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Free SSAT Math Practice Test — Grade 6

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 · Algebraic ExpressionsIntro
An animal shelter feeds each dog 4 cups of kibble per day. The shelter also adds a fixed 5-cup vitamin supplement to the food supply each day, no matter how many dogs are present. If d stands for the number of dogs at the shelter, the total cups of food needed each day is 4d + 5. How many total cups of food are needed on a day when there are 6 dogs at the shelter?
A15
B29
C10
D24
E30
Show answer & explanation
Let's work it out
Substitute d = 6 into the expression 4d + 5: multiply 4 by 6 to get 24, then add the fixed supplement of 5 to get 29 total cups.
Answer: B) 29
Why the other choices are tempting: The value 10 comes from adding 4 and 6 instead of multiplying. The value 24 comes from multiplying correctly but forgetting to add the 5-cup supplement. The value 15 comes from adding all three numbers 4, 6, and 5. The value 30 comes from multiplying the supplement (5) by the number of dogs (6) instead of using the coefficient 4.
Question 2 · Algebraic ExpressionsIntro
Sam has 3 bags of apples. Each bag has 4 apples in it. His mom adds 2 more apples to his collection. Which expression shows how many apples Sam has in all?
A(3 x 4) + 2
B(3 + 4) + 2
C(3 x 4) - 2
D3 x (4 + 2)
E(3 + 4) x 2
Show answer & explanation
Let's work it out
1.Step 1: Sam has 3 bags with 4 apples in each bag.
2.To find the total number of apples in the bags, multiply: 3 x 4 = 12.
3.Step 2: His mom then adds 2 more apples to his collection, so add 2 to the result: 12 + 2 = 14.
4.Step 3: The expression that represents this situation is (3 x 4) + 2, where the multiplication is performed first to find the apples in the bags, and then 2 is added.
Answer: A) (3 x 4) + 2
Question 3 · Equations & InequalitiesEasy
Marcus scored some points in a game. Then he scored 9 more points and doubled his total score. His final score was 50 points. How many points did Marcus have at the start?
A25
B32
C16
D21
E41
Show answer & explanation
Let's work it out
1.Let p = the number of points Marcus started with.
2.Step 1: After scoring 9 more: p + 9.
3.Step 2: After doubling: 2 x (p + 9) = 50.
4.Step 3: Divide both sides by 2: p + 9 = 25.
5.Step 4: Subtract 9 from both sides: p = 16.
6.Marcus started with 16 points.
Answer: C) 16
Question 4 · Coordinate GraphsEasy
A treasure map uses a coordinate plane where each unit represents 1 mile. The starting point is at (2, 3). The treasure is buried 4 miles to the right and 5 miles down from the starting point. What are the coordinates of the treasure?
A(6, 8)
B(6, -2)
C(2, -2)
D(-2, 8)
E(4, -5)
Show answer & explanation
Let's work it out
1.Starting at (2, 3): moving 4 miles to the right means adding 4 to the x-coordinate: 2 + 4 = 6.
2.Moving 5 miles down means subtracting 5 from the y-coordinate: 3 - 5 = -2.
3.So the treasure is at (6, -2).
Answer: B) (6, -2)
Question 5 · Pre-AlgebraEasy
A flower shop has 30 roses. The shop owner puts an equal number of roses into 5 vases. Then 3 more roses are added to each vase. How many roses are in each vase now?
A8
B11
C7
D9
E6
Show answer & explanation
Let's work it out
1.Step 1: Divide the roses equally into 5 vases.
2.30 / 5 = 6 roses per vase.
3.Step 2: Add 3 more roses to each vase.
4.6 + 3 = 9 roses per vase.
Answer: D) 9
Why the other choices are tempting: The answer is 9.
Question 6 · Coordinate GraphsEasy
A community center is laid out on a coordinate grid where each unit represents 1 yard. The gym entrance is at point (1, 2) and the cafeteria entrance is at point (1, 8). A hallway runs straight from the gym entrance to the cafeteria entrance. If a student walks from the gym entrance to the cafeteria entrance and stops at every point that has a whole-number y-coordinate, how many total points does the student stand on, including the starting and ending points?
A5
B6
C7
D8
E2
Show answer & explanation
Let's work it out
1.Step 1: The student walks from (1, 2) to (1, 8) along the vertical line x = 1.
2.Step 2: The y-coordinates with whole numbers along this path are: 2, 3, 4, 5, 6, 7, 8.
3.Step 3: Count them: 2, 3, 4, 5, 6, 7, 8 -- that is 7 points total.
4.The correct answer is C (7).
