# SHSAT Math FREE Sample Practice Questions

Preparing for the SHSAT Math test? To do your best on the SHSAT Math test, you need to review and practice real SHSAT Math questions. There’s nothing like working on SHSAT Math sample questions to hone your math skills and put you more at ease when taking the SHSAT Math test. The sample math questions you’ll find here are brief samples designed to give you the insights you need to be as prepared as possible for your SHSAT Math test.

Check out our sample SHSAT Math practice questions to find out what areas you need to practice more before taking the SHSAT Math test!

Start preparing for the 2022 SHSAT Math test with our free sample practice questions. Also, 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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**10 Sample SHSAT Math Practice Questions**

1- Jason needs a score of 75 average in his writing class to pass. On his first 4 exams, he earned scores of 68, 72, 85, and 90. What is the minimum score Jason can earn on his fifth and final test to pass? __________

2- Anita’s trick–or–treat bag contains 12 pieces of chocolate, 18 suckers, 18 pieces of gum, 24 pieces of licorice. If she randomly pulls a piece of candy from her bag, what is the probability of her pulling out a piece of sucker?

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

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

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

D. \(\frac{1}{12}\)

3- What is the perimeter of a square in centimeters that has an area of \(595.36 cm^2 \)?

A. 97.2

B. 97.6

C. 97.7

D. 97.9

4- The perimeter of a rectangular yard is 60 meters. What is its length if its width is twice its length?

A. 10 meters

B. 18 meters

C. 20 meters

D. 24 meters

5- The average of 6 numbers is 12. The average of 4 of those numbers is 10. What is the average of the other two numbers?

A. 10

B. 12

C. 14

D. 16

6- If \(40\%\) of a number is 4, what is the number?

A. 4

B. 8

C. 10

D. 12

7- The average of five numbers is 24. If a sixth number 42 is added, then, which of the following is the new average?

A. 25B. 26

C. 27

D. 42

8- The ratio of boys and girls in a class is 4:7. If there are 44 students in the class, how many more boys should be enrolled to make the ratio 1:1?

A. 8

B. 10

C. 12

D. 14

9- What is the slope of the line: \(4x-2y=6\)? __________

10- A football team had $20,000 to spend on supplies. The team spent $14,000 on new balls. New sports shoes cost $120 each. Which of the following inequalities represents the number of new shoes the team can purchase?

A. \(120x+14,000 ≤ 20,000\)

B. \(20x+14,000 ≥ 20,000\)

C. \(14,000x+120 ≤ 20,000\)

D. \(14,000x+12,0 ≥ 20,000\)

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## Answers:

1- **60**

Jason needs a score of 75 on average to pass five exams. Therefore, the sum of 5 exams must be at least \(5 \times 75 = 375\)

The sum of 4 exams is:

\(68 + 72 + 85 + 90 = 315\).

The minimum score Jason can earn on his fifth and final test to pass is:

\(375 – 315 = 60\)

2- **B**

Probability \(= \frac{number \space of \space desired \space outcomes}{number \space of \space total \space outcomes} = \frac{18}{12+18+18+24} = \frac{18}{72} = \frac{1}{4}\)

3-** B**

The area of the square is 595.36. Therefore, the side of the square is the square root of the area.

\(\sqrt{595.36}=24.4\)

Four times the size of the square is the perimeter:\(4 \times 24.4 = 97.6\)

4- **A**

The width of the rectangle is twice its length. Let \(x\) be the length. Then, width \(=2x\)

Perimeter of the rectangle is (2 (width + length) \(= 2(2x+x)=60 {\Rightarrow} 6x=60 {\Rightarrow} x=10\)

The length of the rectangle is 10 meters.

5- **D**

average \(= \frac{sum \space of \space terms}{number \space of \space terms} {\Rightarrow} (average \space of \space 6 \space numbers) \space 12 = \frac{sum \space of \space terms}{6} ⇒\) sum of 6 numbers is

\(12 {\times} 6 = 72\)

(average of 4 numbers) 10 \(= \frac{sum \space of \space terms}{4}{\Rightarrow}\) sum of 4 numbers is \(10 {\times} 4 = 40\)

sum of 6 numbers \(-\) sum of 4 numbers = sum of 2 numbers

\(72 – 40 = 32\)

average of 2 numbers \(= \frac{32}{2} = 16 \)

6- **C**

Let \(x\) be the number. Write the equation and solve for \(x\).

\(40\%\) of \(x=4{\Rightarrow} 0.40 x=4 {\Rightarrow} x=4 {\div}0.40=10\)

7- **C**

First, find the sum of five numbers.

average \(=\frac{ sum \space of \space terms }{ number \space of \space terms } ⇒ 24 = \frac{ sum \space of \space 5 \space numbers }{5}

⇒\) sum of 5 numbers \(= 24 × 5 = 120\)

The sum of 5 numbers is 120. If a sixth number, 42 is added to these numbers, then the sum of 6 numbers is 162.

\(120 + 42 = 162\)

average \(=\frac{ sum \space of \space terms }{ number \space of \space terms } = \frac{162}{6}=27\)

8- **C**

The ratio of boys to girls is 4:7.

Therefore, there are 4 boys out of 11 students.

First, divide the total number of students by 11, then multiply the result by 4.

\(44 {\div} 11 = 4 {\Rightarrow} 4 {\times} 4 = 16\)

There are 16 boys and \(28 (44 – 16)\) girls. So, 12 more boys should be enrolled to make the ratio 1:1

9- **2**

Solve for \(y\).

\(4x-2y=6 {\Rightarrow} -2y=6-4x {\Rightarrow} y=2x-3\)

The slope of the line is 2.

10- **A**

Let \(x\) be the number of new shoes the team can purchase. Therefore, the team can purchase \(120 x\).

The team had $20,000 and spent $14000. Now the team can spend on new shoes $6000 at most.

Now, write the inequality:

\(120x+14,000 {\leq}20,000\)

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