SHSAT Math Practice

Question 1

A football squad had a budget of $20,000 for supplies. New balls cost $14,000 for the team. Each pair of new sports shoes costs $120. Which of the following inequities represents the team's ability to buy new shoes?

Accepted Answer

120𝑥 + 14,000 ≤ 20,000

Answer

The total budget is $20,000. The team already spent $14,000 on new balls. Each pair of new sports shoes costs $120, and 'x' represents the number of pairs of shoes. The total cost of shoes (120x) plus the cost of balls ($14,000) must be less than or equal to the total budget ($20,000), hence 120x + 14,000 ≤ 20,000.

Question 2

In a class, the ratio of boys to girls is 4:7. How many more boys should be enrolled in a class with 44 students to achieve a 1:1 ratio?

Accepted Answer

12

Answer

With 44 students and a boy-to-girl ratio of 4:7, there are 4 parts boys and 7 parts girls, totaling 11 parts. Each part represents 44 students / 11 parts = 4 students. So, there are 4 * 4 = 16 boys and 7 * 4 = 28 girls. To achieve a 1:1 ratio, the number of boys needs to equal the number of girls (28). Therefore, 28 - 16 = 12 more boys are needed.

Question 3

A rectangular yard has a perimeter of 60 meters. If its width is double its length, what is its length?

Accepted Answer

10 meters

Answer

The perimeter of a rectangle is calculated as 2(length + width). Let the length be 'L'. The problem states the width is double its length, so width = 2L. Given the perimeter is 60 meters, we set up the equation: 2(L + 2L) = 60. This simplifies to 2(3L) = 60, or 6L = 60. Dividing by 6, we find L = 10 meters.

Question 4

What is the slope of a perpendicular line?
4𝑥−2𝑦 = 12?

Accepted Answer

- 1/2

Answer

First, find the slope of the given line 4x - 2y = 12 by rearranging it into slope-intercept form (y = mx + b). Subtract 4x from both sides to get -2y = -4x + 12, then divide by -2 to get y = 2x - 6. The slope of this line (m1) is 2. The slope of a perpendicular line (m2) is the negative reciprocal of m1, which is -1/2.

Question 5

In the following system of equations, what is the value of x?
2𝑥+5𝑦 = 11
4𝑥−2𝑦 = −14

Accepted Answer

-2

Answer

To solve this system of equations for x, we can use the elimination method. Multiply the first equation (2x + 5y = 11) by 2 to get 4x + 10y = 22. Now, subtract the second equation (4x - 2y = -14) from this new equation: (4x + 10y) - (4x - 2y) = 22 - (-14), which simplifies to 12y = 36, so y = 3. Substitute y = 3 into the first equation: 2x + 5(3) = 11, which becomes 2x + 15 = 11. Subtract 15 from both sides: 2x = -4. Finally, divide by 2 to find x = -2.

SHSAT Practice Test

SHSAT Practice Test

SHSAT Math Practice