: Illinois Learning Standards for Mathematics, standard 4.OA.3
A blue ribbon is 6 inches long. A red ribbon is 4 times as long. How long is the red ribbon?Answer: 24 inches. Source: Illinois Learning Standards for Mathematics, standard 4.OA.2
A pattern starts at 3 and follows the rule "add 6": 3, 9, 15, 21. Which statement is true about every number in the pattern?Answer: Every number is odd. Source: Illinois Learning Standards for Mathematics, standard 4.OA.5
Show all 40 questions (37 more)
Operations and algebraic thinking, continued
A van holds 8 students. 53 students are going on a trip. What is the fewest vans needed?Answer: 7. Source: Illinois Learning Standards for Mathematics, standard 4.OA.3
Exactly one of these numbers is prime. Which one?Answer: 31. Source: Illinois Learning Standards for Mathematics, standard 4.OA.4
Jo read 27 pages. That is 3 times as many pages as Sam read. How many pages did Sam read?Answer: 9. Source: Illinois Learning Standards for Mathematics, standard 4.OA.2
Which statement matches the equation 35 = 5 × 7?Answer: 35 is 5 times as many as 7. Source: Illinois Learning Standards for Mathematics, standard 4.OA.1
Number and operations in base ten 11
In 4,400, how does the value of the 4 in the thousands place compare with the value of the 4 in the hundreds place?Answer: It is 10 times as much. Source: Illinois Learning Standards for Mathematics, standard 4.NBT.1
What is 6 × 348?Answer: 2,088. Source: Illinois Learning Standards for Mathematics, standard 4.NBT.5
What is 23 × 45?Answer: 1,035. Source: Illinois Learning Standards for Mathematics, standard 4.NBT.5
What is 752 ÷ 4?Answer: 188. Source: Illinois Learning Standards for Mathematics, standard 4.NBT.6
What is 5,738 + 2,496?Answer: 8,234. Source: Illinois Learning Standards for Mathematics, standard 4.NBT.4
What is 7,385 rounded to the nearest hundred?Answer: 7,400. Source: Illinois Learning Standards for Mathematics, standard 4.NBT.3
What is 9,003 − 4,567?Answer: 4,436. Source: Illinois Learning Standards for Mathematics, standard 4.NBT.4
What is 68,452 rounded to the nearest thousand?Answer: 68,000. Source: Illinois Learning Standards for Mathematics, standard 4.NBT.3
What is the remainder when 185 is divided by 6?Answer: 5. Source: Illinois Learning Standards for Mathematics, standard 4.NBT.6
Which comparison of whole numbers is true?Answer: 45,810 > 45,180. Source: Illinois Learning Standards for Mathematics, standard 4.NBT.2
Which is 60,000 + 2,000 + 40 + 9 in standard form?Answer: 62,049. Source: Illinois Learning Standards for Mathematics, standard 4.NBT.2
Number and operations: fractions 13
A recipe uses 3/4 cup of milk and 2/4 cup of water. How much liquid is that in all?Answer: 1 1/4 cups. Source: Illinois Learning Standards for Mathematics, standard 4.NF.3d
Each of 5 friends eats 3/8 of a pizza. How much pizza do they eat in all?Answer: 1 7/8 pizzas. Source: Illinois Learning Standards for Mathematics, standard 4.NF.4c
Ravi shades 2/5 of a paper strip. Which fraction names the same shaded amount?Answer: 4/10. Source: Illinois Learning Standards for Mathematics, standard 4.NF.1
What is 3 2/5 + 1 4/5?Answer: 5 1/5. Source: Illinois Learning Standards for Mathematics, standard 4.NF.3c
What is 4 × 2/3?Answer: 8/3. Source: Illinois Learning Standards for Mathematics, standard 4.NF.4b
What is 5/8 − 2/8?Answer: 3/8. Source: Illinois Learning Standards for Mathematics, standard 4.NF.3a
What is 5/10 + 7/100?Answer: 57/100. Source: Illinois Learning Standards for Mathematics, standard 4.NF.5
Which decimal is equal to 62/100?Answer: 0.62. Source: Illinois Learning Standards for Mathematics, standard 4.NF.6
Which fraction is equivalent to 8/12?Answer: 2/3. Source: Illinois Learning Standards for Mathematics, standard 4.NF.1
Which of these decimal comparisons is true?Answer: 0.5 > 0.45. Source: Illinois Learning Standards for Mathematics, standard 4.NF.7
Which of these fraction comparisons is true?Answer: 3/4 > 2/3. Source: Illinois Learning Standards for Mathematics, standard 4.NF.2
Which of these fractions is greater than 1/2?Answer: 4/6. Source: Illinois Learning Standards for Mathematics, standard 4.NF.2
Which sum equals 5/6?Answer: 1/6 + 1/6 + 3/6. Source: Illinois Learning Standards for Mathematics, standard 4.NF.3b
Measurement and data 6
A bag of flour has a mass of 3 kilograms. How many grams is that?Answer: 3,000. Source: Illinois Learning Standards for Mathematics, standard 4.MD.1
A hike starts at 9:30 a.m. and takes 2 hours 45 minutes. What time does it end?Answer: 12:15 p.m. Source: Illinois Learning Standards for Mathematics, standard 4.MD.2
