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The real test: mathematics, grades 3 to 8
Grades 3 to 5
150 minutes in two parts of 75 minutes. 49 to 51 points.
Grades 6 to 8
180 minutes in two parts of 90 minutes. 52 to 54 points.
Modeling and reasoning
A minimum of 20% of each test. It draws on the same standards as the reporting categories.
Proficient
A score of 700 or higher shows a student has met the state standards for the subject and grade.
How it is given
Online and scored by machine. Some item types give partial credit.
7 × 8 can be split into (7 × 5) + (7 × ?). What number is missing?Ohio's Learning Standards for Mathematics (2017), standard 3.OA.5
45 ÷ 5 = ? Which multiplication fact helps find the answer?Ohio's Learning Standards for Mathematics (2017), standard 3.OA.6
54 crayons are shared equally among 6 tables. How many crayons does each table get?Ohio's Learning Standards for Mathematics (2017), standard 3.OA.3
Show all 40 questions (37 more)
Multiplication and Division, continued
A baker puts 6 muffins in each box. How many muffins are in 7 boxes?Ohio's Learning Standards for Mathematics (2017), standard 3.OA.3
Mia buys 4 packs of stickers. Each pack has 8 stickers. She gives 5 stickers to a friend. How many stickers does she have left?Ohio's Learning Standards for Mathematics (2017), standard 3.OA.8
The numbers 4, 8, 12, 16 follow a rule. Which number comes next?Ohio's Learning Standards for Mathematics (2017), standard 3.OA.9
Tom has 50 marbles. He puts 6 marbles into each of 7 cups. How many marbles are left over?Ohio's Learning Standards for Mathematics (2017), standard 3.OA.8
What is 7 × 60?Ohio's Learning Standards for Mathematics (2017), standard 3.NBT.3
What number makes this equation true? 8 × ? = 56Ohio's Learning Standards for Mathematics (2017), standard 3.OA.4
Which situation can be shown by 4 × 7?Ohio's Learning Standards for Mathematics (2017), standard 3.OA.1
Number and Operations 10
A bar graph shows favorite fruits: 12 students pick apples, 7 pick grapes and 9 pick bananas. How many students voted in all?Ohio's Learning Standards for Mathematics (2017), standard 3.MD.3
A movie starts at 6:20 and lasts 50 minutes. What time does it end?Ohio's Learning Standards for Mathematics (2017), standard 3.MD.1
A pitcher holds 2 liters of juice. How many liters do 6 of these pitchers hold?Ohio's Learning Standards for Mathematics (2017), standard 3.MD.2
In a picture graph, each star stands for 5 books. Ana has 6 stars and Ben has 4 stars. How many more books did Ana read than Ben?Ohio's Learning Standards for Mathematics (2017), standard 3.MD.3
Leo has 2 quarters, 3 dimes and 4 pennies. How many cents does he have?Ohio's Learning Standards for Mathematics (2017), standard 3.MD.1
Soccer practice starts at 3:45 and ends at 4:30. How many minutes long is practice?Ohio's Learning Standards for Mathematics (2017), standard 3.MD.1
What is 351 rounded to the nearest ten?Ohio's Learning Standards for Mathematics (2017), standard 3.NBT.1
What is 458 + 367?Ohio's Learning Standards for Mathematics (2017), standard 3.NBT.2
What is 468 rounded to the nearest hundred?Ohio's Learning Standards for Mathematics (2017), standard 3.NBT.1
What is 632 − 257?Ohio's Learning Standards for Mathematics (2017), standard 3.NBT.2
Geometry 10
A floor is 9 feet long and 6 feet wide. How many 1-foot square tiles cover it?Ohio's Learning Standards for Mathematics (2017), standard 3.MD.7
A garden is made of two rectangles joined together. One is 6 feet by 3 feet. The other is 4 feet by 2 feet. What is the total area?Ohio's Learning Standards for Mathematics (2017), standard 3.MD.7
A rectangle has an area of 24 square feet. It is 6 feet long. What is its perimeter?Ohio's Learning Standards for Mathematics (2017), standard 3.MD.8
A rectangle is 8 units long and 5 units wide. What is its area?Ohio's Learning Standards for Mathematics (2017), standard 3.MD.7
A rectangle is 9 feet long and 4 feet wide. What is its perimeter?Ohio's Learning Standards for Mathematics (2017), standard 3.MD.8
A rectangle is covered by 3 rows of unit squares with no gaps. Each row has 7 squares. What is its area?Ohio's Learning Standards for Mathematics (2017), standard 3.MD.6
A rectangle is cut into 6 parts that all have the same area. What fraction of the whole rectangle is one part?Ohio's Learning Standards for Mathematics (2017), standard 3.G.2
A shape has 5 sides. Each side is 6 cm long. What is its perimeter?Ohio's Learning Standards for Mathematics (2017), standard 3.MD.8
