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.

The Absolute Best Book to Ace the SSAT Upper Level Math Test

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

Download

$27.99 Original price was: $27.99.$17.99Current price is: $17.99.

Rated 4.35 out of 5 based on 161 customer ratings

Satisfied 148 Students

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.

Frequently Asked Questions

How many math questions are on the SSAT Upper Level?

50 questions total in the Quantitative portion, split into two separate 25-minute sections of 25 questions each. The two sections are interleaved with the Verbal and Reading sections during the test day.

Is a calculator allowed on the SSAT?

No. No calculators are allowed on any portion of the SSAT, including both math sections. Practice arithmetic, fractions, and mental algebra by hand from the very first day of your prep.

What grades take the SSAT Upper Level?

The Upper Level SSAT is for students currently in grades 8 through 11 who are applying for admission to grades 9 through 12 at private schools. Younger students take the Middle Level (grades 5-7) or Lower Level (grades 3-4) versions.

How is the SSAT scored?

Each section gets a scaled score between 500 and 800. The Upper Level reports Quantitative, Verbal, and Reading scaled scores plus a total. You also get a percentile rank against other SSAT-takers in your same grade. Most competitive private schools look at percentile, not the raw scaled score.

Does the SSAT penalize guessing?

Yes. You lose 1/4 point for each wrong answer; correct answers earn 1 point; blanks earn 0. If you can eliminate at least one of the five choices, the expected value of guessing turns positive — so educated guessing usually beats leaving blanks.

What math topics are on the SSAT Upper Level?

Number sense and operations (about 20%), algebra (about 30%), geometry and measurement (about 30%), and data analysis/probability (about 20%). Specific topics include fractions and decimals, ratios and proportions, linear equations, exponents, area and volume, the Pythagorean theorem, and basic statistics.

How long is the full SSAT Upper Level test?

About 3 hours 5 minutes of actual testing time. That covers a 25-minute writing sample, two 25-minute Quantitative sections, a 40-minute Reading section, a 30-minute Verbal section, and a 16-minute experimental section, with short breaks built in.

Can I retake the SSAT?

Yes. The SSAT is offered on 8 standard test dates per year, and you can take it as many times as you like during your application cycle. Most schools accept your highest score; some look at all attempts. Check each school’s policy.

How long should I study for the SSAT Upper Level Math?

If you’re a strong math student in grade 8 or 9, 4-6 weeks of consistent practice is usually enough. If math feels rough, 8-12 weeks at 30 minutes per day works better. Start with a full diagnostic to identify your weak topics, then drill those before timed practice.

Where can I find more SSAT Upper Level practice?

EffortlessMath has the SSAT Upper Level Math Formula Cheat Sheet, the SSAT Upper Level Math for Beginners workbook, and the SSAT Upper Level Math Test Prep Bundle with multiple full-length practice tests.

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)