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Free SSAT Math Practice Test — Grade 5

Math only, deliberately — the real SSAT (published by the Enrollment Management Association) also has verbal and reading sections, which we don't cover.

20 real practice questions at SSAT Middle Level difficulty, drawn from the same calibrated bank our adaptive practice uses. Work through them right here — every question has the answer and a step-by-step explanation one tap away.

Question 1 · Arithmetic & Number SenseIntro
Marcus is buying a small paint brush at his school craft fair. He pays with 1 quarter, 2 nickels, and 3 pennies. How many cents does he pay in all?
A38 cents
B48 cents
C30 cents
D13 cents
E23 cents
Show answer & explanation
Let's work it out
1.Each coin has a set value: 1 quarter equals 25 cents, each nickel equals 5 cents so 2 nickels equal 10 cents, and 3 pennies equal 3 cents.
2.Adding these gives 25 + 10 + 3 = 38 cents.
Answer: A) 38 cents
Question 2 · GeometryIntro
Two adjacent angles together form a right angle. One angle measures 47.5 degrees. What is the measure of the other angle?
A95 degrees
B137.5 degrees
C42.5 degrees
D132.5 degrees
E43 degrees
Show answer & explanation
Let's work it out
1.Two adjacent angles that together form a right angle must add up to 90 degrees.
2.Subtracting the known angle from 90 gives 90 - 47.5 = 42.5 degrees.
Answer: C) 42.5 degrees
Question 3 · Coordinate GraphsEasy
A worker at a hardware store marks shelf spots on a grid where each unit equals 1 foot. She wants to place a point one-half of a foot to the right of the y-axis and 3 feet above the x-axis. Which point shows that location?
A(1, 3)
B(12\frac{1}{2}, 3)
C(2, 3)
D(3, 12\frac{1}{2})
E(12\frac{1}{2}, 2)
Show answer & explanation
Let's work it out
1.The description says one-half of a foot to the right of the y-axis, which is the x-coordinate, and 3 feet above the x-axis, which is the y-coordinate.
2.The ordered pair is written (x, y), so the correct location is (12\frac{1}{2}, 3).
Answer: B) (12\frac{1}{2}, 3)
Question 4 · Data & StatisticsEasy
A music teacher surveyed 20 students about their favorite genre of music. Five students chose Rock, seven chose Pop, three chose Jazz, and the rest chose Classical. A student is making a bar graph of these results, where the height of each bar shows the number of students who chose that genre. What height should the bar for Jazz be drawn to?
A5
B4
C3
D20
E7
Show answer & explanation
Let's work it out
1.First, find how many students chose each genre.
2.Rock = 5, Pop = 7, Jazz = 3, and Classical = 20 - 5 - 7 - 3 = 5.
3.On a bar graph, the height of each bar equals the number of students in that category.
4.Since 3 students chose Jazz, the Jazz bar should be drawn to a height of 3.
Answer: C) 3
Question 5 · Data & StatisticsEasy
A nature club measured the lengths of five caterpillars found in the school garden, each to the nearest quarter inch. Their lengths were 12\frac{1}{2}, 34\frac{3}{4}, 14\frac{1}{4}, 34\frac{3}{4}, and 12\frac{1}{2} inch. About how many inches is the total combined length of all five caterpillars?
A4 inches
B3 inches
C5 inches
D1 inch
E2 inches
Show answer & explanation
Let's work it out
1.Add all five lengths by converting to fourths: ½ = 2/4, ¾ = 3/4, ¼ = 1/4, ¾ = 3/4, ½ = 2/4.
2.Sum the numerators: 2 + 3 + 1 + 3 + 2 = 11, giving 11/4 = 2¾ inches.
3.Since 2¾ is three-quarters of the way between 2 and 3, it is closer to 3 than to 2, so the total combined length is about 3 inches.
Answer: B) 3 inches
Question 6 · Data & StatisticsEasy
During a woodworking project, a student measures seven pieces of lumber and records each length in feet: 2, 4, 3, 6, 1, 3, and 5 feet. The student then makes a bar graph with one bar for each piece of wood, where the height of each bar equals the length of that piece. What height should the tallest bar on this graph be drawn to?
A24
B5
C6
D7
E1
Show answer & explanation
Let's work it out
1.To draw a bar graph, each bar is drawn to the height that matches the measurement of that piece of wood.
2.The tallest bar will represent the longest piece of lumber.
