FREE SSAT Upper Level Math Practice Test

Interactive SSAT Upper Level Math Practice Test (Timed, 50 Questions)

Take our free, full-length SSAT Upper Level Quantitative (Math) practice test below. It mirrors the real exam: two sections of 25 questions (50 total) in 60 minutes, no calculator, with the SSAT guessing penalty built into the score. You’ll get an estimated 500–800 Quantitative score, full step-by-step explanations, and a personalized study plan. Scroll down for more practice and tips.

For this practice test, we’ve selected 20 real questions from past exams for your SSAT Upper-Level Practice test. You will have the chance to try out the most common SSAT Upper-Level Math questions. For every question, there is an in-depth explanation of how to solve the question and how to avoid mistakes next time.

Use our free SSAT Upper-Level Math practice tests and study resources (updated for 2026) to ace the SSAT Upper-Level Math test! Make sure to follow some of the related links at the bottom of this post to get a better idea of what kind of mathematics questions you need to practice.

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SSAT Upper Level Math for Beginners 2026 The Ultimate Step by Step Guide to Preparing for the SSAT Upper Level Math Test

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1- The capacity of a red box is \(20\%\) bigger than the capacity of a blue box. If the red box can hold \(60\) books, how many books can the blue box hold?

A. \(30\)

B. \(40\)

C. \(45\)

D. \(48\)

E. \(50\)

2- If \(2x+y+z=10\) and \(x+y-z=4\), what is the value of \(x\)?

A. \(2\)

B. \(3\)

C. \(4\)

D. \(7\)

E. It cannot be determined from the information given

3- What is the perimeter of the figure below?
\(\)

A. \(25\)

B. \(28\)

C. \(30\)

D. \(32\)

E. \(34\)

4- A tank originally contained \(60.4\) liters of petrol. After \(4.86\) liters and then \(23.9\) liters were used, \(11.22\) liters were added back. How much petrol is now in the tank?

A. \(20.34\) liters

B. \(26.5\) liters

C. \(28\) liters

D. \(28.79\) liters

E. \(42.86\) liters

5- If \(a×b\) is divisible by \(4\), which of the following expressions must also be divisible by \(4\)?

A. \( 2a-5b\)

B. \(3a-b\)

C. \(2a×3b\)

D. \(\frac{a}{b}\)

E. \(\frac{a \times b}{3}\)

6- Which of the following could be the value of \(x\) if \(\frac{6}{8}+x>2\)?

A. \(\frac{1}{3}\)

B. \(\frac{3}{5}\)

C. \(\frac{6}{5}\)

D. \(\frac{4}{3}\)

E. \(\frac{2}{3}\)

7- If a gas tank can hold \(20\) gallons, how many gallons does it contain when it is \(\frac{3}{4}\) full?

A. \(135\)

B. \(52.5\)

C. \(50\)

D. \(20\)

E. \(15\)

8- In the following figure, point \(Q\) lies on line \(n\), what is the value of \(y\) if \(x=35\)?
\(\)

A. \(10\)

B. \(25\)

C. \(30\)

D. \(40\)

E. \(50\)

9- A number is chosen at random from \(1\) to \(20\). Find the probability of not selecting a composite number. (A composite number is a number that is divisible by itself, \(1\) and at least one other whole number)

A. \(\frac{1}{20}\)

B. \(\frac{2}{5}\)

C. \(\frac{9}{20}\)

D. \(1\)

E. \(0\)

10- Solve: \(615÷4=\)?

A. \(\frac{600}{4}×\frac{10}{4}×\frac{5}{4}\)

B. \(600×\frac{10}{4}×\frac{5}{4}\)

C. \(\frac{600}{4}+\frac{10}{4}+\frac{5}{4}\)

D. \(\frac{600}{4}\div\frac{10}{4}\div\frac{5}{4}\)

E. \(\frac{6}{4}+\frac{1}{4}+\frac{5}{4}\)

11- What is the average of the circumference of figure A and the area of figure B? ((\pi=3))
\(\)

A. \(75\)

B. \(70\)

C. \(60\)

D. \(50\)

E. \(44\)

12- What is the value of the \(“9″\) in number \(131.493\)?

A. \( 9\) ones

B. \( 9\) tenths

C. \( 9\) hundredths

D. \( 9\) tens

E. \( 9\) thousandths

13- If \(x-20=-20\), then \(x×20=\) ?

A. \(0\)

B. \(10\)

C. \(20\)

D. \(40\)

E. \(60\)

14- \(0.04 × 13.00=\)?

