# Algebra II and Trigonometry

## Description

### Class Goals

1. To provide the students with the ability to identify, classify, execute and present the solutions to well-posed algebraic problems. Some of the problems will be more difficult than those encountered in Algebra I. Other problems will be multifaceted, sequential or interdependently sequential. Finally, there will be problems which are both more difficult than those in Algebra I and also multifaceted, sequential or interdependently sequential.
2. To provide the students with the ability to excel at the following: abstract and concrete problem solving; converting real world problems into well-posed algebraic problems; reduction of algebraic problems into solvable component sub-problems; classification of problems; profitable approaches for solving classes of problems; choice and staging of solution process (algorithm); execution of solutions; and the presentation of solutions.

### Topics

Algebra:

1. Numbers and their properties
2. Polynomials, rational expressions
4. 1st/2nd degree equation and inequality
5. Word problems
6. Graphing
7. Relations, functions, and graphs
8. Polynomial and rational functions
9. Exponential and logarithmic functions
10. Systems of linear equations and inequalities
11. Matrices and determinants (option)
12. Complex numbers
13. Theory of equations
14. Sequences, series and induction (option)
15. Combinatorics [counting techniques]

Trigonometry:

1. Periodicity, periodic function/relation
2. Circular trig functions, graphs, ratios
3. Basic identities and sums
4. Triangular/circular areas, circumscription, and inscription
5. Inverse trigonometric relations, functions, and graphs
6. Hyperbolic functions, and identities
7. Elementary spherical trigonometry

We also set aside time to work with students on whatever problems they may have with their school work (before class, during the class’ “school work” segment, during break, after PACE, or by voice telephone or e-mail during the week). Mathematics Projects are strongly encouraged. Topics may include: Real/Complex Functions, Discrete/Continuous Statistics, Matrices/ determinants, Sequences/Series, Combinatorics, Differential Equations.

## Final Exam

Algebra II Take Home Final Exam: May 2006

## Assignments: Chapters 6, 7, and 8

PACE-Monmouth Algebra II Assignments: Make a copy of this and keep it for reference in your notebooks.

Here are the assignments for chapters 6, 7, and 8. Our general method for solving algebra problems is provided elsewhere. Please read, study, understand, and use this study method. Do as many problems as you can, but do not hurry, use the method described at the end of this e-letter. Correctness, accuracy, precision, and speed will come with practice.

Chapter 6 Polynomials: Supplementary Exercises

6-20 (a), (b), (c), (e), (f), & (h); 6-22 (b), (d), & (e); 6-23 (a), (c), (d), & (f); 6-24 (a), (c), (d), & (e); 6-25 (b), (d), & (e); 6-26 (a), (c), (e), (f), (g), (h), & (j); 6-27 all; 6-28 (b), (d), (f), (g), (h)*, (i), (j)*, (k), (o), (p), (q), & (r); 6-29 (a), (b), (d), (h), (i), (j), (k), & (l); 6-30 (b), (h), (j), (k), (m), & (n); 6-31 (a), (d), (e), (f), (g), (i), & (k); 6-32 (a), (d), (f), (h), & (j); 6-33 (a), (c), (d), (f), (k), (l), & (n); 6-34 (a), (b), (d), (f)*, (g)*, (h)*, (i)*, (j)*, (k), (m), (n), (o), & (p); 6-35 all

Chapter 7 Factoring Polynomials: Supplementary Exercises

7-12 all; 7-13 (a), (d), (e), (g), (h), (i), (j); 7-14 (a), (b), (c), (d), (g), (j), & (l); 7-15 all; 7-16 (c), (e), (g), (i), (l), (o)*; 7-17 (b), (d), (e), (f), (g), (h), (j), (k), (l), (n), (o); 7-18 (c), (d), (f), (g), (j)*, (k), (m), (n), & (o)

Life is challenging!: the following problems are classed as “challenges” since we have not had the time to cover them in our Saturday classes. If you need help please call me, and leave a question and return call number at 732_530_8444 Extension 3462 – I will get back to you as soon as I am able. So here are the “challenging Problems for my brave students: 7-19 (a), (b), (c), (e), (f), (h), (i), (m); 7-20 (a), (b), (c), (d), (f), (g), (i), (j), (k), (n), & (o); 7-21 all; 7-22 all

Chapter 8 Rational Expressions and Equations: Supplementary Exercises

8-16 all; 8-17 (a), (b), (c), (d), (e), & (f); 8-18 (a), (c), (d), (e), & (f); 8-19 (b), (c), (d), (e), (f); 8-20 (a), (b), (c), (d), (e), (f), (g), (h), (i), (j), (k); 8-21 all; 8-22 (a), (c), (d), (e), (f), (g), (h), (i), & (j); 8-23 all; 8-24 all; 8-25 all; 8-26 all; 8-27 all; 8-28 all

[Note: If you wish your SAT score to be in the top ½ of 1 percentile of our nation (or even better) you probably need to practice, practice, practice. Consider how many U.S. and foreign students are taking the SATs and ACTs to get into college in the U.S.A. – not the hundreds or thousands that may be in your township or county high schools, but 1.4 million students!].

If the students are 1/8 “A”, ¼ “B”, ½ “C”, and 1/8 “D” students {or more optimistically 1/8 “A”, ½ “B”, ¼ “C”, and 1/8 “D”}.

You are competing with (1.25 x 10-1 ) x (1.4 x 106) = 1.75 x 105) “A” students = 175,000 “A” students to get best scores.

½ of a percent of 1.4 million means being one of the top 7 thousand student scorers in 1.4 million.

So you are competing with 175,000 “A” students to become one of the top 7,000. [Note: we are including students from most of the best public, parochial, and super-rich private high schools on this planet!]

### Independent Reading, Study, and Assignments

Section 7-7 Factoring by Grouping
Assignment: Supplementary Exercises 7-19 Factor each polynomial by grouping

Section 7-8 Factoring Trinomials Using the ac Method
Assignment: Supplementary Exercises 7-20 Factor each trinomial by the ac method

Section 7-9 Factoring Using the General Strategy
Assignment: Supplementary Exercises 7-21 Completely factor each polynomial using the general strategy

Section 7-10 Solving Problems by Factoring Polynomials
Assignment: Supplementary Exercises 7-22 Geometric diagonals, counting, and telephone switchboard calculations

General Division (Yes, there can be remainders. Not all divisions are factorizations.): Here are ten (10) division problems for you to try this week. Have fun! We will not have time, in class, to go over these, but if you want to show me your work, we can go over it during break, after PACE – in the forum Saturday afternoon, or over the telephone (at some conveniently appointed time), or I can take them home to grade them (you will get them back in, at most, two weeks).

1. Divide (8x8 + 6x6 + 4x4 + 2x2 + 1) by:
a. (x4 - x2 + 1)
b. (x3 - x + 1)
c. (x2 – x – 1)

2. Divide (3x5 + 11x4 + 6x3 + 5x2 + 9x + 4) by:
a. (x2 + 2x + 5)
b. (x3 - 6x2 + 3)
c. (x4 - x + 3)

3. Divide (x8 – x7 + x6 – x5 + x4 – x3 + x2 – x + 1) by:
a. (x – 1)
b. (x + 1)

4. Divide (x7 - x6 + x5 - x4 + x3 - x2 + x - 1) by:
a. (x2 – 3)
b. (x2 + 1)

Two or more per day may help to keep the Educational Loans away!