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Free SSAT Math Practice Test — Grade 7

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
Mia is knitting a set of scarves. She buys 8 spools of yarn, each containing 3.75 yards. After finishing all the scarves, she has 1.2 yards of yarn left over. How many yards of yarn did Mia use on her scarves?
A28.8
B4.95
C15.0
D30.0
E26.55
Show answer & explanation
Let's work it out
1.Multiply the number of spools by the yards per spool to find the total yarn purchased: 8 × 3.75 = 30.0 yards.
2.Since Mia had 1.2 yards remaining after finishing the scarves, subtract to find the yarn she used: 30.0 - 1.2 = 28.8 yards.
Answer: A) 28.8
Question 2 · ProportionsIntro
A large batch of spiced granola calls for 3 cups of rolled oats and 900 grams of honey. Priya wants to make a bigger batch using the same recipe ratio but with 5 cups of rolled oats. How many grams of honey does she need?
A2700
B4500
C1125
D540
E1500
Show answer & explanation
Let's work it out
1.The recipe keeps rolled oats and honey in a constant ratio: 3 cups of oats to 900 grams of honey.
2.Setting up the proportion 3900\frac{3}{900} = 5x\frac{5}{x} and cross-multiplying gives x = (900 x 5) / 3 = 4500 / 3 = 1500 grams.
Answer: E) 1500
Why the other choices are tempting: The value 1125 comes from dividing 900 by 4 (instead of 3) to find a per-cup rate and then multiplying by 5. The value 540 comes from inverting the proportion, dividing 900 by 5 and multiplying by 3. The value 2700 comes from adding 2 extra batches of 900 (one for each extra cup) to the original 900. The value 4500 comes from multiplying 900 by 5 without dividing by 3.
Question 3 · Arithmetic & Number SenseEasy
If the sequence 3, 6, 10, 20, x, 48, 52 follows the same repeating pattern throughout, what is the value of x?
A24
B44
C40
D34
E26
Show answer & explanation
Let's work it out
1.The sequence alternates between multiplying by 2 and adding 4.
2.After 20, the next step is addition, so x = 20 + 4 = 24.
3.The next two steps confirm the pattern because 24 multiplied by 2 is 48, and 48 + 4 = 52.
Answer: A) 24
Question 4 · IntegersEasy
A pot of soup sits in a refrigerator at 3.5 degrees Celsius. A student takes it out and heats it on the stove, raising the temperature by 12 degrees. The soup then cools by 8.5 degrees when the stove is turned to low, and cools by another 4 degrees after the pot is moved off the burner. What is the final temperature of the soup in degrees Celsius?
A28
B-21
C-0.5
D3
E7
Show answer & explanation
Let's work it out
1.Start with the initial temperature of 3.5 degrees and apply each change in order.
2.After heating: 3.5 + 12 = 15.5 degrees.
3.After the first cooling: 15.5 - 8.5 = 7 degrees.
4.After the second cooling: 7 - 4 = 3 degrees.
Answer: D) 3
Why the other choices are tempting: The value -0.5 results from forgetting to include the starting temperature of 3.5 and computing 0 + 12 - 8.5 - 4. The value 7 results from stopping after the first two changes and ignoring the final 4-degree drop. The value 28 results from treating both cooling steps as temperature increases and adding all four values. The value -21 results from subtracting the 12-degree heating step instead of adding it.
Question 5 · ProportionsEasy
On a map, 2 inches represents 10 miles. The distance between Town A and Town B on the map is 7 inches. What is the actual distance between the two towns?
A30 miles
B35 miles
C49 miles
D70 miles
E40 miles
Show answer & explanation
Let's work it out
1.The map scale tells us that 2 inches represents 10 miles.
2.First, find the unit rate by dividing: 10 miles ÷ 2 inches = 5 miles per inch.
3.Then multiply by the map distance: 7 inches × 5 miles/inch = 35 miles.
4.The correct answer is B.
Answer: B) 35 miles
Question 6 · Data & StatisticsEasy
A pet store sold the following number of fish each day for one week: 12, 9, 15, 9, 11, 14, and 9. What is the difference between the greatest number of fish sold in a day and the least number of fish sold in a day?
AA) 3
BB) 5
CC) 6
DD) 7
EE) 9
Show answer & explanation
Let's work it out
1.First find the greatest value: 15.
2.Then find the least value: 9.
3.Subtract: 15 - 9 = 6.
4.The difference (range) is 6.
Answer: C) C) 6
Question 7 · Fractions & DecimalsStandard
Let S = 11×2\frac{1}{1×2} + 12×3\frac{1}{2×3} + 13×4\frac{1}{3×4} +... + 199×100\frac{1}{99×100}. Which of the following equals S?
