Q: A rectangular garden has a length of 12 meters and a width of 7 meters. What is the perimeter of the garden?

$$P = 2 \times (12 + 7) = 38$$ meters

Q: A chemist mixes 250 mL of a 20% saline solution with 150 mL of a 40% saline solution. What is the percent concentration of the resulting mixture?

$$\frac{250 \times 0.20 + 150 \times 0.40}{250 + 150} \times 100 = 28.75\%$$

Q: A recipe calls for $$\frac{3}{4}$$ cup of sugar. If you want to make half the recipe, how much sugar should you use?

$$\frac{3}{4} \times \frac{1}{2} = \frac{3}{8}$$ cup

Q: If $$x = 4$$ and $$y = -2$$, what is the value of $$2x^2 - 3y$?

$$2 \times 4^2$ - 3 \times (-2) = 32 + 6 = 38$$

Q: A rectangular box has a length of 10 cm, width of 4 cm, and height of 5 cm. What is its volume?

$$10 \times 4 \times 5 = 200 cm$^3$$

Question 1

A rectangular garden has a length of 12 meters and a width of 7 meters. What is the perimeter of the garden?

Accepted Answer

$$P = 2 	imes (12 + 7) = 38$$ meters

Question 2

Which of the following is the correct simplification of the expression $$3(x + 4) - 2x$$?

Accepted Answer

$$x + 12$$

Question 3

A chemist mixes 250 mL of a 20% saline solution with 150 mL of a 40% saline solution. What is the percent concentration of the resulting mixture?

Accepted Answer

$$\frac{250 	imes 0.20 + 150 	imes 0.40}{250 + 150} 	imes 100 = 28.75\%$$

Question 4

Solve for $$x in $$the equation $$5x - 7 = 18.$$

Accepted Answer

$$x = 5$$

Question 5

A store is offering a 15% discount on a jacket that originally costs $80. What is the sale price of the jacket?

Accepted Answer

$$80 - (0.15 	imes 80) = 68$$

Question 6

Which of the following is the solution to the inequality $$2x + 5 \u003c 13$$?

Accepted Answer

$$x \u003c 4$$

Question 7

A triangle has side lengths of 6 cm, 8 cm, and 10 cm. Is this triangle a right triangle?

Accepted Answer

Yes, because $$6^2$$ + $$8^2$$ = $$10^2$$

Question 8

Simplify the expression $$2^3$$ 	imes $$2^4.$$

Accepted Answer

$$2^{3+4}$$ = $$2^7 = 128$

Question 9

A recipe calls for $$\frac{3}{4}$$ cup of sugar. If you want to make half the recipe, how much sugar should you use?

Accepted Answer

$$\frac{3}{4} 	imes \frac{1}{2} = \frac{3}{8}$$ cup

Question 10

Which of the following is the correct order of operations to evaluate $$5 + 2 	imes (3^2$ - 1)$$?

Accepted Answer

First, calculate $$3^2$$, then subtract 1, multiply by 2, and finally add 5

Question 11

A car travels 180 miles in 3 hours. What is the average speed of the car in miles per hour?

Accepted Answer

$$\frac{180}{3} = 60$$ miles per hour

Question 12

If $$x = 4$$ and $$y = -2$$, what is the value of $$2x^2 - 3y$?

Accepted Answer

$$2 	imes 4^2$ - 3 	imes (-2) = 32 + 6 = 38$$

Question 13

Which of the following is the correct factorization of $$x^2 - 9$?

Accepted Answer

$$(x - 3)(x + 3)$$

Question 14

A student scored 78, 85, 92, and 75 on four tests. What is the mean (average) score?

Accepted Answer

$$\frac{78 + 85 + 92 + 75}{4} = 82.5$$

Question 15

Which of the following is equivalent to $$\frac{5}{8} + \frac{1}{4}$$?

Accepted Answer

$$\frac{5}{8} + \frac{2}{8} = \frac{7}{8}$$

Question 16

A rectangular box has a length of 10 cm, width of 4 cm, and height of 5 cm. What is its volume?

Accepted Answer

$$10 	imes 4 	imes 5 = 200 cm$^3$$

Question 17

Which of the following is the solution to the equation $$\frac{2}{3}x = 8$$?

Accepted Answer

$$x = 12$$

Question 18

A circle has a radius of 7 cm. What is its circumference? (Use $$\pi \approx 3.14)$$

Accepted Answer

$$2 	imes 3.14 	imes 7 = 43.96 cm$$

Question 19

If the probability of raining tomorrow is $$0.3$$, what is the probability that it will not rain?

Accepted Answer

$$1 - 0.3 = 0.7$$

Pre-Algebra Course Syllabus and Foundations for Intermediate Algebra

Study Guide - Practice Questions

Study Guide - Flashcards