3.Scanning the seven lengths -- 2, 4, 3, 6, 1, 3, and 5 feet -- the greatest value is 6 feet, so the tallest bar should be drawn to a height of 6.
Answer: C) 6
Question 7 · Arithmetic & Number SenseStandard
A weather station recorded that a nature preserve received four and sixty-two thousandths inches of rain during a single storm. A student volunteer is entering this amount into a data log. Which decimal correctly represents this rainfall total?
A40.62
B4.062
C4.62
D4.602
E4.026
Show answer & explanation
Let's work it out
1.To convert a number word to a decimal, identify each part by its place value.
2.Four and sixty-two thousandths means 4 ones, plus sixty-two in the thousandths position.
3.Because sixty-two thousandths occupies the hundredths and thousandths places (with nothing in the tenths place), a zero must be written as a placeholder in the tenths column.
4.This gives 4.062: the digit 0 in the tenths place, 6 in the hundredths place, and 2 in the thousandths place.
Answer: B) 4.062
Question 8 · Fractions & DecimalsStandard
Bar chart: Runner Distance per LapBar chart: Runner Distance per Lap. Horizontal axis: Lap. Vertical axis: Miles. Values: Lap 1 0.9, Lap 2 0.9, Lap 3 0.9. Runner Distance per Lap 00.250.50.7510.90.90.9Lap 1Lap 2Lap 3LapMiles
Each lap of a running track is 0.9 miles long. During practice, a runner completed a total of 2.7 miles. How many full laps did the runner complete?
A0.67
B3
C0.3
D2.43
E1.5
Show answer & explanation
Let's work it out
1.To find the number of laps, divide the total distance by the length of one lap: 2.7 ÷ 0.9.
2.Rewrite both numbers as whole numbers by multiplying each by 10: 27 ÷ 9 = 3.
3.The runner completed 3 full laps, so the answer is B.
4.A student who divides in the wrong order gets 0.9 ÷ 2.7 ≈ 0.33, close to distractor A (0.67, which comes from a similar reversal error).
5.A student who multiplies instead of divides gets 2.7 × 0.9 = 2.43, which is distractor D.
6.A student who subtracts gets 2.7 − 0.9 = 1.8, or makes a related subtraction error landing near distractor C (0.3).
7.Distractor E (1.5) could come from a student who misreads one of the values and adds or uses an incorrect operation.
Answer: B) 3
Question 9 · GeometryStandard
QuadrilateralQuadrilateral ABCD. Side length: AB 14 cm. ABCD14 cm
In the figure, parallelogram ABCD has a base AB = 14 cm and a height of 5 cm. What is the area of the parallelogram?
A19 cm²
B38 cm²
C70 cm²
D140 cm²
E35 cm²
Show answer & explanation
Let's work it out
Area of a parallelogram = base × height = 14 × 5 = 70 cm².
Answer: C) 70 cm²
Question 10 · Coordinate GraphsStandard
Coordinate gridCoordinate grid, x-axis from 0 to 6, y-axis from 0 to 6. Points: F at (4.8, 4), G at (4, 4.8), H at (4.8, 3.2), J at (4.8, 5.6), K at (3.1, 4). x y 123456123456FGHJK
Starting at the origin, move 1.7 units right and 2.4 units up. Then move 3.1 more units right. The final upward movement is 0.8 unit less than the first upward movement. The graph shows five labeled points. Which point is the final position?
AJ
BG
CK
DH
EF
Show answer & explanation
Let's work it out
1.The final upward movement is 2.4 - 0.8 = 1.6 units.
2.The total movements are 1.7 + 3.1 = 4.8 units right and 2.4 + 1.6 = 4.0 units up.
3.The position (4.8, 4.0) is point F.
Answer: E) F
Question 11 · Data & StatisticsStandard
A wildlife club counted animals in four habitats: Forest: 7, Meadow: 5, River: 9, Hillside: 3. You're making a bar graph with one bar for each habitat. How tall should the Forest bar be?
A5
B7
C9
D8
E6
Show answer & explanation
Let's work it out
1.When creating a bar graph from a data table, each bar must reach a height equal to the data value for that category.
2.The Forest habitat had 7 animal sightings, so the Forest bar must reach the value 7 on the vertical axis.
Answer: B) 7
Question 12 · Arithmetic & Number SenseStandard
Number Pattern
InputOutput
314
623
932
12N
The table shows a number pattern. Each row follows the same rule. What is the value of N?
