Question 1

Solve the inequality. ​   ​

Accepted Answer

A)  x  18 
C)  x > -18 
D)  x  14 
A)  x  18 
C)  x > -18 
D)  x  14

Question 2

The retirement plan for Pennsylvania state employees is based on the following formula: "2.5% of average final compensation multiplied by years of credited service" (Source: Pennsylvania State Employees Retirement System, 2001). Let p represent annual retirement pension and y denote the years of service. For someone with average final compensation of $70,000, write the linear equation that gives p in terms of y. ​

Accepted Answer

A)    
B)    
C)  ​   
D)    
E)    
A)    
B)    
C)  ​   
D)    
E)

Question 3

The equation in this problem leads to a linear equation. Solve for x. Because the solution to the linear equation may not be a solution to the original equation, be sure to check the solution in the original equation. ​   ​

Accepted Answer

A)  x = 2 
B)  x = -2 
C)  x = 4 
D)  x = 6 
E)  x =   
A)  x = 2 
B)  x = -2 
C)  x = 4 
D)  x = 6 
E)  x =

Question 4

Solve the system of equations by using graphical methods. ​
​   ​

Accepted Answer

A)  (2,5) 
B)  (-2,-5) 
C)  (5,-2 
D)  (-5,5) 
E)  There are infinitely many solutions to the equations. 
A)  (2,5) 
B)  (-2,-5) 
C)  (5,-2 
D)  (-5,5) 
E)  There are infinitely many solutions to the equations.

Question 5

In wildlife management, the capture-mark-recapture technique is used to estimate the populations of fish or birds in an area or to measure the infestation of insects such as Japanese beetles. Suppose 100 individuals of the species being studied are caught, marked, and released, and one week later 100 more are caught. To estimate the total number of individuals, the following relationship is used: ​   ​
Suppose that 1000 beetles are captured, marked, and released. Suppose further that in the second capture of 1000 it is found that 61 are marked. What is the population estimate?
​

Accepted Answer

A)  61,000 
B)  269 
C)  61 
D)  16,393 
E)  3,721 
A)  61,000 
B)  269 
C)  61 
D)  16,393 
E)  3,721

Question 6

If   , find   . ​

Accepted Answer

A)  3 
B)  15 
C)  27 
D)  -3 
E)  45 
A)  3 
B)  15 
C)  27 
D)  -3 
E)  45

Question 7

A biologist has a 40% solution and a 10% solution of the same plant nutrient. How many cubic centimeters of each solution should be mixed to obtain 40 cc of a 25% solution? ​

Accepted Answer

A)  The biologist should mix 30 cc of 40% solution with 10 cc of 10% solution. 
B)  The biologist should mix 20 cc of 40% solution with 20 cc of 10% solution. 
C)  The biologist should mix 5 cc of 40% solution with 35 cc of 10% solution. 
D)  The biologist should mix 10 cc of 40% solution with 30 cc of 10% solution. 
E)  The biologist should mix 15 cc of 40% solution with 25 cc of 10% solution. 
A)  The biologist should mix 30 cc of 40% solution with 10 cc of 10% solution. 
B)  The biologist should mix 20 cc of 40% solution with 20 cc of 10% solution. 
C)  The biologist should mix 5 cc of 40% solution with 35 cc of 10% solution. 
D)  The biologist should mix 10 cc of 40% solution with 30 cc of 10% solution. 
E)  The biologist should mix 15 cc of 40% solution with 25 cc of 10% solution.

Question 8

Solve the equation. ​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 9

Let   . Find   . ​

Accepted Answer

A)    
B)  ​   
C)  ​   
D)    
E)    
A)    
B)  ​   
C)  ​   
D)    
E)

Question 10

​Use a graphing utility with the specified range to graph the equation. Is the graph below the graph of the given equation? ​     ​
​​   ​

Accepted Answer

A) True 
 B)False

Question 11

Data from 2003 for various groups shows that for each $100 increase in the median weekly income for whites, the median weekly income of blacks increases by $60.4. When the median weekly income for whites was $665 and for blacks was $517. Let W represent the median weekly income for whites and B the median weekly income for blacks, and write the equation of the line that gives B as a linear function of W. ​

Accepted Answer

A)    
B)  ​   
C)    
D)    
E)    
A)    
B)  ​   
C)    
D)    
E)

Question 12

If   , find   . ​

Accepted Answer

A)    
B)    
C)    
D)    
E)  ​   
A)    
B)    
C)    
D)    
E)  ​

Question 13

​Graph the equation with a standard window   and   on a graphing utility. Does the graph appear to be a linear function? ​
​   ​
​

Accepted Answer

A) True 
 B)False

Question 14

Solve the system by elimination, or by any convenient method. ​   ​

Accepted Answer

A)  ​   and   
B)  ​   and   
C)  ​​   and   
D)  There are infinitely many solutions. 
E)  There is no solution. 
A)  ​   and   
B)  ​   and   
C)  ​​   and   
D)  There are infinitely many solutions. 
E)  There is no solution.

Question 15

A glass of skim milk supplies 0.1 mg of iron, 8.5 g of protein, and 1 g of carbohydrates. A quarter pound of lean red meat provides 3.4 mg of iron, 22 g of protein, and 20 g of carbohydrates. Two slices of whole grain bread supply 2.2 mg of iron, 10 g of protein, and 12 g of carbohydrates. If a person on a special diet must have 9.1 mg of iron, 62.5 g of protein, and 53 g of carbohydrates, how many glasses of skim milk, how many quarter-pound servings of meat, and how many two-slice servings of whole grain bread will supply this? ​

Accepted Answer

A)  The requirements will be met with 1 glass of milk, 2 servings of meat and 1 serving of bread. 
B)  The requirements will be met with 4 glasses of milk, 1 serving of meat and 5 servings of bread. 
C)  The requirements will be met with 5 glasses of milk, 2 servings of meat and 1 serving of bread. 
D)  The requirements will be met with 3 glasses of milk, 2 servings of meat and 4 servings of bread. 
E)  The requirements will be met with 2 glasses of milk, 1 serving of meat and 5 servings of bread. 
A)  The requirements will be met with 1 glass of milk, 2 servings of meat and 1 serving of bread. 
B)  The requirements will be met with 4 glasses of milk, 1 serving of meat and 5 servings of bread. 
C)  The requirements will be met with 5 glasses of milk, 2 servings of meat and 1 serving of bread. 
D)  The requirements will be met with 3 glasses of milk, 2 servings of meat and 4 servings of bread. 
E)  The requirements will be met with 2 glasses of milk, 1 serving of meat and 5 servings of bread.

Question 16

If   and   , find   and simplify. ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 17

Solve the inequality and choose the graph of the solution. ​   ​

Accepted Answer

A)  ​   ​ 
B)  ​   ​ 
C)  ​   ​ 
D)  ​   ​ 
E)  ​   ​ 
A)  ​   ​ 
B)  ​   ​ 
C)  ​   ​ 
D)  ​   ​ 
E)  ​   ​

Question 18

For   and   , find   . ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 19

If   , find   . ​

Accepted Answer

A)  39 
B)  -15 
C)  45 
D)  -3 
E)  -21 
A)  39 
B)  -15 
C)  45 
D)  -3 
E)  -21

Question 20

Write the equation and graph the line that passes through the given point and has the slope indicated. ​
​(4,-2) with slope 2
​

Accepted Answer

A)  ​     
B)  ​  
​   
C)      
D)      
E)    ​   
A)  ​     
B)  ​  
​   
C)      
D)      
E)    ​

Solve the inequality.

The equation in this problem leads to a linear equation. Solve for x. Because the solution to the linear equation may not be a solution to the original equation, be sure to check the solution in the original equation.

Solve the system of equations by using graphical methods.

If , find .

A biologist has a 40% solution and a 10% solution of the same plant nutrient. How many cubic centimeters of each solution should be mixed to obtain 40 cc of a 25% solution?

Solve the equation.

Let . Find .

Use a graphing utility with the specified range to graph the equation. Is the graph below the graph of the given equation?

If , find .

Graph the equation with a standard window and on a graphing utility. Does the graph appear to be a linear function?

Solve the system by elimination, or by any convenient method.

If and , find and simplify.

Solve the inequality and choose the graph of the solution.

For and , find .

If , find .

Write the equation and graph the line that passes through the given point and has the slope indicated. (4,-2) with slope 2

Quadratic and Other Special Functions

Matrices

Inequalities and Linear Programming

Exponential and Logarithmic Functions

Mathematics of Finance

Introduction to Probability

Further Topics in Probability and Data Description

Derivatives

Derivatives

Derivatives Continued

Indefinite Integrals

Definite Integrals - Techniques

A: Definite Integrals - Techniques

Functions of Two or More Variables

Algebraic Concepts 2

Algebraic Concepts 3

Algebraic Concepts 4

Algebraic Concepts 5

Filters

Exam 1: Linear Equations and Functions

Solve the inequality. ​ ​

The equation in this problem leads to a linear equation. Solve for x. Because the solution to the linear equation may not be a solution to the original equation, be sure to check the solution in the original equation. ​ ​

Solve the system of equations by using graphical methods. ​ ​ ​

If , find . ​

A biologist has a 40% solution and a 10% solution of the same plant nutrient. How many cubic centimeters of each solution should be mixed to obtain 40 cc of a 25% solution? ​

Solve the equation. ​ ​

Let . Find . ​

​Use a graphing utility with the specified range to graph the equation. Is the graph below the graph of the given equation? ​ ​ ​​ ​

If , find . ​

​Graph the equation with a standard window and on a graphing utility. Does the graph appear to be a linear function? ​ ​ ​ ​

Solve the system by elimination, or by any convenient method. ​ ​

If and , find and simplify. ​

Solve the inequality and choose the graph of the solution. ​ ​

For and , find . ​

If , find . ​

Write the equation and graph the line that passes through the given point and has the slope indicated. ​ ​(4,-2) with slope 2 ​

Quadratic and Other Special Functions

Matrices

Inequalities and Linear Programming

Exponential and Logarithmic Functions

Mathematics of Finance

Introduction to Probability

Further Topics in Probability and Data Description

Derivatives

Derivatives

Derivatives Continued

Indefinite Integrals

Definite Integrals - Techniques

A: Definite Integrals - Techniques

Functions of Two or More Variables

Algebraic Concepts 2

Algebraic Concepts 3

Algebraic Concepts 4

Algebraic Concepts 5

Filters

Solve the inequality.

The equation in this problem leads to a linear equation. Solve for x. Because the solution to the linear equation may not be a solution to the original equation, be sure to check the solution in the original equation.

Solve the system of equations by using graphical methods.

If , find .

A biologist has a 40% solution and a 10% solution of the same plant nutrient. How many cubic centimeters of each solution should be mixed to obtain 40 cc of a 25% solution?

Solve the equation.

Let . Find .

Use a graphing utility with the specified range to graph the equation. Is the graph below the graph of the given equation?

If , find .

Graph the equation with a standard window and on a graphing utility. Does the graph appear to be a linear function?

Solve the system by elimination, or by any convenient method.

If and , find and simplify.

Solve the inequality and choose the graph of the solution.

For and , find .

If , find .

Write the equation and graph the line that passes through the given point and has the slope indicated. (4,-2) with slope 2