Answer: C) 7
Question 7 · Arithmetic & Number SenseStandard
QuadrilateralQuadrilateral. Side lengths: 12 ft, 9 ft, 12 ft (house wall), 9 ft. 12 ft9 ft12 ft (house wall)9 ft
A homeowner is building a rectangular garden against the side of the house. The garden will be 12 feet long and 9 feet wide. Because one of the long sides borders the house wall, that side does not need any fencing. How many feet of fencing are needed for the other three sides?
A30
B21
C18
D33
E42
Show answer & explanation
Let's work it out
1.The garden has four sides: two long sides of 12 ft and two short sides of 9 ft.
2.Since one long side (12 ft) runs along the house wall and needs no fencing, only the remaining three sides require fencing: 12 + 9 + 9 = 30 ft.
Answer: A) 30
Why the other choices are tempting: The value 42 is the full perimeter of all four sides: 2 x (12 + 9) = 42, which ignores that one side is the house wall. The value 18 comes from adding only the two short sides and forgetting the opposite long side: 9 + 9 = 18. The value 33 comes from adding three sides but using 12 + 12 + 9 = 33, counting the house-wall side instead of excluding it and including both short sides. The value 21 comes from adding only one long side and one short side: 12 + 9 = 21.
Question 8 · Equations & InequalitiesStandard
To model negative integers in math class, Ms. Rao uses one red counter for each unit below zero. She has the same number of cards labeled -6 as cards labeled -9. Modeling every card uses 180 red counters altogether. How many cards of each label does she have?
A60
B12
C15
D20
E30
Show answer & explanation
Let's work it out
1.Let n be the number of cards of each label.
2.The counter total gives 6n + 9n = 180, so 15n = 180.
3.Dividing by 15 gives n = 12 cards of each label.
Answer: B) 12
Question 9 · GeometryStandard
QuadrilateralQuadrilateral. Side lengths: distance from −8 to 0, distance from −6 to 0. distance from −3 to 0distance from −2 to 0distance from −8 to 0distance from −6 to 0
Mara is cutting a rectangular opening from a sheet of cardstock to make a frame for a paper mosaic. Each labeled side length in the diagram is described as a distance from a negative number to 0 on a number line. What is the area of the cardstock that remains?
A48
B20
C18
D6
E42
Show answer & explanation
Let's work it out
1.The outer rectangle measures 8 centimeters by 6 centimeters, so its area is 48 square centimeters.
2.The opening measures 3 centimeters by 2 centimeters, so its area is 6 square centimeters.
3.Subtracting gives 48 − 6 = 42 square centimeters of cardstock.
Answer: E) 42
Question 10 · PercentagesStandard
Pie chart: School Annual Budget DistributionPie chart: School Annual Budget Distribution. Segments: Academics (40%) 40, Technology (25%) 25, Arts (12%) 12, Sports (15%) 15, Administration (8%) 8. 40% 25% 12% 15% 8% Academics (40%) (40) Technology (25%) (25) Arts (12%) (12) Sports (15%) (15) Administration (8%) (8)School Annual Budget Distribution
The pie chart shows how a school's annual budget of $500,000 is distributed across five departments. How much money is allocated to the Sports department?
AA) $45,000
BB. $100,000
CC) $60,000
DD) $75,000
EE) $90,000
Show answer & explanation
Let's work it out
1.From the pie chart, the Sports department represents 15% of the total budget.
2.Amount = 15% × $500,000 = 0.15 × $500,000 = $75,000.
3.The correct answer is $75,000.
Answer: D) D) $75,000
Question 11 · Pre-AlgebraStandard
One quantity, p, is 0.4 times another quantity, q. Which statement must be true about q?
A0.4 times p
B0.6 times p
C2.5 times p
D4 times p
E0.4 less than p
Show answer & explanation
Let's work it out
1.The relationship can be written as p = 0.4q.
2.Dividing by 0.4 gives q = 2.5p, so q is 2.5 times p.
Answer: C) 2.5 times p
Question 12 · Data & StatisticsStandard
Bar chart: Books Read Last MonthBar chart: Books Read Last Month. Horizontal axis: Student. Vertical axis: Number of Books. Values: Ava 3, Ben 6, Cara 5, Dan 6, Eli 5. Books Read Last Month 024636565AvaBenCaraDanEliStudentNumber of Books
The bar chart shows the number of books five students read last month. What is the difference between the mean (average) number of books read and the median number of books read?
A0
B1
C2
D6
E4
Show answer & explanation
Let's work it out
1.From the bar chart, the five students' values are: Ava = 3, Ben = 6, Cara = 5, Dan = 6, Eli = 5.