A square has a perimeter of 28 inches. How long is each side?Ohio's Learning Standards for Mathematics (2017), standard 3.MD.8
Which shape always has 4 equal sides and 4 square corners?Ohio's Learning Standards for Mathematics (2017), standard 3.G.1
Fractions 10
A number line from 0 to 1 is split into 4 equal parts. What number is at the third mark after 0?Ohio's Learning Standards for Mathematics (2017), standard 3.NF.2
A pizza is cut into 8 equal slices. Sam eats 3 slices. What fraction of the pizza does Sam eat?Ohio's Learning Standards for Mathematics (2017), standard 3.NF.1
A rope is cut into 6 equal pieces. Jo uses 5 of them. What fraction of the rope is left?Ohio's Learning Standards for Mathematics (2017), standard 3.NF.1
Four pencils are measured to the nearest quarter inch: 5 1/4, 5 3/4, 5 1/2 and 6 inches. Which length is the shortest?Ohio's Learning Standards for Mathematics (2017), standard 3.MD.4
On a number line, which whole number is at the same point as 8/4?Ohio's Learning Standards for Mathematics (2017), standard 3.NF.2
Two pies are the same size. Ava eats 3/4 of one pie. Ben eats 3/8 of the other. Who eats more pie?Ohio's Learning Standards for Mathematics (2017), standard 3.NF.3
Which fraction is equal to 1/2?Ohio's Learning Standards for Mathematics (2017), standard 3.NF.3
Which fraction is equal to 2/3?Ohio's Learning Standards for Mathematics (2017), standard 3.NF.3
Which fraction is equal to 3?Ohio's Learning Standards for Mathematics (2017), standard 3.NF.3
Which fraction is the greatest?Ohio's Learning Standards for Mathematics (2017), standard 3.NF.3
86 students are going on a trip. Each van holds 9 students. What is the fewest vans needed so that every student has a seat?Ohio's Learning Standards for Mathematics (2017), standard 4.OA.3
A bike costs 6 times as much as a helmet. The helmet costs $24. How much does the bike cost?Ohio's Learning Standards for Mathematics (2017), standard 4.OA.2
A pattern starts at 4 and follows the rule "add 7." What is the fifth number in the pattern?Ohio's Learning Standards for Mathematics (2017), standard 4.OA.5
Show all 40 questions (37 more)
Multiplication and Division, continued
A rectangular rug has an area of 72 square feet. It is 8 feet wide. How long is the rug?Ohio's Learning Standards for Mathematics (2017), standard 4.MD.3
A store has 250 pencils. It sells 6 boxes of 24 pencils. How many pencils are left?Ohio's Learning Standards for Mathematics (2017), standard 4.OA.3
A tree is 36 feet tall. It is 4 times as tall as a bush. How tall is the bush?Ohio's Learning Standards for Mathematics (2017), standard 4.OA.2
How many hundreds are in 4,000?Ohio's Learning Standards for Mathematics (2017), standard 4.NBT.1
Ty buys a sandwich for $3.25 and a juice for $1.40. He pays with a $5 bill. How much change does he get?Ohio's Learning Standards for Mathematics (2017), standard 4.MD.2
What is 6 × 2,315?Ohio's Learning Standards for Mathematics (2017), standard 4.NBT.5
What is 34 × 26?Ohio's Learning Standards for Mathematics (2017), standard 4.NBT.5
What is 1,256 ÷ 4?Ohio's Learning Standards for Mathematics (2017), standard 4.NBT.6
What is 38,605 + 4,728?Ohio's Learning Standards for Mathematics (2017), standard 4.NBT.4
What is 47,382 rounded to the nearest thousand?Ohio's Learning Standards for Mathematics (2017), standard 4.NBT.3
Which list shows all the factors of 18?Ohio's Learning Standards for Mathematics (2017), standard 4.OA.4
Which number is 60,000 + 400 + 8?Ohio's Learning Standards for Mathematics (2017), standard 4.NBT.2
Which number is prime?Ohio's Learning Standards for Mathematics (2017), standard 4.OA.4
Fractions 14
A line plot shows the lengths of four bugs in inches: 2/8, 3/8, 3/8 and 7/8. How much longer is the longest bug than the shortest?Ohio's Learning Standards for Mathematics (2017), standard 4.MD.4
Rosa has 2 3/4 feet of ribbon. She buys 1 2/4 feet more. How much ribbon does she have now?Ohio's Learning Standards for Mathematics (2017), standard 4.NF.3
What is 3 1/5 − 1 3/5?Ohio's Learning Standards for Mathematics (2017), standard 4.NF.3
What is 3 7/100 written as a decimal?Ohio's Learning Standards for Mathematics (2017), standard 4.NF.6
What is 3/8 + 4/8?Ohio's Learning Standards for Mathematics (2017), standard 4.NF.3
What is 3/10 + 4/100?Ohio's Learning Standards for Mathematics (2017), standard 4.NF.5
What is 5 × 2/3?Ohio's Learning Standards for Mathematics (2017), standard 4.NF.4
