Question 1

A line passes through the points $$A(4, -10)$$ and $$B(-8, -12). $$What is the slope of the line?

Accepted Answer

Question 2

Given the function $$f(x) = 2x^2$ - x + 5$$, what is $$f(-1)$$?

Accepted Answer

Question 3

Find the equation of the line parallel to $$2x + 3y = -6$$ and passing through the point $$(-1, 3).$$

Accepted Answer

$$2x + 3y = 7$$

Question 4

The weight $$W of an $$object varies inversely as the square of the distance $$d$$ from the center of the Earth. At sea level ($$d = 3978$$ miles), an astronaut weighs $$220$$ pounds. What is the astronaut's weight when he is $$200$$ miles above the surface?

Accepted Answer

$$W = 220 \left(\frac{3978^2$}{4178^2$}\right)$$ lbs

Question 5

Find the $$x-$$intercepts of $$5x - 2y = 10.$$

Accepted Answer

$$(2, 0)$$

Question 6

Solve the inequality $$2x - 1 \geq 5$$ and express the solution in interval notation.

Accepted Answer

$$[3, \infty)$$

Question 7

A boat moves at a rate of $$11 mi/h in $$still water. If the river current flows at a rate of $$5 mi/h$$, how long does it take for the boat to travel $$33$$ miles upstream?

Accepted Answer

$$3$$ hours

Question 8

Given $$m(x) = x^3$ - 5x$$, find and simplify the difference quotient $$\frac{m(x+h) - m(x)}{h}.$$

Accepted Answer

$$3x^2 + 3xh$$ + $$h^2 - 5$

Question 9

Given the quadratic equation $$y = 5x^2$ - 10x + 7$$, what is the axis of symmetry?

Accepted Answer

$$x = 2$$

Question 10

Find the domain of the function $$f(x) = \frac{2}{x-4}.$$

Accepted Answer

$$x 
eq 4$$

Question 11

If the minimum wage was $$3.10 in 1980 and 5.15 in 2006$$, what was the average rate of change in the minimum wage from 1980 to 2006?

Accepted Answer

$$0.08$$ per year

Question 12

Given $$g(x) = x^2$ - 2x + 3$$, find the remainder when $$g(x) is $$divided by $$x + 2.$$

Accepted Answer

$$7$$

Question 13

A rectangular box with a square piece of sheet metal, requires a square of side $$7$$ centimeters. Turn up the edges to form an open box. If the box is to hold $$112$$ cubic centimeters, what should be the dimensions of the piece of sheet metal?

Accepted Answer

$$7 	imes 7 cm$$

Question 14

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

Accepted Answer

$$x \geq 3$$

Question 15

Find the $$y-$$intercept of the line $$5x - 2y = 10.$$

Accepted Answer

$$(0, -5)$$

Question 16

Given $$f(x) = x^2$ + 3x + 1$$, find $$f(-2).$$

Accepted Answer

$$-1$$

Question 17

Given the function $$h(x) = \sqrt{4 - x}$$, what is the domain of $$h$$?

Accepted Answer

$$x \leq 4$$

Question 18

A parabola has a vertex at the point $$(3, 4)$$ and passes through the point $$(-1, 7). $$What is its equation in vertex form?

Accepted Answer

$$y = a(x - 3)^2$ + 4$$, where $$a = \frac{7 - 4}{(-1 - 3)^2$}$$

Question 19

Given $$f(x) = \frac{x^2$ + 3x + 1}{4x^2$ + 9}$$, find all vertical asymptotes.

Accepted Answer

No vertical asymptotes

Precalculus Midterm Exam Review: Key Concepts and Practice Problems

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