2.To find the median, sort the values in ascending order: 3, 5, 5, 6, 6.
3.The middle value (3rd of 5) is 5, so the median = 5.
4.To find the mean, sum all values: 3 + 5 + 5 + 6 + 6 = 25, then divide by 5: 25 ÷ 5 = 5.
5.The difference between the mean and the median is 5 − 5 = 0.
Answer: A) 0
Question 13 · GeometryStandard
HexagonHexagon. Side lengths: 800 feet, 300 feet, 300 feet, 500 feet, 600 feet. 800 feet300 feet300 feet500 feet600 feet
A wildlife rescue center is building a fence around the right-angled tortoise habitat shown. What is the total perimeter of the habitat?
A3,800 feet
B2,200 feet
C2,800 feet
D3,100 feet
E2,500 feet
Show answer & explanation
Let's work it out
1.The horizontal sides running left must have the same total length as the horizontal side running right.
2.Therefore, the unlabeled side is 800 - 500 = 300 feet.
3.Adding all six side lengths gives a perimeter of 2,800 feet.
Answer: C) 2,800 feet
Question 14 · Data & StatisticsStandard
Bar chart: Average Monthly TemperaturesBar chart: Average Monthly Temperatures. Horizontal axis: Month. Vertical axis: Temperature (°F). Values: Jan 52, Feb 58, Mar 64, Apr 66, May 72, Jun 78. Average Monthly Temperatures 020406080525864667278JanFebMarAprMayJunMonthTemperature (°F)
The bar chart shows the average monthly temperatures (in °F) for a city over six months. What is the median temperature for the six months shown?
AA) 62°F
BB) 65°F
CC) 67°F
DD) 70°F
E66°F
Show answer & explanation
Let's work it out
1.The six monthly temperatures from the chart are: January = 52°F, February = 58°F, March = 64°F, April = 66°F, May = 72°F, June = 78°F.
2.Arranging these in ascending order gives: 52, 58, 64, 66, 72, 78.
3.Since there are six values, the median is the average of the 3rd and 4th values.
4.Taking (64 + 66) / 2 = 130 / 2 = 65°F.
5.Therefore, the median temperature for the six months is 65°F.
Answer: B) B) 65°F
Question 15 · Arithmetic & Number SenseHard
Catering Order
ItemBatchesPrice per Batch (dollars)
Soup3400
Bread5200
Dessert2350
A catering company charges for a cooking order using the following rule: multiply each batch count by its price per batch, add those products together, add a flat delivery fee of 150 dollars, then subtract a bulk discount of 500 dollars. The table shows the order. What is the total cost of this catering order in dollars?
A2900
B2550
C2700
D3550
E3050
Show answer & explanation
Let's work it out
1.To find the total cost, follow the pricing rule step by step.
2.Step 1: Multiply each item's batch count by its price per batch. - Soup: 3 × 400 = 1200 - Bread: 5 × 200 = 1000 - Dessert: 2 × 350 = 700 Step 2: Add those products together.
3.1200 + 1000 + 700 = 2900 Step 3: Add the flat delivery fee of 150 dollars.
4.2900 + 150 = 3050 Step 4: Subtract the bulk discount of 500 dollars.
5.3050 − 500 = 2550 The total cost of the catering order is 2550 dollars.
6.For reference, common errors include forgetting to subtract the discount (yielding 3050), adding the discount instead of subtracting it (yielding 3550), or omitting the delivery fee entirely and skipping the discount (yielding 2900).
Answer: B) 2550
Question 16 · Fractions & DecimalsHard
Wildlife Park Animal Distribution
SectionFraction of All Animals
Lions Enclosure38\frac{3}{8}
Bird Sanctuary14\frac{1}{4}
A wildlife park is home to 1200 animals in total. The table shows the fraction of all the animals found in two of the park's sections. How many more animals are in the Lions Enclosure than in the Bird Sanctuary?
A300
B600
C450
D750
E150
Show answer & explanation
Let's work it out
1.Start by finding the number of animals in each section.
2.The Lions Enclosure contains 38\frac{3}{8} of all 1200 animals: (38\frac{3}{8}) × 1200 = 450 animals.
3.The Bird Sanctuary contains 14\frac{1}{4} of all 1200 animals: (14\frac{1}{4}) × 1200 = 300 animals.
4.To find how many more animals are in the Lions Enclosure than in the Bird Sanctuary, subtract: 450 − 300 = 150 animals.