A line plot shows ribbon lengths in inches: 1/2, 1/2, 3/4, 1 1/4, 1 1/4 and 1 1/4. What is the difference between the longest and the shortest ribbon?Answer: 3/4 inch. Source: Illinois Learning Standards for Mathematics, standard 4.MD.4
A rectangle has an area of 72 square feet and a width of 8 feet. What is its length?Answer: 9 feet. Source: Illinois Learning Standards for Mathematics, standard 4.MD.3
An angle of 130° is split into two parts. One part measures 55°. What does the other part measure?Answer: 75°. Source: Illinois Learning Standards for Mathematics, standard 4.MD.7
How many inches are in 4 feet?Answer: 48. Source: Illinois Learning Standards for Mathematics, standard 4.MD.1
Geometry 3
A triangle has one angle of 110°. What kind of triangle is it?Answer: Obtuse triangle. Source: Illinois Learning Standards for Mathematics, standard 4.G.2
How many lines of symmetry does a rectangle that is not a square have?Answer: 2. Source: Illinois Learning Standards for Mathematics, standard 4.G.3
Two lines in the same plane never meet, no matter how far they are extended. What are they called?Answer: Parallel lines. Source: Illinois Learning Standards for Mathematics, standard 4.G.1
How this list was compiled: Outline: the Illinois Assessment of Readiness Grade 4 Mathematics Blueprint of the Illinois State Board of Education, https://www.isbe.net/Documents/IAR-Grade-4-Math-Blueprint.pdf, linked from https://www.isbe.net/Pages/IAR.aspx, read 2026-10-07. Each question names the standard it practices in the Illinois Learning Standards for Mathematics, https://www.isbe.net/Documents/math-standards.pdf, read 2026-10-07. Every answer that is a number was worked out a second time from the numbers in the question. Licence: Own work. Questions, answer choices and explanations were written for this site. Nothing is copied or reworded from the Illinois Assessment of Readiness, a practice item or released item of the state, an example in the standards or another practice test.
Grade 5: all 40 questions with answers
Operations and algebraic thinking 4
How does the value of 4 × (316 + 58) compare with the value of 316 + 58?Answer: It is 4 times as large. Source: Illinois Learning Standards for Mathematics, standard 5.OA.2
Pattern A starts at 0 and adds 2. Pattern B starts at 0 and adds 6. How does each term of Pattern B compare with the matching term of Pattern A?Answer: It is 3 times as large. Source: Illinois Learning Standards for Mathematics, standard 5.OA.3
What is the value of 6 × (9 + 2) − 8?Answer: 58. Source: Illinois Learning Standards for Mathematics, standard 5.OA.1
Show all 40 questions (37 more)
Operations and algebraic thinking, continued
Which expression means "add 9 and 5, then multiply by 2"?Answer: 2 × (9 + 5). Source: Illinois Learning Standards for Mathematics, standard 5.OA.2
Number and operations in base ten 12
In 7.77, how does the value of the 7 in the tenths place compare with the value of the 7 in the hundredths place?Answer: It is 10 times as much. Source: Illinois Learning Standards for Mathematics, standard 5.NBT.1
What is 0.6 × 0.4?Answer: 0.24. Source: Illinois Learning Standards for Mathematics, standard 5.NBT.7
What is 0.675 rounded to the nearest hundredth?Answer: 0.68. Source: Illinois Learning Standards for Mathematics, standard 5.NBT.4
What is 3.45 + 12.7?Answer: 16.15. Source: Illinois Learning Standards for Mathematics, standard 5.NBT.7
What is 4.6 × 10²?Answer: 460. Source: Illinois Learning Standards for Mathematics, standard 5.NBT.2
What is 5.6 ÷ 0.7?Answer: 8. Source: Illinois Learning Standards for Mathematics, standard 5.NBT.7
What is 12.846 rounded to the nearest tenth?Answer: 12.8. Source: Illinois Learning Standards for Mathematics, standard 5.NBT.4
What is 304 × 26?Answer: 7,904. Source: Illinois Learning Standards for Mathematics, standard 5.NBT.5
What is 730 ÷ 10³?Answer: 0.73. Source: Illinois Learning Standards for Mathematics, standard 5.NBT.2
What is 1,656 ÷ 24?Answer: 69. Source: Illinois Learning Standards for Mathematics, standard 5.NBT.6
Which decimal comparison is correct?Answer: 3.207 < 3.27. Source: Illinois Learning Standards for Mathematics, standard 5.NBT.3b
Which decimal is 6 × 10 + 4 × 1 + 3 × (1/10) + 8 × (1/1000)?Answer: 64.308. Source: Illinois Learning Standards for Mathematics, standard 5.NBT.3a
Number and operations: fractions 13
4 friends share 3 granola bars equally. How much does each friend get?Answer: 3/4 of a bar. Source: Illinois Learning Standards for Mathematics, standard 5.NF.3