Which comparison of decimals is true?Ohio's Learning Standards for Mathematics (2017), standard 4.NF.7
Which comparison of fractions is true?Ohio's Learning Standards for Mathematics (2017), standard 4.NF.2
Which decimal is the greatest?Ohio's Learning Standards for Mathematics (2017), standard 4.NF.7
Which fraction is equivalent to 2/3?Ohio's Learning Standards for Mathematics (2017), standard 4.NF.1
Which fraction is greater than 1/2?Ohio's Learning Standards for Mathematics (2017), standard 4.NF.2
Which product is equal to 7/5?Ohio's Learning Standards for Mathematics (2017), standard 4.NF.4
Which sum is equal to 5/6?Ohio's Learning Standards for Mathematics (2017), standard 4.NF.3
Geometry 10
A 125° angle is split into two smaller angles. One of them measures 48°. What does the other one measure?Ohio's Learning Standards for Mathematics (2017), standard 4.MD.7
A bag of apples has a mass of 4 kilograms 250 grams. What is its mass in grams?Ohio's Learning Standards for Mathematics (2017), standard 4.MD.1
A full turn around a circle is 360°. An angle turns through 1/4 of the circle. What is the measure of the angle?Ohio's Learning Standards for Mathematics (2017), standard 4.MD.5
A ribbon is 2 meters 35 centimeters long. How long is it in centimeters?Ohio's Learning Standards for Mathematics (2017), standard 4.MD.1
A triangle has one angle that measures 90°. What kind of triangle is it?Ohio's Learning Standards for Mathematics (2017), standard 4.G.2
An angle measures 130°. What kind of angle is it?Ohio's Learning Standards for Mathematics (2017), standard 4.G.1
How many meters are in 6 kilometers?Ohio's Learning Standards for Mathematics (2017), standard 4.MD.1
How many pairs of parallel sides does a rectangle have?Ohio's Learning Standards for Mathematics (2017), standard 4.G.2
Three angles together make a straight line, which measures 180°. Two of the angles measure 65° and 40°. What does the third angle measure?Ohio's Learning Standards for Mathematics (2017), standard 4.MD.7
Two lines cross and form four right angles. What are the lines called?Ohio's Learning Standards for Mathematics (2017), standard 4.G.1
A board is 7/8 yard long. Dan cuts off 1/2 yard. How much of the board is left?Ohio's Learning Standards for Mathematics (2017), standard 5.NF.2
A garden bed is 2 1/2 yards long and 1 1/2 yards wide. What is its area?Ohio's Learning Standards for Mathematics (2017), standard 5.NF.6
A line plot shows the water in four cups: 1/4, 1/2, 1/2 and 3/4 cup. If the water is shared equally among the four cups, how much is in each?Ohio's Learning Standards for Mathematics (2017), standard 5.MD.2
Show all 40 questions (37 more)
Fractions, continued
A recipe uses 2/3 cup of milk. Lee makes 1 1/2 times the recipe. How much milk does she need?Ohio's Learning Standards for Mathematics (2017), standard 5.NF.6
Four friends share 3 pounds of trail mix equally. How much does each friend get?Ohio's Learning Standards for Mathematics (2017), standard 5.NF.3
How many 1/4-cup servings are in 3 cups of yogurt?Ohio's Learning Standards for Mathematics (2017), standard 5.NF.7
Jada walked 3/4 mile to the park and then 5/8 mile to the library. How far did she walk in all?Ohio's Learning Standards for Mathematics (2017), standard 5.NF.2
Nine feet of rope is cut into 4 equal pieces. How long is each piece?Ohio's Learning Standards for Mathematics (2017), standard 5.NF.3
What is 1 3/4 + 2 2/3?Ohio's Learning Standards for Mathematics (2017), standard 5.NF.1
What is 1/5 ÷ 3?Ohio's Learning Standards for Mathematics (2017), standard 5.NF.7
What is 2/3 + 1/4?Ohio's Learning Standards for Mathematics (2017), standard 5.NF.1
What is 2/3 × 3/5?Ohio's Learning Standards for Mathematics (2017), standard 5.NF.4
What is 3 1/2 − 1 1/3?Ohio's Learning Standards for Mathematics (2017), standard 5.NF.1
What is 3/4 × 2/9?Ohio's Learning Standards for Mathematics (2017), standard 5.NF.4
Decimals 16
The 4 in 0.04 is worth what fraction of the 4 in 0.4?Ohio's Learning Standards for Mathematics (2017), standard 5.NBT.1
A baker packs 925 rolls into bags of 12. How many full bags does she fill?Ohio's Learning Standards for Mathematics (2017), standard 5.NBT.6
How many minutes are in 2 1/2 hours?Ohio's Learning Standards for Mathematics (2017), standard 5.MD.1
Nora buys a notebook for $3.75 and a pen for $1.48. She pays with a $10 bill. How much change does she get?Ohio's Learning Standards for Mathematics (2017), standard 5.NBT.7
