College Algebra

Exam File - Spring 2000

 

Exam #1

1.)        For the following questions, consider this chart from USA Today.

a.)        What percentage of those questioned drink less than two servings per day of milk?

b.)        If you were to draw a pie chart to illustrate this data, what would the angle be for the portion representing those who consume two servings a day?

 

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

1.1

1.4

2.2

3.4

3.7

y

8.2

9.1

9.8

11.4

12.2

            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?

xmin

 

xmax

 

xscl

 

ymin

 

ymax

 

yscl

 

5.)        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.

6.)        Suppose the graph shown is the graph of f(x).  On the same set of axes, show the graph of    -2f(x-3) + 1.

 

 

 

 

 

 

 

7.)        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.

 

8.)        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?

 

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

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

a.)        Find the local maximum.

b.)        Find the local minimum.

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

a.)        Graph the line.

            b.)        Find the x-intercept.

            c.)        Find the y-intercept.

12.)     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.

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

14.)     Find the domain of the function

15.)     Who invented the  pie chart?

 

Test #2

 

1.)        Consider the following table of values.

x

14

17

19

21

22

y

43

68

78

70

55

            Find an equation for the quadratic function that best fits this data.

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

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

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

3.)        In a basketball game, the Bulls scored 103 points and made three times as many field goals (2 points each) as free throws (1 point each).  They also made eleven 3 point baskets.  The coach wondered how many field goals they scored.

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

problem.

            b.)        Use the equation in part a.) to find out how many field goals they had.

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

            x3 + 3.2x2 - 7.25x - 6.3 = 0

5.)        Solve each of the following equations EXACTLY!!

            a.)        |3x - 2| = 11                                        b.)        x2 + x - 1 = 3

            c.)                                          d.)       

6.)        Solve each of the following inequalities.

            a.)        -3x - 5 > 4

            b.)        x2 + 2x - 8 £ 0

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

8.)        Given the following table of values, find the third degree function that best fits the

            data.

x

11

13

15

16

17

19

22

24

y

8

9

13

12

8

7

11

12

 

Test #3

 

1.)        Is f(x) = 2x + 3  a one-to-one function?  Give a reason for your answer.

2.)        Find the inverse of the function f(x) = 3 - 4x.

3.)        Write 6 log b2 + 5 log(b) - 3 log b as a single logarithmic expression.

For #4 - 6, use logb 2 = .2173, logb 3 = .3527 and logb 5 = .4187 to find the given quantities.

4.)        logb 2/3                       5.)        logb 20                        6.)        log3 2

In #7 - 10, solve the given equation exactly.

7.)        4x = 8              8.)        52x = 70                      9.)        log2 x + log2 (x - 4) = 2

10.)     log(log x) = 3

11.)     Suppose you invest $8000 at an interest rate of 8 percent compounded quarterly.

a.)        Find the balance after 4 years.

b.)        How long do you need to leave the money for it to double?

12.)     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?