Question 1

Which of the following is the correct solution to the equation $$2x - 5 = 9$$?

Accepted Answer

$$x = 7$$

Question 2

A chemist mixes a solution that is 30% acid with a solution that is 50% acid to obtain 10 liters of a 40% acid solution. How many liters of the 30% solution should be used?

Accepted Answer

$$4$$ liters

Question 3

Which of the following is the correct form of the quadratic formula for solving $$ax^2 + bx + c = 0$?

Accepted Answer

$$x = \frac{-b \pm \sqrt{b^2$ - 4ac}}{2a}$$

Question 4

Solve the inequality $$3x - 7 \u003c 2x + 5.$$

Accepted Answer

$$x \u003c 12$$

Question 5

Which of the following is the correct distance between the points $$(2, 3)$$ and $$(7, 11)$$?

Accepted Answer

$$\sqrt{89}$$

Question 6

If $$f(x) = 2x^2$ - 3x + 1$$, what is $$f(-2)$$?

Accepted Answer

$$15$$

Question 7

Which of the following equations represents a circle with center $$(3, -2)$$ and radius $$5$$?

Accepted Answer

$$(x - 3)^2$ + (y + 2)^2$ = 25$$

Question 8

Which of the following is the correct solution to $$|2x - 1| = 7$$?

Accepted Answer

$$x = 4 or$$ $$x = -3$$

Question 9

A car travels at a constant speed and covers 180 miles in 3 hours. What is the equation relating distance $$d$$ and time $$t$$ for this car?

Accepted Answer

$$d = 60t$$

Question 10

Which of the following is the correct midpoint of the segment joining $$(1, 4)$$ and $$(5, 12)$$?

Accepted Answer

$$(3, 8)$$

Question 11

Which of the following is the correct equation of a line passing through $$(2, 5)$$ with slope $$-3$$?

Accepted Answer

$$y - 5 = -3(x - 2)$$

Question 12

Which of the following is the correct solution to the radical equation $$\sqrt{x + 5} = 4$$?

Accepted Answer

$$x = 11$$

Question 13

If $$f(x) = x^2$ - 4x + 7$$, what is the vertex of the parabola?

Accepted Answer

$$(2, 3)$$

Question 14

Which of the following is the correct form for a function that is even?

Accepted Answer

$$f(-x) = f(x)$$

Question 15

Which of the following is the correct equation for a line with $$y-$$intercept $$-2$$ and passing through $$(4, 6)$$?

Accepted Answer

$$y = 2x - 2$$

Question 16

Which of the following is the correct solution to the inequality $$x^2 - 4$$ \u003c 0$$?

Accepted Answer

$$-2 \u003c x \u003c 2$$

Question 17

Which of the following is the correct equation for a circle with diameter endpoints $$(0, 0)$$ and $$(6, 8)$$?

Accepted Answer

$$(x - 3)^2$ + (y - 4)^2$ = 25$$

Question 18

Which of the following is the correct solution to the equation $$x^2 + 4x + 8 = 0$ in the complex number system?

Accepted Answer

$$x = -2 \pm 2i$$

Question 19

Which of the following is the correct equation for a function that is odd?

Accepted Answer

$$f(-x) = -f(x)$$

Question 20

A company’s profit $$P (in $$thousands of dollars) is modeled by $$P(x) = -2x^2$ + 12x - 9$$, where $$x is $$the number of units sold (in thousands). What is the maximum profit, and for how many units sold does it occur?

Accepted Answer

Maximum profit is $$27$$ thousand dollars at $$x = 3$$ thousand units

Precalculus Study Guide: Suggested Exercises Overview

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