The value of the 5 in 3,542 is how many times the value of the 5 in 3,452?Ohio's Learning Standards for Mathematics (2017), standard 5.NBT.1
What is 4.7 × 1,000?Ohio's Learning Standards for Mathematics (2017), standard 5.NBT.2
What is 6.847 rounded to the nearest tenth?Ohio's Learning Standards for Mathematics (2017), standard 5.NBT.4
What is 12.5 − 3.78?Ohio's Learning Standards for Mathematics (2017), standard 5.NBT.7
What is 52.6 ÷ 100?Ohio's Learning Standards for Mathematics (2017), standard 5.NBT.2
What is 307 × 46?Ohio's Learning Standards for Mathematics (2017), standard 5.NBT.5
What is 426 × 38?Ohio's Learning Standards for Mathematics (2017), standard 5.NBT.5
What is 1,512 ÷ 24?Ohio's Learning Standards for Mathematics (2017), standard 5.NBT.6
What is the value of (40 − 16) ÷ (2 + 6)?Ohio's Learning Standards for Mathematics (2017), standard 5.OA.1
What is the value of 3 × (4 + 6) − 8?Ohio's Learning Standards for Mathematics (2017), standard 5.OA.1
Which number is the least?Ohio's Learning Standards for Mathematics (2017), standard 5.NBT.3
Which number is three and forty-two thousandths?Ohio's Learning Standards for Mathematics (2017), standard 5.NBT.3
Geometry 10
A box has a volume of 96 cubic inches. Its base is 6 inches by 4 inches. How tall is the box?Ohio's Learning Standards for Mathematics (2017), standard 5.MD.5
A box is 6 inches long, 4 inches wide and 5 inches tall. What is its volume?Ohio's Learning Standards for Mathematics (2017), standard 5.MD.5
A box is packed with 3 layers of unit cubes. Each layer has 4 rows of 5 cubes. How many cubes fill the box?Ohio's Learning Standards for Mathematics (2017), standard 5.MD.4
A solid is made of two boxes that do not overlap. One has a volume of 36 cubic feet. The other is 2 feet by 3 feet by 4 feet. What is the total volume?Ohio's Learning Standards for Mathematics (2017), standard 5.MD.5
A unit cube has edges 1 cm long. A box is packed full with 30 unit cubes and no gaps. What is the volume of the box?Ohio's Learning Standards for Mathematics (2017), standard 5.MD.3
On a coordinate grid, point A is at (2, 5) and point B is at (2, 9). How many units apart are the points?Ohio's Learning Standards for Mathematics (2017), standard 5.G.2
On a coordinate grid, what does the first number in the ordered pair (4, 7) tell you to do?Ohio's Learning Standards for Mathematics (2017), standard 5.G.1
Pattern A starts at 0 and adds 3 each time. Pattern B starts at 0 and adds 6 each time. When Pattern A reaches 12, what is the matching number in Pattern B?Ohio's Learning Standards for Mathematics (2017), standard 5.OA.3
Point P is at (3, 2). Point Q is 5 units straight up from P. What are the coordinates of Q?Ohio's Learning Standards for Mathematics (2017), standard 5.G.2
Which statement is true?Ohio's Learning Standards for Mathematics (2017), standard 5.G.4
15 is 25% of what number?Ohio's Learning Standards for Mathematics (2017), standard 6.RP.3
A 12-ounce bag of rice costs $3.00. What is the cost per ounce?Ohio's Learning Standards for Mathematics (2017), standard 6.RP.2
A bag has 4 red tiles and 10 blue tiles. What is the ratio of blue tiles to all tiles, in simplest form?Ohio's Learning Standards for Mathematics (2017), standard 6.RP.1
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Ratios and Proportions, continued
A car travels 150 miles on 6 gallons of gas. How many miles does it travel per gallon?Ohio's Learning Standards for Mathematics (2017), standard 6.RP.2
A class has 12 girls and 16 boys. What is the ratio of girls to boys in simplest form?Ohio's Learning Standards for Mathematics (2017), standard 6.RP.1
A class has 40 students. 35% of them play an instrument. How many students play an instrument?Ohio's Learning Standards for Mathematics (2017), standard 6.RP.3
A machine fills 240 bottles in 8 minutes. At that rate, how many minutes does it take to fill 600 bottles?Ohio's Learning Standards for Mathematics (2017), standard 6.RP.3
A printer prints 45 pages in 3 minutes. At this rate, how many pages does it print in 8 minutes?Ohio's Learning Standards for Mathematics (2017), standard 6.RP.3
A table of equal ratios shows 4 pencils for $1 and 12 pencils for $3. How many pencils can be bought for $7?Ohio's Learning Standards for Mathematics (2017), standard 6.RP.3
What is 30% of 80?Ohio's Learning Standards for Mathematics (2017), standard 6.RP.3
Expressions and Equations 14
A pack of 6 juice boxes costs $4.50. Each box costs the same amount, c. What value of c makes 6c = 4.50 true?Ohio's Learning Standards for Mathematics (2017), standard 6.EE.7
