College Algebra Test File
Fall 99
Exam #1
1.) Consider the following table of values.
|
x |
14 |
17 |
19 |
21 |
22 |
|
y |
103 |
88 |
68 |
70 |
55 |
a.) Find an equation for the linear regression line for this data.
b.) Find the correlation coefficient.
c.) Does the line fit the data well? Why or why not?
d.) What window settings would you use for a scatter plot of this data?
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xmin |
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xmax |
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xscl |
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ymin |
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ymax |
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yscl |
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2.) Find an equation of the line that passes through the points (4, 2) and (8, -1).
3.) Find an equation of the line that passes through the point (4, 2) and is perpendicular to the line
x + y = 1.
4.) Consider the function f(x) = (x - 1)(x - 2)(x + 2).
a.) Draw the graph of the function in the following zstandard window.
b.) Find the point at which the local maximum occurs.
c.) Find the point at which the local minimum occurs.
5.) Find the following for the circle x2 + y2 + 4x - 8y + 4 = 0.
a.) center b.) radius c.) graph
6.) Graph the following function.
7.) Consider the function f(x) = 2x2 - 3x + 1. Find the following.
a.) f(2) b.) f(a + 3) c.) f(x2)
8.) a.) Suppose y varies directly as x. If y = 3, when x = 9, find y when x = 4.
b.) Suppose y varies jointly with x and the inverse of z. If y = 3, when x = 9 and z = 6, find y when x = 4 and z = 2.
9.) Consider the points (4, -1) and (-5, -8).
a.) Find the distance between the points.
b.) Find the midpoint of the line segment connecting the two points.
10.) Consider the following pie chart.
a.) What is the angle of the portion representing food?
b.) What is the total percentage spent on food and rent?
Exam #2
1.) Suppose the graph in the left hand grid is f(x). On the right hand grid, graph
-f(x-3).
2.) Suppose f(x) = 2x - 3 and g(x) = x2 - x.
a.) Find (f + g)(3).
b.) Find the domain of 
c.) Find (f
3.) 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). Fill in the blanks in the list below giving the settings for your graph.
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x min |
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x max |
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y min |
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y max |
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c.) For what value of x is the area largest?
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.) 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 #3
1.) Let f(x) = 3x2 + 2x - 1. Find the vertex and all intercepts. Graph the function.
2.) Is f(x) = |2x| a one-to-one function? Give a reason for your answer.
3.) Find the inverse of the function f(x) = 3x - 1.
4.) Write 6 log b1/2 + (1/5) log(1/b) - 2 log b as a single logarithmic expression.
For #5 - 7, use logb 2 = .2173, logb 3 = .3527 and logb 5 = .4187 to find the given quantities.
5.) logb 2/3
6.) logb 20
7.) log3 2
In #8 - 11, solve the given equation.
8.) 49x = 343
9.) 52x = 70
10.) log2 x + log2 (x - 4) = 2
11.) log(log x) = 1
12.) Suppose you invest $8000 at an interest rate of 8 percent compounded monthly.
a.) Find the balance after 4 years.
b.) How long do you need to leave the money for it to double?
13.) Given the following table of values, find the quadratic function that best fits the data.
|
x |
11 |
13 |
15 |
16 |
17 |
19 |
22 |
24 |
|
y |
8 |
5 |
3 |
2 |
4 |
7 |
11 |
12 |
Test #4
1.) 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 3 days?
b.) When will the colony have a population of 10,000?
2.) 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 |
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1987 |
$11,260 |
|
1988 |
$11,733 |
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1989 |
$12,424 |
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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 2020 if the data continues to fit this curve?
3.) Solve the following system of equations. Do not use your calculator.
3x – 6y = 2
5x + 4y = 1
4.) Solve the following system of equations. Do not use your calculator.
x – 2y + 3z = 7
2x + y + z = 4
-3x + 2y – 2z = -10
5.) 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
6.) Solve the following system of equations.
x2 + y2 = 10
xy = 3
7.) 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?
8.) The half-life of radium is 1690 years. If 10 grams are present now, how much will be present in 50 years?
Final
See the department web page for the final exam.