Question 1

Which of the following is the correct solution set for the equation $$\sqrt{2x-1} - \sqrt{x-5} = 3$$?

Accepted Answer

$$x = 10$$

Question 2

Given the polynomial equation $$x^6$$ - $$7x^3 - 8 = 0$, which substitution can be used to reduce it to a quadratic equation?

Accepted Answer

Let $$y = x^3$, so the equation becomes y^2$ - 7y - 8 = 0$$

Question 3

Solve the inequality $$2 + |2x - 3| \leq 4$$ and express the solution in interval notation.

Accepted Answer

$$[0.5, 2.5]$$

Question 4

Which of the following is the standard form $$a + bi of $$the expression $$(3 + i) + 3(-5 + 2i)$$?

Accepted Answer

$$-12 + 7i$$

Question 5

Express $$\dfrac{3}{3 + i} in $$standard form $$a + bi.$$

Accepted Answer

$$\dfrac{3}{10} - \dfrac{3}{10}i$$

Question 6

What is the solution to $$p^2 + 14p - 38 = 0$ by completing the square?

Accepted Answer

$$p = -7 \pm \sqrt{87}$$

Question 7

Solve $$4x^2 + 11x - 20 = 0$ using the quadratic formula.

Accepted Answer

$$x = 1.25$$, $$x = -4$$

Question 8

For the function $$y = -x^2$ + 4$$, which of the following statements is true about its graph?

Accepted Answer

It opens downward and has a vertex at $$(0, 4)$$

Question 9

Which of the following is the $$y-$$intercept of the graph $$y = -x^2$ + 4$$?

Accepted Answer

$$(0, 4)$$

Question 10

If $$y = -x^2$ + 4$$ models the height (in meters) of a ball thrown upward from the ground, what is the maximum height reached by the ball?

Accepted Answer

$$4$$ meters

Question 11

Which of the following describes the symmetry of the graph $$y = -x^2$ + 4$$?

Accepted Answer

It is symmetric about the $$y-$$axis

Question 12

Given the equation $$x^6$$ - $$7x^3 - 8 = 0$, what are the real solutions?

Accepted Answer

$$x = 2$$, $$x = -1$$

Question 13

Which interval represents the solution set for $$2 + |2x - 3| \leq 4$$?

Accepted Answer

$$[0.5, 2.5]$$

Question 14

A chemical reaction is modeled by $$y = -x^2$ + 4$$, where $$y is $$the concentration of a reactant and $$x is $$time in hours. At what time does the concentration reach zero?

Accepted Answer

$$x = 2$$ hours and $$x = -2$$ hours

Question 15

Which of the following is the correct standard form of $$(2 + 5i)^2$?

Accepted Answer

$$-21 + 20i$$

Question 16

If $$y = -x^2$ + 4$$ represents the profit (in thousands of dollars) of a business as a function of $$x ($$number of years since opening), what is the range of possible profits?

Accepted Answer

$$(-\infty, 4]$$

Question 17

Which method is most appropriate for solving $$p^2 + 14p - 38 = 0$ if factoring is not possible?

Accepted Answer

Completing the square

Question 18

A medical dosage is modeled by $$y = -x^2$ + 4$$, where $$y is $$the dosage in mg and $$x is $$time in hours. What is the initial dosage at $$x = 0$$?

Accepted Answer

$$4 mg$$

Question 19

Which of the following is the correct solution to $$\sqrt{2x-1} - \sqrt{x-5} = 3$$?

Accepted Answer

$$x = 10$$

College Algebra: Practice Problems and Concepts

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