Question 1

Find the equation of the line passing through the point $$(2,5)$$ and with a slope of $$-2.$$

Accepted Answer

$$y = -2x + 9$$

Question 2

Solve for $$x in $$the equation $$\frac{1}{x} = 3.$$

Accepted Answer

Question 3

A chemist has two containers of saline solution. One is $$40\%$$ saline and the other is $$12\%$$ saline. How many liters of each should be mixed to obtain $$30$$ liters of a $$30\%$$ saline solution?

Accepted Answer

$$20$$ liters of $$40\%$$ and $$10$$ liters of $$12\%$$

Question 4

Which of the following is the correct factorization of $$2x^2 + 5x - 3$?

Accepted Answer

$$(2x - 1)(x + 3)$$

Question 5

Given the function $$f(x) = |x|$$, which of the following graphs best represents it?

Accepted Answer

A V-shaped graph opening upwards with vertex at the origin

Question 6

Find the local maximum of the function $$f(x) = -x^2$ + 4x + 1.$$

Accepted Answer

$$f(2) = 5$$

Question 7

A farmer is building three pens to hold his three horses. He has $$200$$ feet of fencing and wants to maximize the area. If the pens are arranged in a row, what should be the dimensions of each pen?

Accepted Answer

$$25 ft by$$ $$16.67 ft$

Question 8

Which of the following is equivalent to $$\log_2$ 8$$?

Accepted Answer

$$3$$

Question 9

Simplify the expression $$\log_5$ 25.$$

Accepted Answer

$$2$$

Question 10

If $$\log_a b = 2$$ and $$\log_a c = 3$$, what is $$\log_a (b^2$ c)$$?

Accepted Answer

$$7$$

Question 11

Which of the following is the solution to $$2x^2 - 5x + 2 = 0$?

Accepted Answer

$$x = 2, x = \frac{1}{2}$$

Question 12

A rope is tied between two trees $$11$$ feet apart, and the rope hangs down $$4$$ feet at the center. What is the length of the rope, rounded to three decimal places?

Accepted Answer

$$12.083 ft$$

Question 13

Which of the following is the correct logarithmic form of $$a^x = b$$?

Accepted Answer

$$x = \log_a b$$

Question 14

Find the intersection point of the circle $$x^2$$ + $$y^2 = 25$ and the line y = 2x$.

Accepted Answer

$$(3, 6)$$ and $$(-3, -6)$$

Question 15

Which of the following is the sum of the series $$\sum_{k=1}^4 (2k+1)$$?

Accepted Answer

$$20$$

Question 16

Given $$f(x) = x^2$ - 4x + 3$$, what is the vertex of the parabola?

Accepted Answer

$$(2, -1)$$

Question 17

Which of the following is equivalent to $$\log_3$ 81$$?

Accepted Answer

$$4$$

Question 18

If $$f(x) = 2x^2$ + 3x - 5$$, what is $$f(-2)$$?

Accepted Answer

$$-7$$

Question 19

Which of the following is the correct simplification of $$\frac{2x^2$ - 8}{x - 2}$$ for $$x 
eq 2$$?

Accepted Answer

$$2(x + 2)$$

Question 20

Given $$f(x) = \sqrt{x-1}$$, what is the domain of $$f$$?

Accepted Answer

$$x \geq 1$$

Precalculus Review Problems: Lines, Functions, Graphs, and Logarithms

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