Question 1

Which of the following is the correct simplification of $$\displaystyle \frac{2x^3$y^2$$}{$$4x^2y$$}$?

Accepted Answer

$$\displaystyle \frac{x^2$y}{2}$$

Question 2

Given the equation $$x^2 - 5x + 6 = 0$, which of the following represents the correct set of solutions?

Accepted Answer

$$x = 2, x = 3$$

Question 3

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

Accepted Answer

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

Question 4

If $$f(x) = \frac{1}{x-2}$$, what is the domain of $$f(x)$$?

Accepted Answer

$$x 
eq 2$$

Question 5

Solve for $$x$$: $$\sqrt{x+5} = 4.$$

Accepted Answer

$$x = 11$$

Question 6

Which of the following is the correct simplification of $$\displaystyle \frac{x^2$ - 4}{x - 2}$$ for $$x 
eq 2$$?

Accepted Answer

$$x + 2$$

Question 7

A rectangular garden has a length that is 3 meters longer than its width. If the area is $$40 m$^2$$, what is the width of the garden?

Accepted Answer

$$5$$ meters

Question 8

Which of the following is the solution to $$2x^2 + 3x - 2 = 0$ using the quadratic formula?

Accepted Answer

$$x = \frac{1}{2}, x = -2$$

Question 9

Which of the following is the correct simplification of $$\displaystyle \frac{3}{x} + \frac{2}{x}$$?

Accepted Answer

$$\displaystyle \frac{5}{x}$$

Question 10

If $$x = 2 is a $$solution to the equation $$ax^2 + bx + c = 0$, which of the following must be true?

Accepted Answer

$$4a + 2b + c = 0$$

Question 11

Which of the following is the correct simplification of $$\sqrt{50}$$?

Accepted Answer

$$\sqrt{25} \cdot \sqrt{2} = 5\sqrt{2}$$

Question 12

A chemist mixes a solution with a concentration of $$x$$ grams per liter with another solution of $$2x$$ grams per liter. If the final mixture is $$10$$ liters with a total of $$15$$ grams of solute, what is the value of $$x$$?

Accepted Answer

$$x = 5$$

Question 13

Which of the following is the correct solution to $$\displaystyle \frac{2}{x} = 4$$?

Accepted Answer

Question 14

Which of the following is the correct simplification of $$\displaystyle \frac{x^2$ - 16}{x + 4}$$ for $$x 
eq -4$$?

Accepted Answer

$$x - 4$$

Question 15

If $$x$$ and $$y$$ are real numbers such that $$x^2$$ + $$y^2 = 25$ and x = 3$, what is the value of y$?

Accepted Answer

$$y = 4 or$$ $$y = -4$$

Math 110 Test 1 Study Guide: Fundamental Concepts of Algebra and Equations

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