A sign says a bridge is only for trucks that weigh less than 10 tons. Which inequality shows the weights w, in tons, that are allowed?Ohio's Learning Standards for Mathematics (2017), standard 6.EE.8
A ticket costs $9. Which expression gives the cost in dollars of n tickets?Ohio's Learning Standards for Mathematics (2017), standard 6.EE.6
A worker earns $12 each hour. The pay p for h hours is p = 12h. Which is the dependent variable?Ohio's Learning Standards for Mathematics (2017), standard 6.EE.9
Solve: x + 18 = 45Ohio's Learning Standards for Mathematics (2017), standard 6.EE.7
Solve: x ÷ 5 = 12Ohio's Learning Standards for Mathematics (2017), standard 6.EE.7
The volume of a cube is s³, where s is the length of an edge. What is the volume when s = 3 cm?Ohio's Learning Standards for Mathematics (2017), standard 6.EE.2
What is the value of 2³ + 4²?Ohio's Learning Standards for Mathematics (2017), standard 6.EE.1
What is the value of 3x + 5 when x = 4?Ohio's Learning Standards for Mathematics (2017), standard 6.EE.2
What is the value of 5² − 3 × 2³?Ohio's Learning Standards for Mathematics (2017), standard 6.EE.1
Which expression is equivalent to 4(x + 3)?Ohio's Learning Standards for Mathematics (2017), standard 6.EE.3
Which expression is equivalent to 5y + 2y + y?Ohio's Learning Standards for Mathematics (2017), standard 6.EE.4
Which expression is equivalent to 20x + 30?Ohio's Learning Standards for Mathematics (2017), standard 6.EE.3
Which value of x makes the inequality x > 12 true?Ohio's Learning Standards for Mathematics (2017), standard 6.EE.5
Geometry and Statistics 8
A box is 4 feet long, 2 1/2 feet wide and 3 feet tall. What is its volume?Ohio's Learning Standards for Mathematics (2017), standard 6.G.2
A box is 5 inches long, 3 inches wide and 2 inches tall. What is its surface area?Ohio's Learning Standards for Mathematics (2017), standard 6.G.4
A shape is made of a 6 cm by 4 cm rectangle with a triangle on top. The triangle has a base of 6 cm and a height of 3 cm. What is the total area?Ohio's Learning Standards for Mathematics (2017), standard 6.G.1
A triangle has a base of 10 cm and a height of 6 cm. What is its area?Ohio's Learning Standards for Mathematics (2017), standard 6.G.1
Five students read 3, 5, 6, 8 and 8 books. What is the mean number of books?Ohio's Learning Standards for Mathematics (2017), standard 6.SP.5
What is the interquartile range of this data set? 1, 3, 5, 9, 11, 15, 17, 21Ohio's Learning Standards for Mathematics (2017), standard 6.SP.5
What is the median of this data set? 4, 9, 2, 7, 12Ohio's Learning Standards for Mathematics (2017), standard 6.SP.5
Which is a statistical question?Ohio's Learning Standards for Mathematics (2017), standard 6.SP.1
The Number System 8
How many 2/3-cup servings are in 4 cups of soup?Ohio's Learning Standards for Mathematics (2017), standard 6.NS.1
The temperature is −12°F in one town and −5°F in another. Which statement is true?Ohio's Learning Standards for Mathematics (2017), standard 6.NS.7
What is 3/4 ÷ 1/8?Ohio's Learning Standards for Mathematics (2017), standard 6.NS.1
What is 4.8 × 0.25?Ohio's Learning Standards for Mathematics (2017), standard 6.NS.3
What is 15.3 ÷ 0.6?Ohio's Learning Standards for Mathematics (2017), standard 6.NS.3
What is the greatest common factor of 36 and 48?Ohio's Learning Standards for Mathematics (2017), standard 6.NS.4
Which integer is the least?Ohio's Learning Standards for Mathematics (2017), standard 6.NS.7
Which point is the reflection of (3, −5) across the y-axis?Ohio's Learning Standards for Mathematics (2017), standard 6.NS.6
A hiker walks 3/4 mile in 1/3 hour. At that rate, what is her speed in miles per hour?Ohio's Learning Standards for Mathematics (2017), standard 7.RP.1
A jacket costs $80. It is on sale for 25% off. What is the sale price?Ohio's Learning Standards for Mathematics (2017), standard 7.RP.3
A meal costs $40. The customer leaves an 18% tip. What is the total paid?Ohio's Learning Standards for Mathematics (2017), standard 7.RP.3
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Ratios and Proportions, continued
A phone costs $250. Sales tax is 6%. What is the total cost?Ohio's Learning Standards for Mathematics (2017), standard 7.RP.3
A recipe uses 1/2 cup of sugar for every 3/4 cup of flour. How much sugar is used for 1 cup of flour?Ohio's Learning Standards for Mathematics (2017), standard 7.RP.1
