ADVANCED ALGEBRA (and Honors)

Welcome to Advanced Algebra! Advanced Algebra will be challenging but rewarding!! This full year course requires that everyone work hard and study for the entirety of the class. You will need a large binder or notebook and a graphing calculator for the course.

Student expectations:

General • keep an organized notebook • take good notes • complete homework every night • be active learners • ask questions and participate in class • seek help outside of class if needed • work with others • work with and without a calculator Specific Math Skills

1) Number Sense a. Know the order of operations b. Read and interpret word problems to provide mathematical expressions to

represent written expressions 2) Algebra

a. Manipulate with ease fractions, decimals and variables in a variety of settings including in equations, expressions, and rational functions

b. Be comfortable with all forms of factoring quadratics, including factoring by grouping

c. Solve equations and inequalities, including but not limited to i. Linear

ii. Quadratic iii. Absolute value iv. Systems of Equations

d. Manipulate equations to solve for a single variable e. Know the Pythagorean Theorem

3) Radical Functions and Rational Exponents a. Add, subtract, multiply and divide radical expressions b. Rationalize denominators c. Simplify expressions with rational exponents

4) Graphing a. Be familiar with the graphs of linear, absolute value, quadratic, and exponential

(growth and decay) functions b. Linear Graphs

i. Be able to find the slope and y-intercept of a line from both a graph and an equation

ii. Be able to determine whether two lines are perpendicular c. Know and apply the distance formula to find the distance between two points on

the coordinate plane

5) Trigonometry a. Understand and use angles of elevation and angles of depression to solve

problems b. Know the trig ratios for sine (sin), cosine (cos), and tangent (tan)

Vocabulary Students should be able to use, describe, and provide examples of the following vocabulary:

• consecutive • coefficient • perimeter • quadrilateral

*NOTE: Show all of your work. Your teacher will give a quiz on this material at the beginning of the year. You should “Google” the topic if you are unsure how to complete the examples. Useful resources are also linked at the end of this document. Some answers are given for particular problems for you to check your work.

Review Problems

I. Order of Operations and Radical Expressions Calculate: Solutions:

Translate each of the following into an algebraic expression. 1) Two-fifths of w is subtracted from 7 __________

2) Add one-third to 2 times y __________

3) 5 minus m __________

4) Three-fifths of the sum of 7 and h __________

5) s squared plus the product of 3 and g plus 6 __________

Solutions Answers for checking your work

II. Laws of Exponents

III. Factoring

Factor each of the following completely or state that it is prime.

VI. Manipulating Equations

For problems 1 – 4, solve the Linear Equation for the indicated variable.

1) 2(g − h) + 3 = 2h; solve for h

2) 3m − 2n2 = 4; solve for n

3) ab2 + c = k; solve for b

4) 3rt − 2mn = 4ab; solve for r Question5.

Question 6.

Theprecedingformulagivesthemonthlypayment m neededtopayoffaloanof P dollarsat r percentannualinterestover N months.Give P intermsof m, r,and N?

Answer:

V. Simplifying Expressions and Solving Equations

Answersforcheckingyourwork Solve each system. Then explain how the solutions would appear on a coordinate grid. 5) 6)

Solve each of the following equations by the method of your choice and check your solutions below. 13. x2 + 4 = 0 14. x2 + x = −1 15. 9y2 + 6y – 8 = 0 16. y2 − 25 = 0 Answers:

Answers

Simplify.

1. 9t + 7z – 7t + 7 – 10t

2. –4b2 + 8b – 5 – 2b2 – 9

3. –k5 m3

–5k4 m4

4 . m · 3 · m · m · 4

5. –3(–3x + 10) + 5(5 + 2x)

6. 4 + 2s – 4s2 + 2s + 4 + 3s2

Answers

1 . –8t + 7z + 7

2. –6b2 + 8b – 14

3. k

5m

4. 12m3

5. 19x – 5

6. –s2 + 4s + 8

VI. Graphing Sketch the graph of each function & state the domain and range of each. Then, choose the name of the function from the word bank below. A) y = x B) y = x2

VII. Linear Functions

Graph each of the following equations, then identify the slope and y-intercept. 1) y = 3x + 4 2) 8x + 2y = 32 3) y =7 4) x = 9

5) Write an equation that creates a line parallel to the function y = ¼ x – 20.

6) Write an equation that creates a line perpendicular to the function y = ¼ x – 20.

VIII. Identifying Functions

Determine whether or not each graph below represents a function.

Identifying Functions from Tables

IX. Trigonometry Finding Trigonometric (Trig) Values 1) In a given triangle, sinΘ= !

!". Find cos θ and tan θ. (Hint: draw the triangle and label the

given side lengths. 2) In a given triangle, cosΘ= !

!. Find sin θ and tan θ. (Hint: draw the triangle and label the

given side lengths.

3) In a given triangle, cosΘ= !!. Find sin θ and tan θ. (Hint: draw the triangle and label the

given side lengths.

4) In a given triangle, cosΘ= ! !!

. Find sin θ and tan θ. (Hint: draw the triangle and label the given side lengths.

Online Instructional Resources

www.virtualnerd.com (Short 5-10 minute videos for classes through Algebra 2) www.math.com (Good for basic math, algebra, and geometry) www.purplemath.com (Click “Lessons” on the homepage) www.intmath.com (Great math lessons and practice problems with solutions) http://www.wtamu.edu/academic/anns/mps/math/mathlab/ (Or search “West Texas A&M Virtual Math Lab” on yahoo) www.khanacademy.org (Videos on just about any topic) www.youtube.com (Short videos on just about any topic. View the ratings and/or user comments first.) https://learnzillion.com/resources/99913-math-instructional-videos/ (collection of short videos/tutorials for all classes; many topics found under the Algebra link) https://www.mathisfun.com/ (simple explanations and examples for sophisticated topics)