Question 1

Which of the following is the correct formula for the distance between two points $$A(x_1$, y_1$)$$ and $$B(x_2$, y_2$) in $$the coordinate plane?

Accepted Answer

$$\sqrt{(x_2$ - x_1$)^2$$ + ($$y_2$$ - $$y_1)^2$}$$

Question 2

Given the equation $$x^2$$ + $$y^2 = 9$, what is the center and radius of the circle?

Accepted Answer

Center: $$(0, 0)$$, Radius: $$3$$

Question 3

What is the slope of the line passing through the points $$(2, 1)$$ and $$(1, 4)$$?

Accepted Answer

$$-3$$

Question 4

Which of the following equations is in slope-intercept form?

Accepted Answer

$$y = mx + b$$

Question 5

If a line is parallel to $$3x - 2y = 8$$, what is its slope?

Accepted Answer

$$\frac{3}{2}$$

Question 6

Solve for $$x$$: $$2x + (3x + 3) = 2x - 18$$

Accepted Answer

$$x = -7$$

Question 7

Which of the following best describes the symmetry of the equation $$y^2$$ - $$x^2 = 9$?

Accepted Answer

Symmetric with respect to the x-axis, y-axis, and the origin

Question 8

Find the midpoint of the segment connecting $$(-2, 3)$$ and $$(1, 4).$$

Accepted Answer

$$\left( -\frac{1}{2}, \frac{7}{2} \right)$$

Question 9

Which of the following is the correct equation for a line with slope $$2$$ passing through the point $$(4, 2)$$?

Accepted Answer

$$y - 2 = 2(x - 4)$$

Question 10

Solve for $$x$$: $$x^2 - 4x = -2$

Accepted Answer

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

Question 11

Given the equation $$y = x^2$ - 2x - 3$$, what are the x-intercepts?

Accepted Answer

$$x = -1, x = 3$$

Question 12

Which of the following is the correct formula for the slope of a line passing through points $$(x_1$, y_1$)$$ and $$(x_2$, y_2$)$$?

Accepted Answer

$$m = \frac{y_2$ - y_1$}{x_2$ - x_1$}$$

Question 13

If a line is perpendicular to $$x + y = 2$$, what is its slope?

Accepted Answer

$$1$$

Question 14

Solve for $$x$$: $$\frac{1}{x-2} = -\frac{3}{x+2} + \frac{2}{x-4}$$

Accepted Answer

$$x = 0$$

Question 15

Which of the following equations represents a circle with center $$(2, -1)$$ and radius $$3$$?

Accepted Answer

$$(x - 2)^2$ + (y + 1)^2$ = 9$$

Question 16

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

Accepted Answer

A parabola opening upwards, narrower than $$y = x^2$

Question 17

Solve for $$x$$: $$\sqrt{2x + 3} + 1 = 7$$

Accepted Answer

$$x = 20$$

Question 18

Which of the following is the correct y-intercept for the line $$3x + 4y = 12$$?

Accepted Answer

$$(0, 3)$$

Question 19

If $$y = 15 = 2x^2$, what is the value of x$ when y = 7$?

Accepted Answer

$$x = \pm 2$$

Question 20

Which of the following equations is equivalent to $$y - 4 = 2(x - 1)$$?

Accepted Answer

$$y = 2x + 2$$

Precalculus Review: Algebra, Graphs, and Equations

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