A199\frac{1}{99}
B100101\frac{100}{101}
C10099\frac{100}{99}
D99100\frac{99}{100}
E98100\frac{98}{100}
Show answer & explanation
Let's work it out
1.Use partial fractions: 1n(n+1)\frac{1}{n(n+1)} = 1n\frac{1}{n} - 1n+1\frac{1}{n+1}.
2.So the sum telescopes: (11\frac{1}{1} - 12\frac{1}{2}) + (12\frac{1}{2} - 13\frac{1}{3}) + ... + (199\frac{1}{99} - 1100\frac{1}{100}) = 1 - 1100\frac{1}{100} = 99100\frac{99}{100}.
Answer: D) 99100\frac{99}{100}
Question 8 · GeometryStandard
QuadrilateralQuadrilateral. Side lengths: 4 1/2 ft, 3 3/4 ft, 4 1/2 ft, 3 3/4 ft. 4 1/2 ft3 3/4 ft4 1/2 ft3 3/4 ft
Mia is buying a rectangular piece of poster board at the art supply store to display her project. The board measures 3 and three-fourths feet long and 4 and one-half feet wide. How many square feet of poster board is she buying?
A16 12\frac{1}{2} square feet
B12 38\frac{3}{8} square feet
C16 78\frac{7}{8} square feet
D8 14\frac{1}{4} square feet
E12 square feet
Show answer & explanation
Let's work it out
1.Convert each mixed number to an improper fraction: 3 and 34\frac{3}{4} equals 154\frac{15}{4}, and 4 and 12\frac{1}{2} equals 92\frac{9}{2}.
2.Multiply to find the area: (154\frac{15}{4}) times (92\frac{9}{2}) equals 1358\frac{135}{8}, which simplifies to 16 and 78\frac{7}{8} square feet.
Answer: C) 16 78\frac{7}{8} square feet
Question 9 · Coordinate GraphsStandard
Coordinate gridCoordinate grid, x-axis from 0 to 10, y-axis from 0 to 10. Points: A at (2, 8), B at (4, 6), C at (6, 6), D at (8, 4), E at (4, 8), F at (9, 3), G at (7, 5). x y 246810246810ABCDEFG
Which ordered pair names the plotted point whose coordinates have a sum equal to the y-coordinate of A plus the x-coordinate of B, and whose x-coordinate is greater than its y-coordinate by the x-coordinate of B?
A(4, 8)
B(9, 3)
C(8, 4)
D(6, 6)
E(7, 5)
Show answer & explanation
Let's work it out
1.The y-coordinate of A is 8, and the x-coordinate of B is 4, so the required coordinate sum is 12.
2.The x-coordinate must also be 4 greater than the y-coordinate.
3.For (8, 4), the coordinates sum to 12 and differ by 4 in the required order.
Answer: C) (8, 4)
Question 10 · IntegersStandard
Bar chart: Animal Depths Relative to Sea Level (meters)Bar chart: Animal Depths Relative to Sea Level (meters). Horizontal axis: Animal. Vertical axis: Depth (m). Values: Sea Lion -3.2, Dolphin -8.6. Animal Depths Relative to Sea Level (meters) -8-6-4-20-3.2-8.6Sea LionDolphinAnimalDepth (m)
The bar chart shows the depths (in meters relative to sea level) of two marine animals observed during a research dive. A sea lion is at -3.2 meters and a dolphin is at -8.6 meters. How many meters below the sea lion is the dolphin?
A11.8
B11.4
C5.0
D5.4
E4.2
Show answer & explanation
Let's work it out
1.To find how many meters below the sea lion the dolphin is, calculate the difference between their depths.
2.The sea lion is at −3.2 meters and the dolphin is at −8.6 meters.
3.Subtract the sea lion's depth from the dolphin's depth in terms of distance: (−3.2) − (−8.6) = −3.2 + 8.6 = 5.4 meters.
4.The dolphin is 5.4 meters below the sea lion.
Answer: D) 5.4
Question 11 · PercentagesStandard
A school store sells notebooks for $4.00 each. During a sale, all notebooks are discounted by 25%. How much does a student pay for 3 notebooks at the sale price?
A$6.00
B$9.00
C$10.00
D$11.00
E$12.00
Show answer & explanation
Let's work it out
1.Step 1: Find the sale price of one notebook.
2.25% of $4.00 = 0.25 x 4 = $1.00 discount.
3.Sale price = $4.00 - $1.00 = $3.00.
4.Step 2: Multiply by 3 notebooks.
5.3 x $3.00 = $9.00.
Answer: B) $9.00
Why the other choices are tempting: The answer is B.