A 1/6-pound block of clay is split equally among 4 students. How much clay does each student get?Answer: 1/24 pound. Source: Illinois Learning Standards for Mathematics, standard 5.NF.7a
A 25-pound sack of rice is shared equally among 4 families. Between which two whole numbers of pounds is each share?Answer: 6 and 7. Source: Illinois Learning Standards for Mathematics, standard 5.NF.3
A rectangle is 3/4 yard long and 2/3 yard wide. What is its area?Answer: 1/2 square yard. Source: Illinois Learning Standards for Mathematics, standard 5.NF.4b
How many 1/4-pound servings can be made from 3 pounds of nuts?Answer: 12. Source: Illinois Learning Standards for Mathematics, standard 5.NF.7c
Kim walks 3/4 mile to the park and then 5/8 mile to the store. How far does she walk in all?Answer: 1 3/8 miles. Source: Illinois Learning Standards for Mathematics, standard 5.NF.2
One batch of bread uses 2 1/2 cups of flour. How much flour do 3 batches use?Answer: 7 1/2 cups. Source: Illinois Learning Standards for Mathematics, standard 5.NF.6
Tom says 1/2 + 2/5 = 3/7. Which statement shows his answer cannot be right?Answer: 3/7 is less than 1/2, but the sum must be more than 1/2. Source: Illinois Learning Standards for Mathematics, standard 5.NF.2
What is 3 1/2 − 1 2/5?Answer: 2 1/10. Source: Illinois Learning Standards for Mathematics, standard 5.NF.1
What is 3/5 of 35?Answer: 21. Source: Illinois Learning Standards for Mathematics, standard 5.NF.4a
What is 5/6 + 1/8?Answer: 23/24. Source: Illinois Learning Standards for Mathematics, standard 5.NF.1
What is 5/8 × 4/15?Answer: 1/6. Source: Illinois Learning Standards for Mathematics, standard 5.NF.4a
Without multiplying, which product is less than 3/4?Answer: 3/4 × 1/2. Source: Illinois Learning Standards for Mathematics, standard 5.NF.5a
Measurement and data 7
A box is packed with 4 layers of unit cubes and no gaps. Each layer has 6 cubes. What is the volume of the box?Answer: 24 cubic units. Source: Illinois Learning Standards for Mathematics, standard 5.MD.4
A cube with edges 1 unit long is used to measure volume. Which statement describes it?Answer: A unit cube, with a volume of 1 cubic unit. Source: Illinois Learning Standards for Mathematics, standard 5.MD.3
A fish tank is 10 inches long, 6 inches wide and 8 inches high. What is its volume?Answer: 480 cubic inches. Source: Illinois Learning Standards for Mathematics, standard 5.MD.5b
A jug holds 6 quarts. One quart is 4 cups. How many cups does the jug hold?Answer: 24. Source: Illinois Learning Standards for Mathematics, standard 5.MD.1
A line plot shows the juice in 4 glasses: 1/4 cup, 1/4 cup, 1/2 cup and 1 cup. If the juice is shared equally among the 4 glasses, how much is in each?Answer: 1/2 cup. Source: Illinois Learning Standards for Mathematics, standard 5.MD.2
A shed is made of two boxes. One is 4 meters by 3 meters by 2 meters. The other is 2 meters by 2 meters by 2 meters. What is the total volume?Answer: 32 cubic meters. Source: Illinois Learning Standards for Mathematics, standard 5.MD.5c
How many centimeters are in 3.5 meters?Answer: 350. Source: Illinois Learning Standards for Mathematics, standard 5.MD.1
Geometry 4
All rectangles have four right angles. A square is a rectangle. What must be true of every square?Answer: It has four right angles. Source: Illinois Learning Standards for Mathematics, standard 5.G.3
On a coordinate grid, how do you reach the point (4, 7) from the origin?Answer: Move 4 units right, then 7 units up. Source: Illinois Learning Standards for Mathematics, standard 5.G.1
Point A is at (2, 5) and point B is at (2, 9) on a coordinate grid. How far apart are they?Answer: 4 units. Source: Illinois Learning Standards for Mathematics, standard 5.G.2
Which shape is always a parallelogram?Answer: Rhombus. Source: Illinois Learning Standards for Mathematics, standard 5.G.4
How this list was compiled: Outline: the Illinois Assessment of Readiness Grade 5 Mathematics Blueprint of the Illinois State Board of Education, https://www.isbe.net/Documents/IAR-Grade-5-Math-Blueprint.pdf, linked from https://www.isbe.net/Pages/IAR.aspx, read 2026-10-07. Each question names the standard it practices in the Illinois Learning Standards for Mathematics, https://www.isbe.net/Documents/math-standards.pdf, read 2026-10-07. Every answer that is a number was worked out a second time from the numbers in the question. Licence: Own work. Questions, answer choices and explanations were written for this site. Nothing is copied or reworded from the Illinois Assessment of Readiness, a practice item or released item of the state, an example in the standards or another practice test.