A salesperson earns a 5% commission. How much does she earn on $3,400 in sales?Ohio's Learning Standards for Mathematics (2017), standard 7.RP.3
A town grew from 2,000 people to 2,300 people. What was the percent increase?Ohio's Learning Standards for Mathematics (2017), standard 7.RP.3
The graph of a proportional relationship passes through the point (1, 3.5). What does this point show?Ohio's Learning Standards for Mathematics (2017), standard 7.RP.2
In a proportional relationship, 3 pounds of nuts cost $7.50 and 5 pounds cost $12.50. What is the constant of proportionality, in dollars per pound?Ohio's Learning Standards for Mathematics (2017), standard 7.RP.2
Which table shows a proportional relationship between x and y?Ohio's Learning Standards for Mathematics (2017), standard 7.RP.2
The Number System 12
A price p is raised by 20%. Which expression gives the new price?Ohio's Learning Standards for Mathematics (2017), standard 7.EE.2
A taxi charges $4 plus $2 per mile. A ride costs $18. How many miles long was the ride?Ohio's Learning Standards for Mathematics (2017), standard 7.EE.4
Ana has $20. She buys 4 notebooks at $3.75 each. How much money does she have left?Ohio's Learning Standards for Mathematics (2017), standard 7.EE.3
At noon the temperature was 5°F. It fell 2.5 degrees each hour for 4 hours. What was the temperature then?Ohio's Learning Standards for Mathematics (2017), standard 7.NS.3
Solve: 3x + 7 = 31Ohio's Learning Standards for Mathematics (2017), standard 7.EE.4
What is (−6) × (−8)?Ohio's Learning Standards for Mathematics (2017), standard 7.NS.2
What is 4 − (−9)?Ohio's Learning Standards for Mathematics (2017), standard 7.NS.1
What is the distance between −6 and 9 on a number line?Ohio's Learning Standards for Mathematics (2017), standard 7.NS.1
What is −3/4 × 2/3?Ohio's Learning Standards for Mathematics (2017), standard 7.NS.2
What is −7 + 12?Ohio's Learning Standards for Mathematics (2017), standard 7.NS.1
What is −8 − 5?Ohio's Learning Standards for Mathematics (2017), standard 7.NS.1
Which expression is equivalent to 3(2x − 4) + 5x?Ohio's Learning Standards for Mathematics (2017), standard 7.EE.1
Geometry 8
A circle has a radius of 5 cm. Using 3.14 for π, what is its area?Ohio's Learning Standards for Mathematics (2017), standard 7.G.4
A right prism has a triangular base with an area of 12 square inches. The prism is 9 inches tall. What is its volume?Ohio's Learning Standards for Mathematics (2017), standard 7.G.6
A right rectangular pyramid is sliced by a plane parallel to its base. What shape is the cross section?Ohio's Learning Standards for Mathematics (2017), standard 7.G.3
The circumference of a circle is 31.4 inches. Using 3.14 for π, what is its diameter?Ohio's Learning Standards for Mathematics (2017), standard 7.G.4
On a map, 1 inch stands for 25 miles. Two towns are 3.5 inches apart on the map. How far apart are the towns?Ohio's Learning Standards for Mathematics (2017), standard 7.G.1
Two angles are supplementary. One measures 112°. What does the other measure?Ohio's Learning Standards for Mathematics (2017), standard 7.G.5
Two lines cross. One of the angles they form measures 50°. What is the measure of the angle vertical to it?Ohio's Learning Standards for Mathematics (2017), standard 7.G.5
Which three side lengths can make a triangle?Ohio's Learning Standards for Mathematics (2017), standard 7.G.2
Statistics and Probability 10
A bag holds 3 red, 5 blue and 2 green marbles. One marble is picked without looking. What is the probability that it is blue?Ohio's Learning Standards for Mathematics (2017), standard 7.SP.7
A coin is tossed and a spinner with 5 equal sections numbered 1 to 5 is spun. What is the probability of getting tails and a 5?Ohio's Learning Standards for Mathematics (2017), standard 7.SP.8
A fair coin is tossed twice. What is the probability of getting heads both times?Ohio's Learning Standards for Mathematics (2017), standard 7.SP.8
A number cube is rolled 60 times and lands on 2 a total of 14 times. What is the experimental probability of rolling a 2?Ohio's Learning Standards for Mathematics (2017), standard 7.SP.6
A school has 600 students. In a random sample of 50 students, 20 say they walk to school. Based on the sample, about how many students in the school walk?Ohio's Learning Standards for Mathematics (2017), standard 7.SP.1
A school wants to learn its students' favorite lunch. Which sample is most likely to represent the whole school?Ohio's Learning Standards for Mathematics (2017), standard 7.SP.1