A38
B41
C44
D47
E43
Show answer & explanation
Let's work it out
1.Examine the pattern in each row using the table values: Input=3→Output=14, Input=6→Output=23, Input=9→Output=32, Input=12→Output=N.
2.Step 1: Identify the rule by testing Input=3: 3×3+5=9+5=14 ✓ Step 2: Verify with Input=6: 6×3+5=18+5=23 ✓ Step 3: Verify with Input=9: 9×3+5=27+5=32 ✓ The rule is: Output = Input×3 + 5 Step 4: Apply the rule to Input=12: 12×3+5=36+5=41 Therefore, N=41.
Answer: B) 41
Question 13 · Coordinate GraphsStandard
Coordinate gridCoordinate grid, x-axis from 0 to 7, y-axis from 0 to 6. Points: A(1,1), B(5,1), C(3,4). Also shown: a triangle with vertices (1, 1), (5, 1), (3, 4). x y 1234567123456ABCA(1,1)B(5,1)C(3,4)
The graph shows triangle ABC with vertices A(1, 1), B(5, 1), and C(3, 4). What is the area of triangle ABC?
A6 square units
B4 square units
C12 square units
D8 square units
E10 square units
Show answer & explanation
Let's work it out
1.The base of triangle ABC runs from A(1,1) to B(5,1), which is a horizontal segment.
2.Base = 5 − 1 = 4 units.
3.The height is the vertical distance from vertex C(3,4) down to the base line y = 1.
4.Height = 4 − 1 = 3 units.
5.Area = (12\frac{1}{2}) × base × height = (12\frac{1}{2}) × 4 × 3 = 6 square units.
Answer: A) 6 square units
Question 14 · Coordinate GraphsStandard
Coordinate gridCoordinate grid, x-axis from 0 to 10, y-axis from 0 to 7. Points: P at (5, 3), Q at (3, 2), R at (9, 1), S at (3, 5), T at (6, 5). x y 2468101234567PQRST
The graph shows five floor markers used during basketball practice. Nia catches a pass at (6, 2). She then runs toward the y-axis until her horizontal distance from it is half what it was, while also moving 3 grid units toward the far end of the court in the positive y-direction. Which marker does she reach?
AS
BT
CR
DQ
EP
Show answer & explanation
Let's work it out
1.Halving the horizontal distance changes the x-coordinate from 6 to 3.
2.Moving 3 units in the positive y-direction changes the y-coordinate from 2 to 5.
3.The position (3, 5) is marked S.
Answer: A) S
Question 15 · Arithmetic & Number SenseHard
Daily Rainfall Over 5 Days
DayRainfall (cm)
Monday1.4
Tuesday2.8
Wednesday0.6
Thursday3.2
Friday2.0
A science class recorded the rainfall each day for 5 days. The amounts were 1.4 cm, 2.8 cm, 0.6 cm, 3.2 cm, and 2.0 cm. What was the average daily rainfall, in centimeters, over those 5 days?
A1.8
B2.2
C1.6
D2.5
E2.0
Show answer & explanation
Let's work it out
1.Add all five rainfall amounts: 1.4 + 2.8 + 0.6 + 3.2 + 2.0 = 10.0 cm.
2.Divide by the number of days (5) to find the average: 10.0 ÷ 5 = 2.0 cm.
3.Choice A (1.8) results from misreading the 2.0 cm day as 1.0 cm, giving a sum of 9.0, then dividing correctly by 5.
4.Choice B (2.2) results from misreading 3.2 cm as 2.0 cm, summing the five values to get 8.8, then dividing by 4 instead of 5.
5.Choice C (1.6) results from omitting the 2.0 cm day entirely, summing the remaining four values to get 8.0, then dividing by 5 instead of 4.
6.Choice D (2.5) results from finding the correct sum of 10.0 but dividing by 4 instead of 5.
Answer: E) 2.0
Question 16 · Fractions & DecimalsHard
Jonah's Hiking Log
DayDistance (miles)
Monday4 and 16\frac{1}{6}
Wednesday2 and 23\frac{2}{3}
The table shows how far Jonah hiked on two days of a camping trip. How many more miles did Jonah hike on Monday than on Wednesday?
A1 and 12\frac{1}{2}
B1 and 56\frac{5}{6}
C2 and 56\frac{5}{6}
D2 and 12\frac{1}{2}
E6 and 56\frac{5}{6}
Show answer & explanation
Let's work it out
1.To find how much farther Monday was, subtract Wednesday's distance from Monday's: 4 and 16\frac{1}{6} minus 2 and 23\frac{2}{3}.
