FREE SSAT Upper Level Math Practice Test

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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>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 \(x=35\)?
\(\img{https://appmanager.effortlessmath.com/public/images/questions/ccvv.png
}\)

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))
\(\img{https://appmanager.effortlessmath.com/public/images/questions/gg2ghhh.png
}\)

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?
\(\img{https://appmanager.effortlessmath.com/public/images/questions/78vblq.png
}\)

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. \(10\%\)

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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:
\(2+6+2+5+2+3+2+7+4+1=34\)
\(\img{https://appmanager.effortlessmath.com/public/images/questions/yyyyyygj.png
}\)

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: \(\frac{30}{60}×100=0.5×100=50\%\)

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The Best Books to Ace the SSAT Upper Level Math Test

SSAT Upper Level Math for Beginners 2023 The Ultimate Step by Step Guide to Preparing for the SSAT Upper Level Math Test

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