# FREE SSAT Upper Level Math Practice Test

Welcome to our FREE SSAT Upper-Level Math practice test, with answer key and answer explanations. This practice test’s realistic format and high-quality practice questions can help you succeed on the SSAT Upper-Level Math test. Not only does the test closely match what you will see on the real SSAT Upper Level, but it also comes with detailed answer explanations.

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 2022) 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**

## 10 Sample **SSAT Upper Level** Math Practice Questions

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

A. \(15\)

B. \(25\)

C. \(40\)

D. \(50\)

E. \(60\)

2- If \(8x+y=24\) and \(x-z=17\), what is the value of \(x\)?

A. \(1\)

B. \(4\)

C. \(9\)

D. \(19\)

E. it cannot be determined from the information given

3- Find the perimeter of the following shape.

\(\img{https://appmanager.effortlessmath.com/public/images/questions/md.png

}\)

A. \(20\)

B. \(21\)

C. \(22\)

D. \(30\)

E. \(34\)

4- There are \(60.4\) liters of gas in a car fuel tank. In the first week and second week of April, the car uses \(94.86\) and \(23.9\) liters of gas respectively. If the car was parked in the third week of April and \(11.22\) liters of gas will be added to the fuel tank, how many liters of gas are in the fuel tank of the car?

A. \(20.41\) 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 expression 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 circumference of figure A and 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. \(10\%\)

**Be**st **SSAT Upper Level** **Math Prep Resource for 2022**

## Answers:

1- **E**

The capacity of a red box is \(20\%\) bigger than the capacity of a blue box and it can hold \(60\) books. Therefore, we want to find a number that \(20\%\) is bigger than that number is \(60\). Let \(x\) be that number. Then: \(1.20×x=60\), Divide both sides of the equation by \(1.2\). Then:

\(x=\frac{60}{1.20}=50\)

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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