A spinner has 8 equal sections numbered 1 to 8. What is the probability of landing on an even number greater than 4?Ohio's Learning Standards for Mathematics (2017), standard 7.SP.7
A spinner lands on red with probability 1/4. About how many times should it land on red in 200 spins?Ohio's Learning Standards for Mathematics (2017), standard 7.SP.6
The data set 2, 4, 6, 8 has a mean of 5. What is its mean absolute deviation?Ohio's Learning Standards for Mathematics (2017), standard 7.SP.3
The probability of an event is 0.95. Which word describes the event?Ohio's Learning Standards for Mathematics (2017), standard 7.SP.5
A line of fit for the height of a plant is y = 1.5x + 4, where y is the height in centimeters after x weeks. According to the model, how tall is the plant after 6 weeks?Ohio's Learning Standards for Mathematics (2017), standard 8.SP.3
Adult tickets cost $8 and child tickets cost $5. A family buys 6 tickets for $39. How many adult tickets did they buy?Ohio's Learning Standards for Mathematics (2017), standard 8.EE.8
The graph of a proportional relationship is a line through (0, 0) and (4, 10). What is the unit rate, which is the slope of the line?Ohio's Learning Standards for Mathematics (2017), standard 8.EE.5
Show all 40 questions (37 more)
Equations and Expressions, continued
How many solutions does the equation 2x + 5 = 2x − 3 have?Ohio's Learning Standards for Mathematics (2017), standard 8.EE.7
How many solutions does the equation 3(x + 2) = 3x + 6 have?Ohio's Learning Standards for Mathematics (2017), standard 8.EE.7
In a survey of 50 students, 30 play a sport. Of those 30, 18 also play an instrument. What fraction of the students who play a sport also play an instrument?Ohio's Learning Standards for Mathematics (2017), standard 8.SP.4
Solve: 4(x − 2) = 2x + 10Ohio's Learning Standards for Mathematics (2017), standard 8.EE.7
Solve: 5x − 8 = 2x + 13Ohio's Learning Standards for Mathematics (2017), standard 8.EE.7
What is the equation of the line with a slope of 3 that crosses the y-axis at (0, −2)?Ohio's Learning Standards for Mathematics (2017), standard 8.EE.6
What is the solution of the system y = 2x + 1 and y = x + 4?Ohio's Learning Standards for Mathematics (2017), standard 8.EE.8
Functions 10
A function has the rule y = 2x + 3. Which input gives an output of 11?Ohio's Learning Standards for Mathematics (2017), standard 8.F.1
A graph shows the distance a car has traveled over time. One part of the graph is a flat, horizontal line. What is the car doing during that part?Ohio's Learning Standards for Mathematics (2017), standard 8.F.5
A gym charges a $25 sign-up fee plus $15 each month. Which equation gives the total cost y after x months?Ohio's Learning Standards for Mathematics (2017), standard 8.F.4
A linear function includes the points (2, 7) and (5, 16). What is its rate of change?Ohio's Learning Standards for Mathematics (2017), standard 8.F.4
A plumber's total charge is y = 60x + 45, where x is the number of hours worked. What does the 45 stand for?Ohio's Learning Standards for Mathematics (2017), standard 8.F.4
Function A is y = 2x + 10. A table for Function B shows y values of 8, 11 and 14 for x values of 0, 1 and 2. Which function has the greater initial value?Ohio's Learning Standards for Mathematics (2017), standard 8.F.2
Function A is y = 4x + 1. Function B is a line through (0, 3) and (2, 13). What is the greater of the two rates of change?Ohio's Learning Standards for Mathematics (2017), standard 8.F.2
Which equation defines a function that is not linear?Ohio's Learning Standards for Mathematics (2017), standard 8.F.3
Which set of ordered pairs is a function?Ohio's Learning Standards for Mathematics (2017), standard 8.F.1
Which table of values shows a linear function?Ohio's Learning Standards for Mathematics (2017), standard 8.F.3
Geometry 12
A 13-foot ladder leans against a wall. Its base is 5 feet from the wall. How high up the wall does the ladder reach?Ohio's Learning Standards for Mathematics (2017), standard 8.G.7
A cylinder has a radius of 3 cm and a height of 10 cm. Using 3.14 for π, what is its volume?Ohio's Learning Standards for Mathematics (2017), standard 8.G.9
A right triangle has legs of 6 cm and 8 cm. How long is the hypotenuse?Ohio's Learning Standards for Mathematics (2017), standard 8.G.7
A sphere has a radius of 3 cm. Using 3.14 for π, what is its volume?Ohio's Learning Standards for Mathematics (2017), standard 8.G.9
