sampletests_collegealgebra

8/2/2019 SampleTests_CollegeAlgebra

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College AlgebraSample Test #1

Solve the following equations:

1. 2x + 1 = 4x - 3 2.

3. 4.

Solve 3 of the following 4 quadratic Equations:

5.

6. , by using Square root property

7.

8.

Problems 10-11: Find the center and radius of each circle AND sketch.

9

10. ,you must complete the square first

Problems 12 - 13 Graph the following Lines:

11. 4x - 5y = 20 12.

Problems 13-16 Solve the following:

13. Find the slope of the line passing through: (-3,6) and (5, -4)

14. Find the slope of the line: 3x - 5y = 10

15. Find the equation of the line that passes through (2,3) and is perpendicular to the

equation : .

16. Find the distance and midpoint between the points (6,3) and (10,6).


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Problems 17-20: Solve ,graph on a Number Line AND write solution using Interval Notation:

17. 4x + 1 < 2x - 5 18. -6 < 4 + 2x < 10

19. 21.

Problem 21: Use Long Division to divide :

21.


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College AlgebraSample Test #2

Determine if each equation defines y as a function of x and state the family to it belongs to:

1. x2+ y2 = 25 2. y = x3 - 3x2 + 2x - 1

3. 3x - 5y = 20 4. y = | x + 2 |

State the domain and range of each relation:

5. y = x2+ 5 6. 7. y = | x - 1|

Problems 8-14:Sketch the graph of each function, andstate the domain and range for each:

8. 3x - 4y = 12 12. y = |x| - 4

9. 13.

10. 14. f(x) = x for x < 0

11. y = 2x - 3 x2 + 3 for x > 0

Problems 15-19: Find the following if: and g(x) = 3x - 1

15. f(7) 16. (f B

g)(2) 17. (f B

g)(x)

18. g-1(x) 19. (f + g)(14)

20. The intensity of the illumination (I) from a light source varies inversely as the square of

the distance (d) from the source. If a flash on a camera has an intensity of 300

candlepower at a distance of 2 meters, then what is the intensity of the flash at a distance

of 10 meters?

Solve 3 of the following 4 problems:

21. Prove if f(x) = x4 - 3x2 + 9 is even, odd or neither. Discuss the symmetry.

22. Graph f(x) = (x - 3)2 State domain, range and where it is increasing and decreasing.23. Jangs Postal Service charges $35 for addressing 200 envelopes, and $60 for 400 of them.

What is the average rate of change of the cost to the number of envelopes?

24. Find the inverse of the function: Draw both f(x) and f -1(x)

on the same graph and state the domain and range of each.


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College Algebra Sample Test #3

1. Find the Vertex, Axis of Symmetry , X&Y Intercepts, Range and graph f(x) = x 2 - 4x - 12

Problems 2 and 3 will come from section 3.4 (Miscellaneous Equations)

2. Solve: |x2 -x - 6 |= 6

3. Solve:

4. Use Descartes Rule of Signs to discuss the possibilities for the roots of: x 3 - 3x2 + 5x + 7

5. Use synthetic division to dividex + 3 intox3 - x2 - 7x + 15. Is -3 a root?. If not, remainder is?

Problems 6 through 8: Find all real and imaginary roots for each function:

6. f(x) = x2 - 9 7. f(x) = 3x3 - 27x2 +60x 8. f(x) = x3 + 4x2 -17x - 60 if4 is a zero.

9. Explain the far left and far right characteristics of each function:

(a) f(x) = x2 - 4x - 9 (b) f(x) = -3x3 - 27x2 +60x (c) f(x) = 2x4 + 7x2 - 6x

10. If f(x) = x 3 - x2 - 9x + 9 and if 1 is a zero,

a) find the other 2 zeros by factoring

b) find the y intercept (x = 0)

c) Find key points: x between two zeros , and calculate its y-value to help graph moreprecisely.

Problems 11 through 13: Graph each function precisely as you did in #10:

11. y = (x - 3)2 12. y = (x - 2)2(x + 1) 13. y = x3 - 4x


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College Algebra Sample Test #4

1. (a) Write log 7x = 2 in exponential.

(b) Write in logarithmic form.

2. Write y + 3 = e 2x in logarithmic form.

3. Write as multiple logarithms of logbx, log by and log bz .

4. Write 5 log 3 x - 4 log 3 y + 2 log 3 z as a single log .

5. Solve for x:

6. Solve for x:

7. Graph:

8. Graph:

9. Graph:

10. Solve the system of equations by the elimination method: 3x - y = 10

4x + 3y = - 4

11. Solve the system of equations by the substitution method: y = 2x + 4

8x - 4y = 7


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Solve the following Word Problems:

12. A sporting goods salesmen sells 2 basketballs and 5 fishing poles for $270. The next day

he sells 4 basketballs and 2 fishing poles for $220. How much does one of each cost?

13. Based on data from the year 2000, the rodent population in a specific field grew

according to the function: P(t) = (500)e . 3662 t

(A) What was the expected population if t = 3.5 ?

(B) What is the current expected population (year 2005)?

(C) In what year will the population reach 4,500?

14. If $32,000 is invested at an annual rate of 8% for 3 years, find the amount in the accountif it is:

A) Compounded quarterly. Use:

B) Compounded continuously. Use:

C) How long would it take for your account to have $960,000 in it if you invested the$32,000 in an 8% account that is compounded monthly? Use (A) formula.


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College Algebra Final Exam Topics

Quadratic Equations

Circles

Inequalities

Parallel Lines

Simple Inequalities

Quadratic Formula

Completing the square

Radical equations

Word problem from Test 2 or Sample Test 2

Distance Formula

Slope-Intercept

Graphing Functions, Domain & Range

Vertex, min, max, domain, range

Composite functions: f(g(x)) and g(f(x))

Inverse functions

Zeros of polynomial functions and their graphs (Synthetic division)

Log and Exponential equations and functions

Population Growth and Compound Interest

Graph Log and ex

Solving systems of equations

Direct Variation Word Problems

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