# FREE SSAT Middle Level Math Practice Test

Welcome to our FREE SSAT Middle-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 Middle-Level Math test. Not only does the test closely match what you will see on the real SSAT Middle 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 Middle-Level Practice test. You will have the chance to try out the most common SSAT Middle-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 Middle-Level Math practice tests and study resources (updated for 2022) to ace the SSAT Middle-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 Middle Level Math Test**

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

1- \(\frac{x}{x-2}=\frac{4}{5}\) ,\(x-5=?\)

A. \(-13\)

B. \(-15\)

C. \(-17\)

D. \(12\)

E. \(15\)

2- A company pays its employer ($7,000) plus \(3\%\) of all sales profit. If \(𝑥\) is the number of all sales profit, which of the following represents the employer’s revenue?

A. \( 0.03x\)

B. \( 0.97x-7,000\)

C. \( 0.03x+7,000\)

D. \( 0.97x+7,000\)

E. \( 0.3x+7,000\)

3- In a certain bookshelf of a library, there are (35) biology books, (85) history books, and (90) language books. What is the ratio of the number of biology books to the total number of books on this bookshelf?

A. \(\frac{1}{4}\)

B. \(\frac{1}{6}\)

C. \(\frac{2}{7}\)

D. \(\frac{3}{8}\)

E. \(\frac{1}{4}\)

4- If \(5,000+A-200=7\),\(400\), then \(A=⋯\)

A. 200

B. 600

C. 1600

D. 2600

E. 3000

5- The circle graph below shows all Mr. Green’s expenses for last month. If he spent ($770) on his car, how much did he spend on his rent?

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

}\)

A. \( $700\)

B. \( $740\)

C. \( $780\)

D. \( $810\)

E. \( $945\)

6- If \(5×M+3=5\) , M equals to ….

A. 2

B. 4

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

D. 6

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

7- Which of the following is equal to \(\frac{52.6}{100}\)?

A. \(52.6\)

B. \(5.26\)

C. \(526.0\)

D. \(0.0526\)

E. \(0.526\)

8- In the following figure, point \(Q\) lies on line \(A\), what is the value of \(y\) if \(x=28\)? (Figure is not drawn to scale)

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

}\)

A. \(32\)

B. \(37\)

C. \(42\)

D. \(45\)

E. \(45\)

9- A container holds \(2.5\) gallons of water when it is \(\frac{5}{24}\) full. How many gallons of water does the container hold when it’s full?

A. \(8\)

B. \(12\)

C. \(16\)

D. \(20\)

E. \(30\)

10- At a Zoo, the ratio of lions to tigers is \(3\) to \(1\). Which of the following could NOT be the total number of lions and tigers in the zoo?

A. \(64\)

B. \(80\)

C. \(98\)

D. \(104\)

E. \(160\)

11- If \(x\) is greater than \(18\), then \(\frac{1}{3}\) of \(x\) must be…

A. Greater than \(3\)

B. Greater than \(6\)

C. Equal to \(6\)

D. Equal to \(3\)

E . Less than \(3\)

12- How long does a \(420\)–miles trip take moving at \(65\) miles per hour (mph)?

A. \(4\) hours

B. \(6\) hours and \(24\) minutes

C. \(8\) hours and \(24\) minutes

D. \(8\) hours and \(30\) minutes

E. \(10\) hours and \(30\) minutes

13- The marked price of a computer is 𝐷 dollar. Its price decreased by \(15\%\) in January and later increased by \(10\%\) in February. What is the final price of the computer in 𝐷 dollar?

A. \(0.80\) D

B. \(0.88\) D

C. \(0.93\) D

D. \(1.20\) D

E. \(1.40\) D

14- If \(0.35\) equals \(350\)𝑀, what is the value of 𝑀?

A. \( 0.001\)

B. \( 0.01\)

C. \(1.0\)

D. \(1.01\)

E. \(1.001\)

15- Jason borrowed \($5,800\) for three months at an annual rate of \(5\%\). How much interest did Jason owe?

A. \( $45\)

B.\($72.50\)

C. \($120\)

D. \($240\)

E. \($480\)

16- If three times a certain number, increased by \(10\), is equal to \(40\), what is the number?

A. \(10\)

B. \(12\)

C. \(18\)

D. \(27\)

E. \(54\)

17- If \(30\) percent of a number is \(150\), then \(15\) percent of the same number is?

A. \(75\)

B. \(79\)

C. \(80\)

D. \( 90\)

E. \(120\)

18- The average of \(13,15,20\) and \(x\) is \(20\). What is the value of \(x\)?

A. \(9\)

B. \(15\)

C. \(18\)

D. \(20\)

E. \(32\)

19- In five successive hours, a car traveled \(40\) 𝑘𝑚,\(45\) 𝑘𝑚,\(50\) 𝑘𝑚,\(35\) 𝑘𝑚 and \(55\) 𝑘𝑚. In the next five hours, it traveled with an average speed of \(55\) 𝑘𝑚 𝑝𝑒𝑟 ℎ𝑜𝑢𝑟. Find the total distance the car traveled in \(10\) hours.