A. \( 5.2\)

B. \( 52.00\)

C. \( 0.52\)

D. \( 5.02\)

E. \( 0.052\)

15- If Logan ran \(3.5\) miles in half an hour, his average speed was?

A. \( 2.25\) miles per hour

B. \(3.5\) miles per hour

C. \( 3.75\) miles per hour

D. \(4.26\) miles per hour

E. \(7\) miles per hour

16- Given the diagram, what is the perimeter of the quadrilateral?
\(\)

A. \(54\)

B. \(70\)

C. \(720\)

D. \(26740\)

E. \(55480\)

17- A pizza maker has M pounds of flour to make pizzas. After he has used \(75\) pounds of flour, how much flour is left? The expression that correctly represents the quantity of flour left is:

A. \( 75+M\)

B. \( \frac{75}{M}\)

C. \( 75-M\)

D. \( M-75\)

E. \( 75M\)

18- Mia plans to buy a bracelet for every one of her \(18\) friends for their party. There are four bracelets in each pack. How many packs must she buy?

A. \(2\)

B. \(3\)

C. \(4\)

D. \(5\)

E. \(10\)

19- The distance between cities A and B is approximately \(3,600\) miles. If Alice drives an average of \(70\) miles per hour, how many hours will it take Alice to drive from city A to city B?

A. Approximately \(70\) hours

B. Approximately \(68\) hours

C. Approximately \(51\) hours

D. Approximately \(37\) hours

E. Approximately \(21\) hours

20- In a classroom of \(60\) students, \(30\) are female. What percentage of the class is male?

A. \( 54\%\)

B. \(50\%\)

C. \(30\%\)

D. \(26\%\)

E. \(10\%\)

Best SSAT Upper Level Math Prep Resource for 2026

Answers:

2- E
We have two equations and three unknown variables, therefore \(x\) cannot be obtained.

3- E
\(x+2=2+2+2→x=4\)
\(y+7+3=6+5→y+10=11→y=1\)
Then, the perimeter is:
\(2+6+2+5+2+3+2+7+4+1=34\)
\(\)

4- ٍE
Amount of available petrol in tank: \(60.4-4.86-23.9+11.22=42.86\) liters

5- C
Let put some values for a and b. If \(a=8\) and \(b=2 →a×b=16 →\frac{16}{4}=8→16\) is divisible by \(4\) then;
A.\(2a-5b=(2×8)-(5×2)=6\) is not divisible by \(4\)
B.\(3a-b=(3×8)-2=24-2=22\) is not divisible by \(4\)
If \(a=10\) and \(b=4 →a×b=40 →\frac{40}{4}=10\) is not divisible by \(4\) then;
C.\(2a×3b=20×(3×4)=20×12=240\) is divisible by \(4\)
D.\(\frac{a}{b}=\frac{10}{4}\) is not divisible by \(4\)
E. \(\frac{a×b}{3}=\frac{10×4}{3}=13.33\)
For choice C, if you try any other numbers for a and b, you will get the same result.

6- D
Let’s review the choices provided:
A.\(x=\frac{1}{3}→ \frac{6}{8}+\frac{1}{3}=\frac{18+8}{24}=\frac{26}{24}≅1.083<2\)
B.\(x=\frac{3}{5}→ \frac{6}{8}+\frac{3}{5}=\frac{30+24}{40}=\frac{54}{40}≅1.35<2\)
C.\(x=\frac{6}{5}→ \frac{6}{8}+\frac{6}{5}=\frac{30+48}{40}=\frac{78}{40}≅1.95<2\)
D.\(x=\frac{4}{3}→ \frac{6}{8}+\frac{4}{3}=\frac{18+32}{24}=\frac{50}{24}≅2.08>2\)
E.\(x=\frac{2}{3}→ \frac{6}{8}+\frac{2}{3}=\frac{18+16}{24}=\frac{34}{24}≅1.41<2\)
Only choice D is correct.