Grade 6: all 40 questions with answers
Ratios and proportional relationships 9
8 pounds of apples cost $12. What is the cost per pound?Answer: $1.50. Source: Illinois Learning Standards for Mathematics, standard 6.RP.2
12 is 25% of what number?Answer: 48. Source: Illinois Learning Standards for Mathematics, standard 6.RP.3c
A bag holds 5 red marbles and 8 blue marbles. What is the ratio of red marbles to all the marbles?Answer: 5 to 13. Source: Illinois Learning Standards for Mathematics, standard 6.RP.1
Show all 40 questions (37 more)
Ratios and proportional relationships, continued
A board is 54 inches long. How long is it in feet?Answer: 4.5 feet. Source: Illinois Learning Standards for Mathematics, standard 6.RP.3d
A car travels 150 miles in 3 hours at a constant speed. How far does it travel in 5 hours?Answer: 250 miles. Source: Illinois Learning Standards for Mathematics, standard 6.RP.3b
A drink mix uses 2 cups of juice for every 3 cups of water. How many cups of water go with 10 cups of juice?Answer: 15. Source: Illinois Learning Standards for Mathematics, standard 6.RP.3a
A printer prints 90 pages in 6 minutes. What is its unit rate?Answer: 15 pages per minute. Source: Illinois Learning Standards for Mathematics, standard 6.RP.2
A school has 80 sixth graders, and 45% of them are in band. How many sixth graders are in band?Answer: 36. Source: Illinois Learning Standards for Mathematics, standard 6.RP.3c
In a class of 24 students, the ratio of students who walk to students who ride is 3 to 5. How many students walk?Answer: 9. Source: Illinois Learning Standards for Mathematics, standard 6.RP.3
The number system 10
6 cups of soup make how many servings of 3/4 cup each?Answer: 8. Source: Illinois Learning Standards for Mathematics, standard 6.NS.1
A diver is 20 feet below sea level. Sea level is 0. Which number shows her position?Answer: −20. Source: Illinois Learning Standards for Mathematics, standard 6.NS.5
The point (3, −4) is reflected across the x-axis. Where does it land?Answer: (3, 4). Source: Illinois Learning Standards for Mathematics, standard 6.NS.6b
What is 6.4 × 0.25?Answer: 1.6. Source: Illinois Learning Standards for Mathematics, standard 6.NS.3
What is 7/8 ÷ 1/16?Answer: 14. Source: Illinois Learning Standards for Mathematics, standard 6.NS.1
What is 9.36 ÷ 1.2?Answer: 7.8. Source: Illinois Learning Standards for Mathematics, standard 6.NS.3
What is 7,616 ÷ 32?Answer: 238. Source: Illinois Learning Standards for Mathematics, standard 6.NS.2
What is the greatest common factor of 48 and 72?Answer: 24. Source: Illinois Learning Standards for Mathematics, standard 6.NS.4
What is the least common multiple of 6 and 15?Answer: 30. Source: Illinois Learning Standards for Mathematics, standard 6.NS.4
Which list puts the integers in order from least to greatest?Answer: −8, −3, 0, 5. Source: Illinois Learning Standards for Mathematics, standard 6.NS.7b
Expressions and equations 12
A car travels 55 miles each hour. Which equation relates the distance d in miles to the time t in hours?Answer: d = 55t. Source: Illinois Learning Standards for Mathematics, standard 6.EE.9
A ride is open to people more than 48 inches tall. Which inequality shows the heights h that are allowed?Answer: h > 48. Source: Illinois Learning Standards for Mathematics, standard 6.EE.8
A ticket costs $8. Which expression gives the cost in dollars of t tickets?Answer: 8t. Source: Illinois Learning Standards for Mathematics, standard 6.EE.6
In the expression 5x + 9, what is the 5 called?Answer: The coefficient. Source: Illinois Learning Standards for Mathematics, standard 6.EE.2b
Solve: 5x = 65.Answer: x = 13. Source: Illinois Learning Standards for Mathematics, standard 6.EE.7
Solve: x + 14 = 31.Answer: x = 17. Source: Illinois Learning Standards for Mathematics, standard 6.EE.7
What is the value of 2⁴ + 3²?Answer: 25. Source: Illinois Learning Standards for Mathematics, standard 6.EE.1
What is the value of 3x² when x = 4?Answer: 48. Source: Illinois Learning Standards for Mathematics, standard 6.EE.2c
Which expression is equivalent to 6(x + 5)?Answer: 6x + 30. Source: Illinois Learning Standards for Mathematics, standard 6.EE.3
Which expression is equivalent to n + n + n + n?Answer: 4n. Source: Illinois Learning Standards for Mathematics, standard 6.EE.4
Which expression means "7 less than a number n"?Answer: n − 7. Source: Illinois Learning Standards for Mathematics, standard 6.EE.2a
Which value of x makes 3x + 2 = 20 true?Answer: 6. Source: Illinois Learning Standards for Mathematics, standard 6.EE.5
Geometry 5
A box is 1/2 foot long, 4 feet wide and 3 feet high. What is its volume?Answer: 6 cubic feet. Source: Illinois Learning Standards for Mathematics, standard 6.G.2