A. \(425\) km

B. \(450\) km

C. \(475\) km

D. \(500\) km

E. \(1,000\) km

20- John has 𝑁 toy cars. Jack has \(6\) more cars than John. If Jack gives John \(3\) cars, how many cars will Jack have, in terms of 𝑁?

A. \( N\)

B. \( N-1\)

C. \( N+1\)

D. \( N+2\)

E. \( N+3\)

**Best SSAT Middle Level Math Prep Resource for 2022**

## Answers:

1- **A**

Use cross product to solve for \((x)\).

\(\frac{x}{x-2}=\frac{4}{5}→5×x=4×(x-2)→5x=4x-8→x=-8, x-5=-8-5=-13\)

2- **C**

\(x\) is the number of all sales profit and \(3\%\) of it is: \(3\%×x=0.03x\), Employer’s revenue: \(0.03x+7,000\)

3-** B**

Number of biology book: \(35\), Total number of books; \(35+85+90=210\)

The ratio of the number of biology books to the total number of books is: \(\frac{35}{210}=\frac{1}{6}\)

4- **D**

\(5,000+A-200=7,400→5,000+A=7,400+200=7,600→A=7,600-5,000=2,600\)

5- **E**

Let \(x\) be all expenses, then \(\frac{22}{100} x=$770 →x=\frac{100×$770}{22}=$3,500\),

He spent for his rent: \(\frac{27}{100}×$3,500=$945\)

6- **C**

\(5×M+3=5→5×M=5-3=2→M=\frac{2}{5}\)

7- **E**

\(\frac{52.6}{100}=0.526\)

8-B

The angles on a straight line add up to \(180\) degrees. Then: \(x+22+y+2x+y=180\), Then, \(3x+2y=180-22→3(28)+2y=158→2y=158-84=74→y=37\)

9- **B**

let \(x\) be the number of gallons of water the container holds when it is full.

Then; \(\frac{5}{24} x=2.5→x=\frac{24×2.5}{5}=12\)

10- **C**

The ratio of lions to tigers is \(3\) to 1 at the zoo. Therefore, the total number of lions and tigers must be divisible by \(4\). From the choices provided, only \(98\) is not divisible by \(4\).

11- **B**

If \(x\) is greater than \(18\), then \(\frac{1}{3}\) of \(x\) must be greater than: \(\frac{1}{3}×18=6.\)

12- **B**

Use distance formula: Distance \(=\) Rate \(×\) time \(⇒ 420=65×T\), divide both sides by \(65. 420÷65= T ⇒ T = 6.4 \) hours. Change hours to minutes for the decimal part.

\(0.4\) hours \(= 0.4×60=24 \) minutes.

13- **D**

To find the discount, multiply the number by (\(100\%-\) rate of discount).Therefore, for the first discount we get: \((D) (100\%-15\%)=(D\) \(0.85)=0.85 D\)

For increase of \(10\%: (0.85 D) (100\%+10\%\)=\(0.85 D\) \(1.10)=0.93 D=\) \(93\%\) of D or \(0.93D\)

14- **A**

\(0.35\) equals \(350M\). Then:\(0.35=350M→M=\frac{0.35}{350}=0.001\)

15- **B**

Use simple interest formula: \(I=prt, (I =\) interest, \(p =\) principal, \(r =\) rate, \(t =\) time)

t is for one year. For (3) months, t is \(\frac{1}{4}\) or \(0.25\).

\(I=(5,800)(0.05)(0.25)=72.50\)

16- **A**

Three times a certain number, increased by \(10\), is equal to \(40\). Write an equation and solve.

\(3x+10=40→3x=40-10=30→x=\frac{30}{3}=10\)

17- **A**

\(30\) percent of a number is (150). Therefore, the number is \(500. 0.30x=150→x=\frac{150}{0.30}=500\)

\(15\) percent of (500) is \(75. 0.15×500=75\)

18- **E**

average \(=\frac{sum \ of \ terms }{number \ of \ terms}⇒ 20= \frac{13+15+20+x}{4 } ⇒80=48+x ⇒ x=32\)

19- **D**

Add the first \(5\) numbers. \(40+45+50+35+55=225\)

To find the distance traveled in the next \(5\) hours, multiply the average by number of hours.

Distance \(=\) Average \(×\) Rate \(=55×5=275\), Add both numbers. \(275+225=500\)

20- **E**

John has N toy cars. Jack has \(6\) more cars than John. Therefore, Jack has \(N+6\) toy cars. Jack gives John \(3\) cars. Now, Jack has \((N+6-3) N+3\) toy cars.

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**The Best Books to Ace the ****SSAT Middle Level** Math **Test**

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