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

Study Guide - Practice Questions

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