A cube has edges 3 inches long. What is its surface area?Answer: 54 square inches. Source: Illinois Learning Standards for Mathematics, standard 6.G.4
A parallelogram has a base of 9 feet and a height of 4 feet. What is its area?Answer: 36 square feet. Source: Illinois Learning Standards for Mathematics, standard 6.G.1
A rectangle has vertices at (1, 2), (1, 5), (8, 5) and (8, 2). What is its perimeter?Answer: 20 units. Source: Illinois Learning Standards for Mathematics, standard 6.G.3
A triangle has a base of 10 centimeters and a height of 6 centimeters. What is its area?Answer: 30 square centimeters. Source: Illinois Learning Standards for Mathematics, standard 6.G.1
Statistics and probability 4
The ages of 6 cousins are 3, 5, 8, 8, 11 and 14. What is the range?Answer: 11. Source: Illinois Learning Standards for Mathematics, standard 6.SP.5c
Five quiz scores are 5, 9, 7, 10 and 2. What is the median?Answer: 7. Source: Illinois Learning Standards for Mathematics, standard 6.SP.5c
The goals a team scored in 5 games are 2, 4, 4, 5 and 10. What is the mean?Answer: 5. Source: Illinois Learning Standards for Mathematics, standard 6.SP.3
Which question below is a statistical question?Answer: How many minutes do students in my class read each night? Source: Illinois Learning Standards for Mathematics, standard 6.SP.1
How this list was compiled: Outline: the Illinois Assessment of Readiness Grade 6 Mathematics Blueprint of the Illinois State Board of Education, https://www.isbe.net/Documents/IAR-Grade-6-Math-Blueprint.pdf, linked from https://www.isbe.net/Pages/IAR.aspx, read 2026-10-07. Each question names the standard it practices in the Illinois Learning Standards for Mathematics, https://www.isbe.net/Documents/math-standards.pdf, read 2026-10-07. Every answer that is a number was worked out a second time from the numbers in the question. Licence: Own work. Questions, answer choices and explanations were written for this site. Nothing is copied or reworded from the Illinois Assessment of Readiness, a practice item or released item of the state, an example in the standards or another practice test.
Grade 7: all 40 questions with answers
Ratios and proportional relationships 9
$500 earns simple interest at 4% per year. How much interest is earned in 3 years?Answer: $60. Source: Illinois Learning Standards for Mathematics, standard 7.RP.3
A $40 jacket is on sale for 15% off. What is the sale price?Answer: $34. Source: Illinois Learning Standards for Mathematics, standard 7.RP.3
A hiker walks 1/2 mile in 1/4 hour. What is her speed in miles per hour?Answer: 2. Source: Illinois Learning Standards for Mathematics, standard 7.RP.1
Show all 40 questions (37 more)
Ratios and proportional relationships, continued
A meal costs $25. A 20% tip is added. What is the total?Answer: $30. Source: Illinois Learning Standards for Mathematics, standard 7.RP.3
A town's population grows from 800 to 920. What is the percent increase?Answer: 15%. Source: Illinois Learning Standards for Mathematics, standard 7.RP.3
The graph of a proportional relationship passes through (1, 6). If x is hours and y is miles, what does this point mean?Answer: The unit rate is 6 miles per hour. Source: Illinois Learning Standards for Mathematics, standard 7.RP.2d
In a proportional relationship, y = 21 when x = 6. What is the constant of proportionality?Answer: 3.5. Source: Illinois Learning Standards for Mathematics, standard 7.RP.2b
Pears cost $1.80 per pound. Which equation gives the cost c in dollars of p pounds?Answer: c = 1.80p. Source: Illinois Learning Standards for Mathematics, standard 7.RP.2c
Which set of (x, y) pairs shows a proportional relationship?Answer: (1, 4), (2, 8), (3, 12). Source: Illinois Learning Standards for Mathematics, standard 7.RP.2a
The number system 9
A submarine is at −150 feet. It rises 40 feet, then dives 75 feet. What is its new position?Answer: −185 feet. Source: Illinois Learning Standards for Mathematics, standard 7.NS.3
The temperature is −4°F in the morning and 11°F in the afternoon. How many degrees did it rise?Answer: 15. Source: Illinois Learning Standards for Mathematics, standard 7.NS.1c
What is (−2/3) × (9/10)?Answer: −3/5. Source: Illinois Learning Standards for Mathematics, standard 7.NS.2c
What is (−9)(−4)?Answer: 36. Source: Illinois Learning Standards for Mathematics, standard 7.NS.2a
What is 7 − (−8)?Answer: 15. Source: Illinois Learning Standards for Mathematics, standard 7.NS.1c
What is −2.5 + 4.75 − 1.25?Answer: 1. Source: Illinois Learning Standards for Mathematics, standard 7.NS.1d
What is −8 + 5?Answer: −3. Source: Illinois Learning Standards for Mathematics, standard 7.NS.1b
