Question 1

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

Question 2

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

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

Study Guide - Practice Questions

Study Guide - Flashcards