Algebra II and Trigonometry

Take Home Final Examination Parts 1 & 2

Directions

Type of Examination: Closed text, open notes. Do your own work. Do not help your classmates. Do not even discuss the examinations with one another until after all of you have mailed your answer-sheets to Mr. Heath. Please report any infractions to our Honor Code to Mr. Heath or Mr. Jones! If you have any difficulty with the examination, check your notebook. Your text is not to be used and would be of little help anyway! If you have not done so already, this examination will help you learn to take and use excellent notes!

Time Suspense

1. Part 1 is due in two weeks, i.e., 18 May 2006
2. Part 2, to be provided before 05 May 2006 will be due a fortnight {two weeks} after it is posted on the PACE website.

Submission Instructions

Complete your examination and mail it to your Lead Instructor at the following address:

Mr. Ernest Alfred Heath Jr.
PACE Algebra 2 Lead Instructor
Pleasure Bay Drive, No. 242
Long Branch, NJ 07740

If you have not handed in your algebra 2 book, send the instructor a letter explaining how you propose to return it, or bring it to the Monmouth County Cotillion {Scholarship Debutante Ball} <06 May '06> or the PACE Banquet <13 May '06>.

Questions

Solve the following problems. Each problem is worth 10 points. No partial credit will be given.

Recommendation: first try timing yourself. Then go over your initial answers carefully to determine where you need further study. Try to complete every problem. You have to score 100% of the normal question to have the opportunity to receive extra credit, so do not waste your time on the extra credit problems unless you have already answered all of the others correctly!

Check your work, check it again, then check it again!

0. 8^4x-1 = 6^1-x, solve for x.

1. x⁶ + 2x³ + 2 = 0

2. 2x⁸ - 4x⁴ + 5 = 0

3. 3 + 2/x² - 4/x⁴ = 0

4. 12x² - 5x - 7 > 0

5. 2x² - 9x - 5 < 0

6. x³ -5x² - 6x > 0

7. Solve the linear system of equations

1x - 2y - 3z = 2
-1x + 4y + 13z = - 4
3x - 5y - 4z = -2

8. Solve the linear system of equations (inequalities for extra credit)

1x - 1y + 1z = (≥) 3
1x + 1y - 1z = (≥) 1
-1z + 1y + 1z = (≤) 7

9. Solve the linear system of equations (inequalities for extra credit)

1/x + 1/y + 0/z = (≤) 5/2
0/x + 1/y + 1/z = (≥) 3
1/x + 0/y + 1/z = (≤) 3/2

10. Solve for x:

12^u = 9^v, where u = 9x² - 1, and v = (1-x)²

Good Luck!

It was an honor to be your Algebra 2 Instructor,

Mr. Ernest

Part 2

----------------PACE-Monmouth at Brookdale Communiversity Algebra 2 Final Examination Part II Starts Here----------

0. 4x⁸ - 4x⁴ + 5 = 0

1. | 1x⁴ + 11x² + 2 | <= 5

2. | 3x⁶ + 18x³ + 2 | <= 5

3. | 3x² + 20x + 2| > 4

4. Find the solution set for this simple system of two simultaneous quadratic inequalities:

3x² + 16x + 1 <= 10

1x² + 10x + 2 >= 05

3. Find the solution set for this simple system of two simultaneous cubic inequalities:

x³ - 15 >= 12

x³ + 14 <= -50

4. Find the solution set for this simple system of simultaneous quadric and hexic inequalities:

x⁴ - x² - 1 <= +1

x⁶ + x³ - 1 >= +1

5. Solve this simple system of four simultaneous linear equations in four unknowns

+1x - 3y + 5z - 7t = +1

+3x + 2y + 7z + 4t = +4

+5x - 7y - 1z - 2t = +3

+7x - 4y - 2z + 2t = +2

6. Solve this simple system of two trigonometric linear equations for the angle A, or the sin(A) or the cos(A). {Please note: if x0 = sin(A0) then A0 = Sin^-1(x0) = Arcsin(x0), and similarly, if if y0 = cos(A0) then A0 = Cos^-1(x0) = Arccos(x0)} [Hint: Avoid distractions}

TVcos(A) + (MAL²)sin(A) = U-PROB-FAIL

(DRINK)cos(A) + (DRUGS)sin(A) = exp(U-DEF-FAIL),

Where TV, MAL2, U-PROB-FAIL, DRINK, DRUGS, U-DEF-FAIL are all real constants. [Hint: substitute simple letters for TV, MAL2, U-PROB-FAIL, DRINK, DRUGS, and exp(U-DEF-FAIL); say a, b, c, d, e, and f; solve the system and then use your answers to substitute back to get your final answer. Perhaps you can use this to show your younger brothers, sisters, and friends how algebra and trigonometry can work together.

7. Divide (9x⁸ + 7x⁶ + 4x⁴ + 2x² + 1) by:

a. x⁴ - x² + 1
b. x³ - x + 1
c. x_² - x + 1

8. Divide (4⁶ + 12x⁵ + 6x⁴ + 3x³ + 2x² + 1x + 1) by:

a. x² - 2x + 5
b. x³ - 6x_² + 3
c. x⁴ - x + 3

9. Divide (x⁸ - x⁷ + x⁶ - x⁵ + x⁴ - x³ + x² - x + 1) by:

a. x⁴ - x² + 1
b. x - 1
c. x + 1

----------------PACE-Monmouth at Brookdale Communiversity Algebra 2 Final Examination Part II Ends Here----------

Students:

Please have a wonderful summer and come back safe and sound! For those interested in studying mathematics this summer (again - its free, the only charges will be for your supplies, time, and attention), either on an independent basis, or as a small seminar of interested future engineers and scientists, we can cover some or all the following this summer:

1*. Solid Geometry

2*. Linear Algebra

3*. Algebra of Groups, Rings, and Fields

4*. Fun with Topology & Geometry

5*. Introductory Probability & Statistics

6*. Trigonometry, Pre-Calculus, Calculus Primers

7*. SAT Math, SAT Math II, and ACT's Math preparation

8*. Consider Kaplan or Princeton SAT/ACT preparation classes

9*. Preparation for the High School Putnam Mathematics

Examination

Call, mech-mail or e-mail me with your requests ASAP.

Ernest Alfred Heath Jr.
Lead Algebra 2 Instructor
PACE at Brookdale Communiversity
Systems and Software Engineering Supervisor
L3 Communications -- ILEX Systems, Inc.
Defense Systems Services Division
Office: 732_380_9400 x3462
Mobile: 732_768_1187
Corporate: <mailto:Ernest.Heath@L-3Com.com> Ernest.Heath@L-3Com.com
Military: <mailto:Ernest.Heath@US.Army.mil> Ernest.Heath@US.Army.mil