Question 12 · ProbabilityStandard
Geometric figureGeometric figure.12345678
A spinner is divided into 8 equal sections numbered 1 through 8. Sections 2, 5, and 7 are shaded. If the spinner is spun once, what is the probability that it lands on a shaded section?
A58\frac{5}{8}
B35\frac{3}{5}
C14\frac{1}{4}
D13\frac{1}{3}
E38\frac{3}{8}
Show answer & explanation
Let's work it out
1.There are 8 equal sections in total.
2.The shaded sections are 2, 5, and 7, giving 3 favorable outcomes.
3.Probability is defined as the number of favorable outcomes divided by the total number of outcomes: 38\frac{3}{8}.
Answer: E) 38\frac{3}{8}
Question 13 · Coordinate GraphsStandard
Coordinate gridCoordinate grid, x-axis from 0 to 10, y-axis from 0 to 10. Points: A at (2, 7), B at (6, 3), C at (4, 8), D at (6, 6), E at (3, 10), F at (3, 3), G at (3, 6). x y 246810246810ABCDEFG
Which ordered pair names the plotted point whose x-coordinate equals the y-coordinate of B and whose y-coordinate equals the difference between the y-coordinate of C and the x-coordinate of A?
A(3, 10)
B(6, 6)
C(6, 3)
D(3, 6)
E(3, 3)
Show answer & explanation
Let's work it out
1.The y-coordinate of B is 3, so the required x-coordinate is 3.
2.The y-coordinate of C is 8, and the x-coordinate of A is 2, so the required y-coordinate is 8 - 2 = 6.
3.The ordered pair is (3, 6).
Answer: D) (3, 6)
Question 14 · ProbabilityStandard
Bar chart: Tiles in a BagBar chart: Tiles in a Bag. Horizontal axis: Color. Vertical axis: Number of Tiles. Values: Red 8, Blue 6, Green 10. Tiles in a Bag 02.557.5108610RedBlueGreenColorNumber of Tiles
The chart shows the number of each color of tile in a bag. If one tile is chosen at random, what is the probability of choosing a red tile?
A16\frac{1}{6}
B14\frac{1}{4}
C13\frac{1}{3}
D25\frac{2}{5}
E38\frac{3}{8}
Show answer & explanation
Let's work it out
1.From the bar chart: Red = 8, Blue = 6, Green = 10.
2.Total tiles = 8 + 6 + 10 = 24.
3.P(red) = 824\frac{8}{24} = 13\frac{1}{3}.
4.The correct answer is C.
Answer: C) 13\frac{1}{3}
Question 15 · Fractions & DecimalsHard
Week 1 Rainfall (inches)
DayRainfall
Day 138\frac{3}{8}
Day 214\frac{1}{4}
Day 358\frac{5}{8}
Day 412\frac{1}{2}
Day 538\frac{3}{8}
Day 614\frac{1}{4}
Day 718\frac{1}{8}
A science station records rainfall data for Week 1 in the table. The combined rainfall for both Week 1 and Week 2 is 6 and 14\frac{1}{4} inches. During Week 2, it rained on exactly 4 days with the same amount of rain each day. How much rain fell on each rainy day of Week 2?
A3 and 34\frac{3}{4} inches
B916\frac{9}{16} inch
C1516\frac{15}{16} inch
D37\frac{3}{7} inch
E6 and 34\frac{3}{4} inches
Show answer & explanation
Let's work it out
1.First, find the total rainfall for Week 1 by adding all seven days.
2.Converting each day's rainfall to a common denominator of 8: 38\frac{3}{8} + 28\frac{2}{8} + 58\frac{5}{8} + 48\frac{4}{8} + 38\frac{3}{8} + 28\frac{2}{8} + 18\frac{1}{8} = 208\frac{20}{8} = 2 and 12\frac{1}{2} inches.
3.Next, subtract the Week 1 total from the combined two-week total to find the Week 2 total: 6 and 14\frac{1}{4} minus 2 and 12\frac{1}{2}.
4.Rewriting with a common denominator of 4 gives 6 and 14\frac{1}{4} minus 2 and 24\frac{2}{4}.
5.Borrowing 1 from the whole number converts this to 5 and 54\frac{5}{4} minus 2 and 24\frac{2}{4} = 3 and 34\frac{3}{4} inches for Week 2.
6.Finally, since it rained equally on exactly 4 days during Week 2, divide the Week 2 total by 4: convert 3 and 34\frac{3}{4} to the improper fraction 154\frac{15}{4}, then divide by 4 to get 154\frac{15}{4} ÷ 4 = 1516\frac{15}{16} inch per rainy day.