A triangle is translated 5 units to the right. Which statement about its image is true?Ohio's Learning Standards for Mathematics (2017), standard 8.G.2
The point (3, −2) is reflected across the x-axis. What are the coordinates of its image?Ohio's Learning Standards for Mathematics (2017), standard 8.G.3
The point (4, 1) is rotated 90° counterclockwise about the origin. What are the coordinates of its image?Ohio's Learning Standards for Mathematics (2017), standard 8.G.3
Two angles of a triangle measure 47° and 68°. What is the measure of the third angle?Ohio's Learning Standards for Mathematics (2017), standard 8.G.5
Two parallel lines are cut by a transversal. One of the angles formed measures 115°. What is the measure of its corresponding angle?Ohio's Learning Standards for Mathematics (2017), standard 8.G.5
Two triangles are similar. The sides of the smaller one are 3, 4 and 5. The shortest side of the larger one is 12. How long is the longest side of the larger triangle?Ohio's Learning Standards for Mathematics (2017), standard 8.G.4
What is the distance between the points (1, 2) and (4, 6)?Ohio's Learning Standards for Mathematics (2017), standard 8.G.8
Which three side lengths make a right triangle?Ohio's Learning Standards for Mathematics (2017), standard 8.G.6
The Number System 8
Between which two whole numbers is √50?Ohio's Learning Standards for Mathematics (2017), standard 8.NS.2
The population of a city is about 4,800,000. What is this number in scientific notation?Ohio's Learning Standards for Mathematics (2017), standard 8.EE.4
What is (3 × 10⁴) × (2 × 10³) in scientific notation?Ohio's Learning Standards for Mathematics (2017), standard 8.EE.4
What is 0.333…, where the 3 repeats forever, written as a fraction?Ohio's Learning Standards for Mathematics (2017), standard 8.NS.1
What is the positive solution of x² = 81?Ohio's Learning Standards for Mathematics (2017), standard 8.EE.2
What is the solution of x³ = 64?Ohio's Learning Standards for Mathematics (2017), standard 8.EE.2
What is the value of 2⁵ × 2³ ÷ 2⁶?Ohio's Learning Standards for Mathematics (2017), standard 8.EE.1
Which number is equal to 3⁻²?Ohio's Learning Standards for Mathematics (2017), standard 8.EE.1
Unofficial practice that follows the blueprints of Ohio's State Tests in mathematics for grades 3 to 8, still called the AIR math test. No question comes from a real test. Not affiliated with the Ohio Department of Education and Workforce.
Read the full guide
What each grade's test puts first
Each blueprint sorts the standards into reporting categories, and the questions for a grade are grouped the same way. Grade 3 splits its points almost evenly among multiplication and division, number and operations, geometry and fractions. Grades 4 and 5 give about three fourths of the test to two categories: multiplication and division with fractions in grade 4, fractions with decimals in grade 5. Grades 6 and 7 add ratios and proportions, and grade 8 adds functions.
How the answers are checked
Every question practices one standard that the blueprint lists for its category, named under the answer. Each numeric answer is arithmetic on the numbers in the question and was worked out twice. Wrong choices are common slips, such as adding instead of multiplying.
Estimate first. If 7 boxes hold 6 muffins each, the answer is near 40, so 13 cannot be right.
Before you compute, say whether the question asks for perimeter or area: the distance around, or the space inside.
Questions and answers
Is this the Ohio AIR math practice test?
It is unofficial practice for the same tests, now named Ohio's State Tests, or OST. AIR stands for American Institutes for Research, the testing company; its testing division became Cambium Assessment in 2020. The state's own practice tests are linked under the questions.
Are these real OST math questions?
No. Every question was written for this site, and none is a released or sample item. The real tests include item types that earn partial credit, which a multiple-choice page cannot copy.
Which grades take a math state test in Ohio?
Grades 3 through 8 each take a mathematics test in the spring. High school students take end-of-course tests in Algebra I and geometry, or in integrated mathematics I and II. This page stops at grade 8.
What is a good score on the Ohio math test?
The state counts a score of 700 or higher as proficient. A percent right on this page is not that score and cannot predict it. Use it to see which reporting category needs more practice.