7- E
\(\frac{3}{4}×20=\frac{60}{4}=15\)

8- B
The angles on a straight line add up to \(180\) degrees. Let’s review the choices provided:
A.\(y=10→ x+25+y+2x+y=35+25+10+2(35)+10=150≠180\)
B.\(y=25→ x+25+y+2x+y=35+25+25+2(35)+25=180\)
C.\(y=30→ x+25+y+2x+y=35+25+30+2(35)+30=190≠180\)
D.\(y=40→ x+25+y+2x+y=35+25+40+2(35)+40=210≠180\)
E.\(y=50→ x+25+y+2x+y=35+25+50+2(35)+50=230≠180\)

9- B

Set of numbers that are not composite between \(1\) and \(20: A={2,3,5,7,11,13,17,19}\)
Probability\(=\frac{number \ of \ desired \ outcomes}{number \ of \ total \ outcomes}= \frac{8}{20}=\frac{2}{5 }\)

10- C
\(615÷4=\frac{615}{4}=\frac{600+10+5}{4}=\frac{600}{4}+\frac{10}{4}+\frac{5}{4 }\)

11- C

Perimeter of figure A is: \(2πr=2π \frac{20}{2}=20π=20×3=60\)
Area of figure B is: \(5×12=60\), Average\(=\frac{60+60}{2}=\frac{120}{2}=60\)

12- C
Digit \(9\) is in the hundredths place.

13- A
\(x-20=-20→x=-20+20→x=0\), Then; \(x×20=0×20=0\)

14- C
\(0.04×13.00=\frac{4}{100}×\frac{13}{1}=\frac{52}{100}=0.52 \)

15- E
His average speed was: \(\frac{3.5}{0.5}=7\) miles per hour

16- B
The perimeter of the quadrilateral is: \(7+21+10+32=70\)

17- D
The amount of flour is: \( M-75\)

18- D
A number of packs needed equal to \(\frac{18}{4}≅4.5\), Then Mia must purchase \(5\) packs.

19- C
The time it takes to drive from city A to city B is \(\frac{3,600}{70}=51.42\), It’s approximately \(51\) hours.

20- B
The number of males in the classroom is: \(60-30=30\)
Then, the percentage of males in the classroom is: \(\frac{30}{60}×100=0.5×100=50\%\)

Looking for the best resource to help you succeed on the SSAT Upper-Level Math test?

The Best Books to Ace the SSAT Upper Level Math Test

Recommended EffortlessMath Books

For a workbook that covers every Quantitative topic on the test, the SSAT Upper Level Math for Beginners walks through each concept with worked examples. For complete prep with multiple full-length practice tests, see the SSAT Upper Level Math Test Prep Bundle (resource currently unavailable).

Frequently Asked Questions

Is there a free SSAT Upper Level practice test?

Yes. You can take a free, full-length SSAT Upper Level math practice test online with 50 Quantitative questions and step-by-step explanations. For the most realistic rehearsal, set a timer, put the calculator away, and work through both math sections in one sitting. Afterward, sort your missed questions by topic, such as fractions, algebra or geometry, so you know exactly what to review before test day.

Is there a free SSAT Upper Level math practice test PDF with answers?

Some free SSAT Upper Level math tests come as printable PDFs, but an interactive test with an answer key is just as useful, since it times you and explains each solution. If you prefer paper, copy the questions into a notebook, solve them by hand, then check the explanations. Working on paper is good practice anyway, because calculators are not allowed on the SSAT.

What math topics are on the SSAT Upper Level?

The SSAT Upper Level math sections cover number sense and operations, algebra, geometry and measurement, and data analysis and probability. Expect fractions, decimals and percents, ratios and proportions, linear equations and inequalities, area, perimeter and volume, and simple probability. For example, you might need to find 30% of 80 (24) or solve 3x + 7 = 22 (x = 5) quickly, without a calculator.

How is the SSAT Upper Level math section timed?

The Upper Level SSAT has two Quantitative sections of 25 questions each, about an hour of math in total, placed between the Verbal, Reading and writing parts of the test. That is a little over a minute per question, so pacing matters. Skip any question that stalls you and come back after the easier ones. Confirm current section times on the official SSAT website.

When are the SSAT Upper Level test dates?

The SSAT Upper Level is offered on several dates through the school year, and many families test in the fall and winter ahead of private school application deadlines. Dates, registration deadlines and testing options change each year, so check the official SSAT website for the current calendar. Register early and leave room for a second attempt in case you want to raise your math score.

What do SSAT Upper Level math practice questions look like?

SSAT Upper Level math questions are multiple choice with five answer choices, A through E, and mix arithmetic, algebra, geometry and data. A typical question: if 2/5 of a class of 30 students are boys, how many are girls? Since 2/5 × 30 = 12 boys, there are 18 girls. Practicing questions like this by hand builds the speed and accuracy you need with no calculator.

Related EffortlessMath Lessons

If a topic on this page feels rusty, these short lessons go deeper:

• SSAT Upper Level Math Formula Cheat Sheet
• How to find the slope of a line
• How to use the Pythagorean theorem
• Rules of exponents
• Order of operations (PEMDAS)