2.Converting 23\frac{2}{3} to sixths gives 46\frac{4}{6}, so the problem becomes 4 and 16\frac{1}{6} minus 2 and 46\frac{4}{6}.
3.Since 16\frac{1}{6} is less than 46\frac{4}{6}, borrow 1 whole from 4, rewriting as 3 and 76\frac{7}{6} minus 2 and 46\frac{4}{6}, which equals 1 and 36\frac{3}{6} = 1 and 12\frac{1}{2} miles.
Answer: A) 1 and 12\frac{1}{2}
Question 17 · GeometryHard
QuadrilateralQuadrilateral. Side lengths: 12 in, 4 in. 12 in4 in
The figure shows the side view of a rectangular brownie pan that is 8 inches wide. For a bake sale, Priya pours batter into the empty pan until it is filled to 34\frac{3}{4} of its depth. How many cubic inches of batter does she pour in?
A96
B288
C312
D384
E72
Show answer & explanation
Let's work it out
1.The figure shows the pan is 12 inches long and 4 inches deep.
2.Filling the pan to 34\frac{3}{4} of its depth means the batter is 34\frac{3}{4} x 4 = 3 inches deep.
3.The batter forms a rectangular prism measuring 12 inches by 8 inches by 3 inches, so its volume is 12 x 8 x 3 = 288 cubic inches.
Answer: B) 288
Question 18 · Fractions & DecimalsHard
QuadrilateralQuadrilateral. Side length: 9 feet. 9 feet
A wood plank in the school workshop is 9 feet long. A student cuts off a piece that is 2 and 56\frac{5}{6} feet long to build a shelf bracket. How many feet of the plank remain after the cut?
A1
B6 and 16\frac{1}{6}
C6 and 56\frac{5}{6}
D7
E7 and 56\frac{5}{6}
Show answer & explanation
Let's work it out
1.To find the remaining length, subtract 2 and 56\frac{5}{6} from 9.
2.Since 9 has no fractional part, rewrite it as 8 and 66\frac{6}{6}.
3.Then subtract the whole parts: 8 − 2 = 6, and subtract the fraction parts: 66\frac{6}{6} − 56\frac{5}{6} = 16\frac{1}{6}.
4.The remaining length is 6 and 16\frac{1}{6} feet, which is answer B.
Answer: B) 6 and 16\frac{1}{6}
Question 19 · GeometryHard
QuadrilateralQuadrilateral. Side lengths: 5/6 yd, 3/4 yd, 5/6 yd, 3/4 yd. 5/6 yd3/4 yd5/6 yd3/4 yd
A classroom wall section is 5/6 of a yard long and 3/4 of a yard wide. A rectangular whiteboard mounted on this wall is 1/3 of a yard long and 1/2 of a yard wide. What is the area of the wall section that is NOT covered by the whiteboard, in square yards?
A1/8
B5/8
C7/24
D1/6
E11/24
Show answer & explanation
Let's work it out
1.The full wall section has area (5/6)*(3/4) = 15/24 = 5/8 square yards.
2.The whiteboard covers (1/3)*(1/2) = 1/6 square yards.
3.Converting to a common denominator of 24, the remaining wall area is 15/24 - 4/24 = 11/24 square yards.
Answer: E) 11/24
Question 20 · Fractions & DecimalsHard
Priya's Bike Ride
LegDistance
Leg 18 and 34\frac{3}{4} miles
Leg 26 and 13\frac{1}{3} miles
The table shows the two legs of Priya's Saturday bike ride. What was the total distance Priya rode?
A15 and 112\frac{1}{12}
B14 and 13\frac{1}{3}
C14 and 112\frac{1}{12}
D15 and 14\frac{1}{4}
E14 and 47\frac{4}{7}
Show answer & explanation
Let's work it out
1.Add 8 and 34\frac{3}{4} and 6 and 13\frac{1}{3}.
2.The least common denominator of 4 and 3 is 12, so 34\frac{3}{4} becomes 912\frac{9}{12} and 13\frac{1}{3} becomes 412\frac{4}{12}.
3.Adding the fractions gives 1312\frac{13}{12}, which equals 1 and 112\frac{1}{12}.
4.The whole-number sum is 8 plus 6 equals 14, and adding the carried 1 gives 15.
5.The total distance is 15 and 112\frac{1}{12} miles.
Answer: A) 15 and 112\frac{1}{12}

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