What is −48 ÷ 6?Answer: −8. Source: Illinois Learning Standards for Mathematics, standard 7.NS.2b
Which decimal is equal to 5/8?Answer: 0.625. Source: Illinois Learning Standards for Mathematics, standard 7.NS.2d
Expressions and equations 10
A board 9 1/2 feet long is cut into 4 equal pieces. How long is each piece?Answer: 2 3/8 feet. Source: Illinois Learning Standards for Mathematics, standard 7.EE.3
A price p is raised by 5%. Which expression gives the new price?Answer: 1.05p. Source: Illinois Learning Standards for Mathematics, standard 7.EE.2
A rectangle has a perimeter of 54 centimeters and a length of 15 centimeters. What is its width?Answer: 12 centimeters. Source: Illinois Learning Standards for Mathematics, standard 7.EE.4a
Jen earns $12.50 an hour. She works 6 hours and then pays $9 for lunch. How much does she have left?Answer: $66. Source: Illinois Learning Standards for Mathematics, standard 7.EE.3
Sam has $60 and saves $15 each week. He wants at least $150. Which inequality gives the number of weeks w?Answer: 60 + 15w ≥ 150. Source: Illinois Learning Standards for Mathematics, standard 7.EE.4b
Solve: 2(x − 4) = 18.Answer: x = 13. Source: Illinois Learning Standards for Mathematics, standard 7.EE.4a
Solve: 4x + 9 = 45.Answer: x = 9. Source: Illinois Learning Standards for Mathematics, standard 7.EE.4a
Solve: 4x − 3 > 17.Answer: x > 5. Source: Illinois Learning Standards for Mathematics, standard 7.EE.4b
Which expression is a factored form of 12x + 18?Answer: 6(2x + 3). Source: Illinois Learning Standards for Mathematics, standard 7.EE.1
Which expression is equivalent to 2(3x − 4) + 5x?Answer: 11x − 8. Source: Illinois Learning Standards for Mathematics, standard 7.EE.1
Geometry 6
A circle has a diameter of 8 inches. Using 3.14 for π, what is its area?Answer: 50.24 square inches. Source: Illinois Learning Standards for Mathematics, standard 7.G.4
A circle has a radius of 6 centimeters. Using 3.14 for π, what is its circumference?Answer: 37.68 centimeters. Source: Illinois Learning Standards for Mathematics, standard 7.G.4
A right rectangular pyramid is sliced parallel to its base. What shape is the cross-section?Answer: A rectangle. Source: Illinois Learning Standards for Mathematics, standard 7.G.3
On a map, 1 inch stands for 20 miles. Two towns are 3.5 inches apart on the map. How far apart are the towns?Answer: 70 miles. Source: Illinois Learning Standards for Mathematics, standard 7.G.1
Two angles are supplementary. One measures 65°. What does the other measure?Answer: 115°. Source: Illinois Learning Standards for Mathematics, standard 7.G.5
Which set of side lengths can form a triangle?Answer: 4, 6 and 9. Source: Illinois Learning Standards for Mathematics, standard 7.G.2
Statistics and probability 6
A bag holds 3 red, 5 green and 2 yellow tiles. One tile is picked at random. What is the probability that it is green?Answer: 1/2. Source: Illinois Learning Standards for Mathematics, standard 7.SP.7a
A coin is flipped and a number cube with faces 1 to 6 is rolled. How many outcomes are in the sample space?Answer: 12. Source: Illinois Learning Standards for Mathematics, standard 7.SP.8b
A school wants to know its students' favorite lunch. Which sample is most likely to represent the whole school?Answer: 40 students chosen at random from all grades. Source: Illinois Learning Standards for Mathematics, standard 7.SP.1
A spinner lands on blue 12 times in 40 spins. Based on this, about how many times will it land on blue in 200 spins?Answer: 60. Source: Illinois Learning Standards for Mathematics, standard 7.SP.6
An event has a probability of 0.5. How likely is it?Answer: Neither likely nor unlikely. Source: Illinois Learning Standards for Mathematics, standard 7.SP.5
In a random sample of 50 students, 15 walk to school. About how many of the school's 600 students walk?Answer: 180. Source: Illinois Learning Standards for Mathematics, standard 7.SP.2
How this list was compiled: Outline: the Illinois Assessment of Readiness Grade 7 Mathematics Blueprint of the Illinois State Board of Education, https://www.isbe.net/Documents/IAR-Grade-7-Math-Blueprint.pdf, linked from https://www.isbe.net/Pages/IAR.aspx, read 2026-10-07. Each question names the standard it practices in the Illinois Learning Standards for Mathematics, https://www.isbe.net/Documents/math-standards.pdf, read 2026-10-07. Every answer that is a number was worked out a second time from the numbers in the question. Licence: Own work. Questions, answer choices and explanations were written for this site. Nothing is copied or reworded from the Illinois Assessment of Readiness, a practice item or released item of the state, an example in the standards or another practice test.
