Q: Solve the inequality and give the answer in interval notation: $$\frac{x^2$ - 4}{x^2$ - x - 12} \leq 0$$

$$[-2,2] \cup (3,\infty)$$,\ x \neq 4$

Question 1

Solve for $$x in $$the equation:

$$\displaystyle \frac{1}{x+3} = \frac{2}{x-1} + \frac{2x+2}{x^2$+2x-15}$$

Accepted Answer

$$x = -2$$

Question 2

An executive invests $$22,000, some at 7\%$$ and the rest at 6\%$$ simple annual interest. If he receives an annual return of 1$$,426, how much did he invest at each rate?

Accepted Answer

$$9,000 at 7$$\%, $$13,000 at 6$$\%$

Question 3

Simplify the quotient and write your answer in $$a + bi$$ form:

$$\displaystyle \frac{3i - 2}{2 - 4i}$$

Accepted Answer

$$\displaystyle \frac{7}{10} + \frac{1}{5}i$$

Question 4

Simplify $$i^{77}.$$

Accepted Answer

$$i$$

Question 5

Solve the quadratic equation: $$3x^2 + 4x - 4 = 0$

Accepted Answer

$$x = \frac{-4 \pm 8}{3}$$

Question 6

Jake drives a tractor from one town to another, a distance of $$120$$ kilometers. He drives $$10$$ kilometers per hour faster on the return trip, cutting $$1$$ hour off the time. How fast does he drive each way?

Accepted Answer

$$30 km/h $$going, $$40 km/h $$returning

Question 7

Solve for $$x$$: $$\sqrt{x^2$ + 1} = \sqrt{2x + 5}$$

Accepted Answer

$$x = 3$$

Question 8

Which of the following relations is a function?

Accepted Answer

$$\{(1,3), (5,4), (2,6), (-1,1)\}$$

Question 9

Determine the domain of the function $$f(x) = \frac{6x}{x^2$ - 4x + 1}.$$

Accepted Answer

$$x 
eq 2 \pm \sqrt{3}$$

Question 10

Given the points $$(-2, -5)$$ and $$(4, -1)$$, what is the equation of the line passing through these points?

Accepted Answer

$$y = \frac{2}{3}x - \frac{17}{3}$$

Question 11

Write the equation of the circle $$x^2$$ + $$y^2 + 2x - 10y + 1 = 0$ in standard form and state the center.

Accepted Answer

$$(x+1)^2$$ + $$(y-5)^2 = 25$, center (-1$$,5)$$

Question 12

Suppose $$A$$ varies directly as $$B$$ and inversely as the square root of $$C. If$$ $$A = 8$$ when $$B = 5$$ and $$C = 100$$, what is the constant of variation?

Accepted Answer

$$16$$

Question 13

Solve the inequality and give the answer in interval notation: $$\frac{x^2$ - 4}{x^2$ - x - 12} \leq 0$$

Accepted Answer

$$[-2,2] \cup (3,\infty)$$,\ x 
eq 4$

Question 14

Given $$g(x) = \sqrt{x^2$ - 2x - 3}$$, what is the domain of $$g(x)$$?

Accepted Answer

$$(-\infty, -1] \cup [3, \infty)$$

Question 15

Find the distance between the points $$(-2, -5)$$ and $$(4, -1).$$

Accepted Answer

$$2\sqrt{10}$$

Question 16

Solve for $$x$$: $$|2x + 3| = |2x - 5|$$

Accepted Answer

$$x = 1, x = -4$$

Question 17

Which of the following best describes the graph of $$x^2$$ + $$y^2 = 100$?

Accepted Answer

A circle centered at the origin with radius $$10$$

Question 18

Solve for $$x$$: $$5e^x + 220 = 0$$

Accepted Answer

No real solution

Question 19

If $$f(x) = \frac{6x}{x^2$ - 4x + 1}$$, which value is NOT in the domain of $$f(x)$$?

Accepted Answer

$$x = 2 + \sqrt{3}$$

College Algebra Practice Test 1: Comprehensive Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards