College Algebra

Exam File

Summer 2001

 

 1.)       Alan, Bob, Chuck and Dave sell cars for "Wecheatem Used Cars."  The following chart gives the numbers of cars each man sold in June. 

 

 

Alan

Bob

Chuck

Dave

Cars Sold

37

48

32

3

a.)        Draw a bar chart to represent the data.  Be sure to label both axes.

b.)        If you were to draw a pie chart to illustrate this data, what would be the angle for the portion representing Bob?

2.)        Find an equation for the line that goes through the points (-2, 1) and (4, -3).

3.)        Consider the circle x2 + 4x + y2 - 8y - 5 = 0.

            a.)        Find the center.                                 b.)        Find the radius.

            c.)        Graph the circle.

4.)        Consider the following data.

x

31.1

31.4

32.2

33.4

33.7

y

18.2

19.1

19.8

21.4

22.2

            a.)        Find an equation for the linear regression line for this data.

            b.)        What viewing window would you use to do a scatter plot for this data?

            c.)        Find the correlation coefficient.

            d.)        Does the line fit the data well?  Why or why not?

5.)        Suppose y varies directly as x.  If y = 3, when x = 9, find y when x = 4.

6.)        Consider the points (4, -4) and (3, 8).

a.)        Find the distance between the points.

b.)        Find the midpoint of the line segment between the two points.

7.)        Consider the following scatter plot.

a.)        On the graph, draw the line that best fits the data.  Don't try to use your calculator, just do it by looking and drawing.

b.)        What would you guess is the correlation coefficient, r, for your line?  Is it a good fit?  Why?

 

8.)        Using zstandard, graph f(x) = (x - 1)(x + 1)(x - 2).  Copy the graph below.

9.)        Consider the line given by 2x + 3y - 6 = 0.

a.)        Graph the line.                       b.)        Find the x-intercept.

            c.)        Find the y-intercept.

10.)     Consider the equation x2 - y2 + y = 4.

a.)        Does this graph have symmetry with respect to the x-axis?  Show your work.

b.)        Does this graph have symmetry with respect to the y-axis?  Show your work.

c.)        Does this graph have symmetry with respect to the origin?  Show your work.

11.)     Find an equation for the line on the point (1, 2) and perpendicular to the line      2x + 3y = 6.

12.)     Who invented the  pie chart?

13.)     y varies jointly as x2 and the inverse of z.  If y = 4 when x = 3 and z = 9, find y when x = 9 and z = 3.

 

Exam #2

 

1.)        Consider the function f(x) = 2x2 - 3x + 1.  Find the following and simplify your answers.

            a.)        f(2)

            b.)        f(a + 3)

            c.)        f(x2)

2.)        Suppose f(x) = 2x - 3 and g(x) = x2 - x.

a.)        Find (f + g)(3).

b.)        Find the domain of

c.)        Find (f ° g)(x).

3.)        Suppose f(x) = 3x + 5 and g(x) = 2x2 - 1.

a.)        Find (f - g)(3). b.)        Find (f ° g)(2). c.)        Find (g ° g)(2).

4.)        Find the domain of the function           

5.)        Graph f(x) = 3 (x + 2)2 - 4.                                                    

6.)        Suppose the graph in the left hand grid is f(x).  On the right hand grid, graph

g(x) = -2 f(x-3) + 1.                                                    

 

 

 

 

 

 

 

 

7.)        Use your calculator to find the positive solution for the following equation.

            x3 + 3.2x2 - 7.25x - 6.3 = 0

For #8 - #11, do not use your calculator.        

8.)        Solve the following equation.  2 (3x - 5) + 4 = x.

9.)        Solve the following equation by factoring.   x2 - 5x - 6 = 8

10.)     Solve the following equation by the quadratic formula.  3x2 - x - 7 = 8

11.)     Solve the following quadratic equation using any non-calculator method. 

                        6x2 + 11x - 35 = 0 

12.)     David has 400 yards of fencing and wishes to enclose a rectangular area. 

a.)        Express the area, A, of the rectangle as a function of the width, x, of the rectangle.

            b.)        Using your calculator, graph A(x). 

            c.)        For what value of x is the area largest?  Explain how you got your answer.

13.)     Graph the following function.

           

 

 

14.)     Consider the function f(x) = (x - 3)(x - 2)(x + 1).

a.)        Draw the graph of the function in the a zstandard window.

            b.)        Find the point at which the local maximum occurs.          

            c.)        Find the point at which the local minimum occurs.           

 

Exam #3

1.)        Solve the equation exactly.  5x - 13 = 112

2.)        Solve the equation exactly.  x2 + x - 1 = 3

3.)        Solve the equation exactly. 

4.)        Solve the equation exactly. 

5.)        Let f(x) = 3x2 + 2x - 1.  Find the vertex and all intercepts.  Graph the function.

6.)        Consider the following table of values

x

11

13

15

16

17

19

22

24

y

8

5

3

2

4

7

11

12

            a.)        Find the quadratic function that best fits the data.

b.)        Draw the scatter plot, together with the quadratic function.  Show your xmin, xmax, ymin, ymax.

            c.)        Does the quadratic function fit the data well?  Why or why not?

7.)        Consider the following table of values.

x

14

17

19

21

22

y

43

68

78

70

55

            Use linear regression and quadratic regression to find which does best in fitting the data.  Give the function that you decide does best and tell why you think it is best.

8.)        Consider the following graph.

 

 

            Is this a one-to-one function?  Why or why not?

 

 

 

9.)        Find the inverse function for f(x) = 2x - 5, if one exists.  If it does not exist, find two different x values that show the function is not one-to-one.

10.)     Consider the quadratic function f(x) = 2(x - 4)2 + 3.

a.)        Does this function have a maximum value?  If so, what is it and where does it occur?  If not, why not?

b.)        Does this function have a minimum value?  If so, what is it and where does it occur?  If not, why not?

11.)     Solve the following inequality.                      -3x - 5 > 4

12.)     Solve the equation exactly. 

13.)     David has 400 yards of fencing and wishes to enclose a rectangular area. 

a.)        Express the area, A, of the rectangle as a function of the width, x, of the rectangle.

b.)        Using your calculator, graph A(x).

c.)        For what value of x is the area largest?

14.)     A sugar molecule is made up of hydrogen, oxygen and carbon.  It has twice as many atoms of hydrogen as it does oxygen and one more atom of carbon than oxygen.  The sugar molecule has a total of 45 atoms.

            a.)        Write an equation, in ONE variable, that can be used to solve this

problem.

            b.)        Use the equation in part a.) to find how many of each kind of atom there

are in the molecule.

 

Exam #4

 

1.)        Does f(x) = |2x| have an inverse function?  Give a reason for your answer.

2.)        The formula gives the average atmospheric pressure, , in pounds per square inch, at an altitudemiles above sea level. 

a.)        Find the atmospheric pressure for an altitude for 2.8 miles.   Round your answer to the nearest tenth.

b.)        If the atmospheric pressure around you is 4.6 pounds per square inch, how far above sea level are you?

3.)        In a zstandard window, graph f(x) = log(x + 6) - 4.  Be sure to include the asymptote (as a dotted line) in your graph.

4.)        Use logb 2 = .2173, logb 3 = .3527 and logb 5 = .4187 to find the given quantities.

a.)        logb (2/3)        b.)        logb 20            c.)        log3 2

5.)        Solve the given equation exactly.  83x-1 = 42x+3

6.)        Solve the given equation exactly.  log2 x + log2 (x - 4) = 2

7.)        Suppose you invest $8000 at an interest rate of 8 percent.

a.)        Find the balance after 4 years if the interest is compounded quarterly.

b.)        Find the balance after 4 years if the interest is compounded continuously

8.)        The population of a colony of mosquitoes obeys the law of exponential growth.  Suppose there are 1000 mosquitoes initially and there are 1800 after 1 day

a.)        What is the size of the colony after 2 weeks?

            b.)        When will the colony have a population of 10,000?

9.)        Solve the following system of equations.  Do not use your calculator.

            3x – 6y = 2                                         5x + 4y = 1

10.)     Solve the following system of equations.  You may use your calculator.

                          x – 2y + 3z =    7                  2x +   y +   z =   4           -3x + 2y – 2z = -10

11.)     Solve the following system of equations.  Feel free to use your calculator.

                        x2 + y2 = 10                                                                        xy = 3

12.)     Consider the sequence below.  Find the first 2 terms and the 33rd term.  Is this sequence a geometric sequence, an arithmetic sequence or neither?

                                                                                   

13.)     The half-life of radium is 1690 years.  If 10 grams are present now, how much will be present in 50 years?

14.)     Use your calculator to find both solutions to the equation 2x/6 - log(15x) = 0.

15.)     Given the following table of values, find the logarithmic function that best fits the

            data.

x

11

13

15

16

17

19

22

24

y

8

10

13

14

15

15

16

17

 

Final Exam  

 

1.)        The following chart gives the number of cars sold by Dewey, Cheatem and Howe Used Cars from January to June.  How many cars were sold in April?

 

 

 

 

 

 

 

 

 

 

2.)        Graph the following function.

           

 

 

3.)        Let f(x) = 3x2 + 2x - 1.  Find the vertex and all intercepts.  Graph the function.

 

 

4.)        Solve the following equation exactly.          5x - 23 = 12

5.)        Solve the following equation exactly.          x2 + x - 1 = 3

6.)        Solve the following equation exactly.         

7.)        Solve the following equation exactly.          log3 x + log3 (x - 4) = 2

8.)        Solve the following equation exactly.          52x = 70

9.)        Use your calculator to find the positive solution(s) for the following equation.

            x3 + 7.2x2 - 7.25x - 5.3 = 0

10.)     The following data represents the amount of money an investor has in an investment account each year for 10 years.  She wishes to determine the effective rate of return on her investment.

Year

Value of Account

1985

$10,000

1986

$10,573

1987

$11,260

1988

$11,733

1989

$12,424

1990

$13,269

1991

$13,968

1992

$14,823

1993

$15,297

1994

$16,539

            a.)        Find the exponential function that best fits this data.

b.)        What would the account be worth in the year 2005 if the data continues to fit this curve?

11.)     Suppose f(x) = 3x + 5 and g(x) = x2 - 1. 

a.)        Find f(2).         b.)        Find (f + g)(3).            c.)        Find the domain of

d.)        Find (f ° g)(2). e.)        Find (g ° g)(2).

12.)     Find the domain of the function

13.)     Consider the function f(x) = (x - 1)(x + 1)(x - 2). 

a.)        Find the local maximum.

b.)        Find the local minimum.

14.)     Use your calculator to solve the following system of equations.

                           x +   y  +   z +  w =   4

                          -x + 2y  +   z         =  0

                          2x + 3y +   z –   w =  6

                        -2x +   y  – 2z + 2w = -1

15.)     Find an equation for the line that goes through the points (-2, 1) and (4, -3).

16.)     Write the first three terms of the sequence defined below.

            an = 2n/n!

17.)     Find the value of the following.                                            

18.)     David has 400 yards of fencing and wishes to enclose a rectangular area. 

a.)        Express the area, A, of the rectangle as a function of the width, x, of the rectangle.

b.)        Using your calculator, graph A(x).

c.)        For what value of x is the area largest?

19.)     A movie theater charges $9 for adults and $7 for senior citizens.  On a day when 325 people paid an admission, the total receipts were $2495.  How many who paid were adults?  How many were seniors?

20.)     The half-life of radium is 1690 years.  If 10 grams are present now, how much will be present in 50 years?