Question 1

Which of the following best describes the coordinates of the origin in the rectangular coordinate system?

Accepted Answer

$$(0, 0)$$

Question 2

A point $$P$$ has coordinates $$(-3, 4). In $$which quadrant does $$P$$ lie?

Accepted Answer

Quadrant II

Question 3

Which of the following points satisfies the equation $$x + y = 5$$?

Accepted Answer

$$(2, 3)$$

Question 4

What is the $$y-$$intercept of the equation $$2x - 3y = 6$$?

Accepted Answer

$$(0, -2)$$

Question 5

Solve the equation $$3(2 - 5x) = 4x + 25$$ for $$x.$$

Accepted Answer

$$x = -rac{1}{7}$$

Question 6

Which of the following is the standard form of the quadratic equation $$-4x^2 + x = 8$?

Accepted Answer

$$-4x^2 + x - 8 = 0$

Question 7

Solve the quadratic equation $$x^2 + x - 6 = 0$ by factoring.

Accepted Answer

$$x = -3, x = 2$$

Question 8

What is the discriminant of the quadratic equation $$x^2 + 8x + 16 = 0$ and what does it tell you about the solutions?

Accepted Answer

The discriminant is $$0$$, so there is one real solution.

Question 9

Which is the correct interval notation for the set $$\{x | 0 \u003c x \u003c 5\}$$?

Accepted Answer

$$(0, 5)$$

Question 10

Solve the inequality $$2x + 12 \u003e 19$$ and express the solution in interval notation.

Accepted Answer

$$(3.5, \infty)$$

Question 11

Which of the following is the conjugate of the complex number $$4 - 5i$$?

Accepted Answer

$$4 + 5i$$

Question 12

Find the product $$(2 + 3i)(2 - 3i).$$

Accepted Answer

$$13$$

Question 13

Solve the quadratic equation $$x^2 - 6x = 5$ using the best method.

Accepted Answer

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

Question 14

Which of the following is the correct solution to $$\frac{1}{4}(x + 2) \geq -1$$?

Accepted Answer

$$x \geq -6$$

Question 15

What is the sum $$(4 - 8i) + (2 - 3i)$$ expressed in standard form?

Accepted Answer

$$6 - 11i$$

Question 16

Which method is best for solving the equation $$(x + 2)^2$ = 9$$?

Accepted Answer

Square root property

Question 17

Solve the rational equation $$\frac{x}{x-1} = 7$$ for $$x.$$

Accepted Answer

$$x = \frac{7}{6}$$

Question 18

Which of the following is the correct standard form for the quadratic equation $$5x^2 = x - 3$?

Accepted Answer

$$5x^2 - x + 3 = 0$

Question 19

If the discriminant $$b^2 - 4ac$ of a quadratic equation is negative, what can you conclude about the solutions?

Accepted Answer

There are two complex (non-real) solutions.

Question 20

Which of the following is the correct solution to $$2x^2 - 16 = 0$?

Accepted Answer

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

Equations and Inequalities: Foundations for Precalculus

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