Grade 8: all 40 questions with answers
The number system 3
Between which two whole numbers is √70?Answer: 8 and 9. Source: Illinois Learning Standards for Mathematics, standard 8.NS.2
Which fraction is equal to the repeating decimal 0.777...?Answer: 7/9. Source: Illinois Learning Standards for Mathematics, standard 8.NS.1
Which number below cannot be written as a fraction of two integers?Answer: √11. Source: Illinois Learning Standards for Mathematics, standard 8.NS.1
Show all 40 questions (37 more)
Expressions and equations 13
A line passes through the origin and has a slope of 3. What is its equation?Answer: y = 3x. Source: Illinois Learning Standards for Mathematics, standard 8.EE.6
Car A travels 120 miles in 2 hours at a steady speed. Car B's distance in miles is d = 55t, where t is hours. Which car is faster?Answer: Car A, at 60 miles per hour. Source: Illinois Learning Standards for Mathematics, standard 8.EE.5
How many solutions does 2(x + 3) = 2x + 6 have?Answer: Infinitely many. Source: Illinois Learning Standards for Mathematics, standard 8.EE.7a
Solve the system: y = 2x and x + y = 12.Answer: (4, 8). Source: Illinois Learning Standards for Mathematics, standard 8.EE.8b
Solve: 7x − 9 = 3x + 19.Answer: x = 7. Source: Illinois Learning Standards for Mathematics, standard 8.EE.7b
Two lines on a graph cross at (2, 5). What does this point represent for the system of two equations?Answer: The one solution of the system. Source: Illinois Learning Standards for Mathematics, standard 8.EE.8a
What are the solutions of x² = 121?Answer: x = 11 and x = −11. Source: Illinois Learning Standards for Mathematics, standard 8.EE.2
What is (3 × 10⁴) × (2 × 10³)?Answer: 6 × 10⁷. Source: Illinois Learning Standards for Mathematics, standard 8.EE.4
What is the cube root of 64?Answer: 4. Source: Illinois Learning Standards for Mathematics, standard 8.EE.2
What is the slope of the line through (2, 3) and (5, 15)?Answer: 4. Source: Illinois Learning Standards for Mathematics, standard 8.EE.6
What is the value of 2⁻³?Answer: 1/8. Source: Illinois Learning Standards for Mathematics, standard 8.EE.1
Which expression is equivalent to 3⁵ × 3⁻²?Answer: 3³. Source: Illinois Learning Standards for Mathematics, standard 8.EE.1
Which is 45,000,000 written in scientific notation?Answer: 4.5 × 10⁷. Source: Illinois Learning Standards for Mathematics, standard 8.EE.3
Functions 9
A candle is 20 centimeters tall and burns down 2 centimeters each hour. How tall is it after 6 hours?Answer: 8 centimeters. Source: Illinois Learning Standards for Mathematics, standard 8.F.4
A function's rule is "multiply the input by 4, then subtract 1." What is the output for an input of 6?Answer: 23. Source: Illinois Learning Standards for Mathematics, standard 8.F.1
A graph of distance over time is a straight line that rises from left to right. What does it show?Answer: Distance increases at a constant rate. Source: Illinois Learning Standards for Mathematics, standard 8.F.5
A linear function has the values (0, 7) and (3, 1). What is its rate of change?Answer: −2. Source: Illinois Learning Standards for Mathematics, standard 8.F.4
A plumber charges a $40 fee plus $65 per hour. Which function gives the cost C in dollars for h hours?Answer: C = 65h + 40. Source: Illinois Learning Standards for Mathematics, standard 8.F.4
Function A is y = 2x + 1. Function B is linear and passes through (0, 0) and (2, 10). Which has the greater rate of change?Answer: Function B, with a rate of 5. Source: Illinois Learning Standards for Mathematics, standard 8.F.2
In y = mx + b, what does b stand for?Answer: The y-value where the line crosses the y-axis. Source: Illinois Learning Standards for Mathematics, standard 8.F.3
Which of these equations does not define a linear function?Answer: y = x² + 1. Source: Illinois Learning Standards for Mathematics, standard 8.F.3
Which set of (x, y) pairs is a function?Answer: (1, 3), (2, 3), (4, 5). Source: Illinois Learning Standards for Mathematics, standard 8.F.1
Geometry 10
A 13-foot ladder leans on a wall with its base 5 feet from the wall. How high up the wall does it reach?Answer: 12 feet. Source: Illinois Learning Standards for Mathematics, standard 8.G.7
A cylinder has a radius of 3 centimeters and a height of 10 centimeters. Using 3.14 for π, what is its volume?Answer: 282.6 cubic centimeters. Source: Illinois Learning Standards for Mathematics, standard 8.G.9
A dilation maps triangle ABC onto triangle DEF. What must be true?Answer: The triangles are similar. Source: Illinois Learning Standards for Mathematics, standard 8.G.4
A right triangle has legs of 9 and 12 units. How long is the hypotenuse?Answer: 15 units. Source: Illinois Learning Standards for Mathematics, standard 8.G.7
A segment 5 units long is rotated 90° about a point. How long is its image?Answer: 5 units. Source: Illinois Learning Standards for Mathematics, standard 8.G.1a
