ADVANCED ALGEBRA (and Honors)

Transcription

1 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

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

3 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

4 II. Laws of Exponents III. Factoring Factor each of the following completely or state that it is prime.

5 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 2n 2 = 4; solve for n 3) ab 2 + c = k; solve for b 4) 3rt 2mn = 4ab; solve for r Question 5. Question 6. The preceding formula gives the monthly payment m needed to pay off a loan of P dollars at r percent annual interest over N months. Give P in terms of m, r, and N?

6 Answer: V. Simplifying Expressions and Solving Equations

7 Answers for checking your work Solve each system. Then explain how the solutions would appear on a coordinate grid. 5) 6)

8 Solve each of the following equations by the method of your choice and check your solutions below. 13. x = x 2 + x = y 2 + 6y 8 = y 2 25 = 0 Answers:

9 Answers

10 Simplify. 1. 9t + 7z 7t t 2. 4b 2 + 8b 5 2b k 5 m 3 5k 4 m 4 4. m 3 m m ( 3x + 10) + 5(5 + 2x) s 4s 2 + 2s s 2 Answers 1. 8t + 7z b 2 + 8b k 5m 4. 12m x 5 6. s 2 + 4s + 8

11 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 = x 2

12 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.

13 Identifying Functions from Tables IX. Trigonometry Finding Trigonometric (Trig) Values 1) In a given triangle, sin Θ=!. Find cos θ and tan θ. (Hint: draw the triangle and label the given side lengths.!" 2) In a given triangle, cos Θ=!!. Find sin θ and tan θ. (Hint: draw the triangle and label the given side lengths.

14 3) In a given triangle, cos Θ=!. Find sin θ and tan θ. (Hint: draw the triangle and label the! given side lengths. 4) In a given triangle, cos Θ=!!. Find sin θ and tan θ. (Hint: draw the triangle and label the! given side lengths. Online Instructional Resources (Short 5-10 minute videos for classes through Algebra 2) (Good for basic math, algebra, and geometry) (Click Lessons on the homepage) (Great math lessons and practice problems with solutions) (Or search West Texas A&M Virtual Math Lab on yahoo) (Videos on just about any topic) (Short videos on just about any topic. View the ratings and/or user comments first.) (collection of short videos/tutorials for all classes; many topics found under the Algebra link) (simple explanations and examples for sophisticated topics)