Answer: E) 150
Question 17 · PercentagesHard
VarietyFraction of Total
Spiced34\frac{3}{4}
Plain14\frac{1}{4}
A cooking club makes 500 cups of trail mix for a fundraiser. According to the recipe chart shown, 34\frac{3}{4} of the total trail mix is the spiced variety. Of the spiced trail mix, 20% is set aside to bring on an upcoming camping trip. How many cups of trail mix are set aside for the camping trip?
A600
B300
C475
D100
E75
Show answer & explanation
Let's work it out
1.First, find how many cups of spiced trail mix exist: 34\frac{3}{4} of 500 = 375 cups.
2.Next, find 20% of that spiced amount, since that is what gets set aside: 20% of 375 = 0.20 x 375 = 75 cups.
Answer: E) 75
Why the other choices are tempting: The value 100 comes from skipping the fraction step and taking 20% of the full 500 cups. The value 300 comes from correctly finding 375 spiced cups and 75 cups set aside, but then subtracting (375 - 75) instead of reporting the 75 as the answer. The value 475 comes from finding 375 cups of spiced mix correctly but then taking 20% of the wrong base (500) and adding it to 375. The value 600 comes from misreading the 20% as a percent increase applied to the whole 500-cup batch.
Question 18 · Ratios & ProportionsHard
Observation Periods (sunny : cloudy)
DayMorning SunnyMorning CloudyAfternoon SunnyAfternoon Cloudy
Day 14254
Day 25346
Day 32448
A school weather club tracked sunny and cloudy observation periods during the morning and afternoon of three days in a row. Their results are shown in the table. Which day had the greatest ratio of total sunny periods to total cloudy periods, and what is that ratio written in simplest form?
A5:4
B3:2
C2:1
D2:3
E1:1
Show answer & explanation
Let's work it out
1.First, find the total sunny and cloudy periods for each day by adding morning and afternoon together.
2.Day 1: sunny = 4 + 5 = 9, cloudy = 2 + 4 = 6, giving a ratio of 9:6.
3.Day 2: sunny = 5 + 4 = 9, cloudy = 3 + 6 = 9, giving a ratio of 9:9.
4.Day 3: sunny = 2 + 4 = 6, cloudy = 4 + 8 = 12, giving a ratio of 6:12.
5.Comparing the three ratios as fractions: Day 1 is 96\frac{9}{6} = 32\frac{3}{2}, Day 2 is 99\frac{9}{9} = 1, and Day 3 is 612\frac{6}{12} = 12\frac{1}{2}.
6.Day 1 has the greatest ratio.
7.Simplifying 9:6 by dividing both parts by 3 gives 3:2.
Answer: B) 3:2
Question 19 · Fractions & DecimalsHard
Weekly Training Log
DayMiles Run
Monday7.2
Tuesday9.6
Wednesdayrest
Thursday11.4
Friday5.4
A middle school cross-country runner kept track of her training distances for one week, shown in the table. Her coach says that next week's total training goal should be 34\frac{3}{4} of this week's total training miles. What is next week's goal in miles?
A8.4
B16.8
C25.92
D25.2
E6.72
Show answer & explanation
Let's work it out
1.Add all the training miles for the week: 7.2 + 9.6 + 11.4 + 5.4 = 33.6 miles total.
2.Next week's goal is 34\frac{3}{4} of 33.6: multiply 33.6 by 3 to get 100.8, then divide by 4 to get 25.2 miles.
Answer: D) 25.2
Why the other choices are tempting: The value 8.4 comes from dividing the weekly total (33.6) by 4 instead of multiplying by 34\frac{3}{4} — a student who computes the average of training days rather than 34\frac{3}{4} of the sum. The value 16.8 comes from adding only the first two training days (7.2 + 9.6) and stopping there. The value 6.72 comes from including the rest day as 0 and averaging all five entries (33.6 divided by 5) instead of finding 34\frac{3}{4} of the total. The value 25.92 comes from computing 34\frac{3}{4} of 34.4 (misreading 11.4 as 12.4 or making an addition error in the sum).
Question 20 · Ratios & ProportionsHard
Maya's Sticker Chart
Stars EarnedStickers Given Out
13
26
412
6?
The table shows how many stickers Maya gives out for every star she earns. Maya has earned 5 stars so far today. If she earns 3 more stars, how many total stickers will she have given out?
A32
B18
C20
D24
E16
Show answer & explanation
Let's work it out
1.From the table, the ratio is 3 stickers per star (for every 1 star, 3 stickers; for every 2 stars, 6 stickers; and so on).
2.Maya started with 5 stars and earns 3 more, giving her 5 + 3 = 8 total stars.
3.Total stickers given out = 8 × 3 = 24, which is answer D.
Answer: D) 24

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