A triangle is dilated by a scale factor of 3 about the origin. One vertex is at (2, −1). Where is its image?Answer: (6, −3). Source: Illinois Learning Standards for Mathematics, standard 8.G.3
The point (3, −2) is translated 4 units left and 5 units up. Where is its image?Answer: (−1, 3). Source: Illinois Learning Standards for Mathematics, standard 8.G.3
Two angles of a triangle measure 52° and 71°. What is the third angle?Answer: 57°. Source: Illinois Learning Standards for Mathematics, standard 8.G.5
Two figures are congruent when one can be moved onto the other by a sequence of which moves?Answer: Rotations, reflections and translations. Source: Illinois Learning Standards for Mathematics, standard 8.G.2
What is the distance between (1, 1) and (4, 5) on a coordinate plane?Answer: 5 units. Source: Illinois Learning Standards for Mathematics, standard 8.G.8
Statistics and probability 5
A line of fit for a plant is h = 1.5w + 4, where h is height in centimeters and w is weeks. What does 1.5 mean?Answer: The plant grows about 1.5 centimeters each week. Source: Illinois Learning Standards for Mathematics, standard 8.SP.3
In a survey of 80 students, 30 play a sport, and 12 of those 30 also play an instrument. Among students who play a sport, what is the relative frequency of playing an instrument?Answer: 40%. Source: Illinois Learning Standards for Mathematics, standard 8.SP.4
On a scatter plot of height and shoe size, one point lies far from all the others. What is that point called?Answer: An outlier. Source: Illinois Learning Standards for Mathematics, standard 8.SP.1
On a scatter plot, the points rise from left to right and lie close to a line. What kind of association is shown?Answer: Positive linear association. Source: Illinois Learning Standards for Mathematics, standard 8.SP.1
Which line is the best fit for a scatter plot with a linear association?Answer: A line that passes close to most of the points. Source: Illinois Learning Standards for Mathematics, standard 8.SP.2
How this list was compiled: Outline: the Illinois Assessment of Readiness Grade 8 Mathematics Blueprint of the Illinois State Board of Education, https://www.isbe.net/Documents/IAR-Grade-8-Math-Blueprint.pdf, linked from https://www.isbe.net/Pages/IAR.aspx, read 2026-10-07. Each question names the standard it practices in the Illinois Learning Standards for Mathematics, https://www.isbe.net/Documents/math-standards.pdf, read 2026-10-07. Every answer that is a number was worked out a second time from the numbers in the question. Licence: Own work. Questions, answer choices and explanations were written for this site. Nothing is copied or reworded from the Illinois Assessment of Readiness, a practice item or released item of the state, an example in the standards or another practice test.
How it works
Unofficial practice for the mathematics part of the Illinois Assessment of Readiness (IAR), grades 3 to 8. Every question was written for this page, and none comes from a real test. Not affiliated with the Illinois State Board of Education.
Read the full guide
What each grade's test weighs most
Each grade's blueprint gives the most points to its major content, and the questions here lean the same way. Grade 3: multiplication, division and fractions. Grade 4: multi-digit numbers and fractions. Grade 5: decimals, fractions and volume. Grade 6: ratios, signed numbers and equations. Grade 7: proportions and rational numbers. Grade 8: linear equations, functions and the Pythagorean theorem.
How the answers are checked
Each question practices one standard of the Illinois Learning Standards, named under its answer. Every answer that is a number was worked out a second time from the numbers in the question. Wrong choices are common slips, such as giving the area when the question asks for the perimeter.
In grades 3 to 5, practice with no calculator, as on the real test.
On the written questions of the real test, a right answer with no work shown does not earn the top score. Practice writing your steps.
Questions and answers
Can you use a calculator on the IAR math test?
Not in grades 3 to 5. Grades 6 and 7 allow a four-function calculator with square root and percent in part of section 1 and in sections 2 and 3. Grade 8 allows a scientific calculator in sections 2 and 3.
How long is IAR math testing?
Three sections of 60 minutes each, 180 minutes in all, in every grade from 3 to 8. The state calls the test points-based, so the number of questions in a section can vary.
What is a passing score on the IAR math test?
The state publishes score levels, not a pass mark. Scores run from 650 to 850 in four levels, and Proficient begins at 732 in grade 3, 740 in grades 4 and 5, 742 in grade 6 and 745 in grades 7 and 8.
Is this the official IAR math practice test?
No. It is unofficial: every question was written for this site, and none is a released or practice item. The state's own practice items show the real question kinds, and the box under the questions links to them.