Answer: C) 1516\frac{15}{16} inch
Question 16 · GeometryHard
Rest-Stop Plot Dimensions
ShapeBase or LengthHeight or Width
Rectangle120 m80 m
Triangle60 m40 m
A highway rest-stop plot has the shape of a rectangle that is 120 meters long and 80 meters wide. A triangular construction zone inside the plot has a base of 60 meters and a height of 40 meters. The table shows these dimensions. What is the area of the rest-stop plot that is open and NOT part of the construction zone, in square meters?
A7200
B9000
C9600
D8400
E1200
Show answer & explanation
Let's work it out
1.First, find the total area of the rectangular rest-stop plot: 120 × 80 = 9,600 square meters.
2.Next, find the area of the triangular construction zone using the triangle area formula: (12\frac{1}{2}) × base × height = (12\frac{1}{2}) × 60 × 40 = 1,200 square meters.
3.Finally, subtract the construction zone area from the total plot area to find the open area: 9,600 − 1,200 = 8,400 square meters.
Answer: D) 8400
Question 17 · PercentagesHard
ColorFraction of Total
Blue35\frac{3}{5}
Red15\frac{1}{5}
Yellow15\frac{1}{5}
A crafter has 200 yards of yarn. According to the table shown, 35\frac{3}{5} of the yarn is blue. Of the blue yarn, 60% is being set aside for a scarf project. How many yards of yarn are being set aside for the scarf?
A48
B144
C72
D120
E36
Show answer & explanation
Let's work it out
1.First, find the total amount of blue yarn by multiplying the total yarn by the blue fraction: (35\frac{3}{5}) × 200 = 120 yards of blue yarn.
2.Next, find how much of that blue yarn is set aside for the scarf by taking 60% of the blue yarn: 0.60 × 120 = 72 yards.
Answer: C) 72
Question 18 · Ratios & ProportionsHard
Wildlife Sanctuary Ratios
Ratio RelationshipValues
Rabbits to Squirrels4 : 7
Birds to Rabbits5 : 4
Number of Rabbits28
A wildlife sanctuary keeps rabbits, squirrels, and birds. The ratio of rabbits to squirrels is 4:7, and the ratio of birds to rabbits is 5:4. If the sanctuary has 28 rabbits, what is the total number of animals in the sanctuary?
A120
B94
C84
D77
E112
Show answer & explanation
Let's work it out
1.Start with the 28 rabbits as the anchor.
2.For the rabbit-to-squirrel ratio of 4:7, the scale factor is 28 ÷ 4 = 7, so there are 7 × 7 = 49 squirrels.
3.For the bird-to-rabbit ratio of 5:4, the same scale factor of 7 applies, so there are 5 × 7 = 35 birds.
4.The total number of animals is 28 + 49 + 35 = 112.
Answer: E) 112
Question 19 · Data & StatisticsHard
Daily High Temperatures
School DayWeek 1Week 2
Monday18.418.9
Tuesday20.121.6
Wednesday19.319.8
Thursday2120.4
Friday17.718.3
A school weather club recorded the daily high temperature, in degrees Celsius, during two five-day weeks. After making the table, the students learned that the Week 2 reading of 21.6 was 2.5 degrees too high. Which ordered pair gives the corrected Week 2 mean minus the Week 1 mean, followed by the corrected Week 2 range minus the Week 1 range?
A(0.5, 0.0)
B(0.0, -1.2)
C(0.0, 0.0)
D(0.0, 1.2)
E(-2.0, 0.0)
Show answer & explanation
Let's work it out
1.Week 1 has a mean of 96.5 divided by 5, or 19.3, and a range of 21.0 minus 17.7, or 3.3.
2.Correcting 21.6 to 19.1 gives Week 2 a mean of 19.3 and a range of 20.4 minus 18.3, or 2.1.
3.The requested differences are 19.3 minus 19.3 and 2.1 minus 3.3, so the ordered pair is (0.0, -1.2).
Answer: B) (0.0, -1.2)
Question 20 · Ratios & ProportionsHard
Highway Trip Data
CarDistance (miles)Time (hours)
Car A136.53
Car B178.53.5
The table shows the distances two cars traveled on a highway. Car A drove 136.5 miles in 3 hours. Car B drove 178.5 miles in 3.5 hours. If both cars continue at their same constant unit rates for a total trip of exactly 4 hours, how many more miles will the faster car have traveled than the slower car?
A11
B18
C204
D22
E88
Show answer & explanation
Let's work it out
1.First, find each car's unit rate.
2.Car A: 136.5 ÷ 3 = 45.5 miles per hour.
3.Car B: 178.5 ÷ 3.5 = 51 miles per hour.
4.Car B is the faster car.
5.Over a total trip of 4 hours, Car B travels 51 × 4 = 204 miles, and Car A travels 45.5 × 4 = 182 miles.
6.The difference is 204 − 182 = 22 miles.
Answer: D) 22

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