Level: Sophomore-Junior
Credit: full year; 1 unit
Description: Algebra 2 with Trigonometry is designed with the average college bound math student in mind. It moves at a slower pace than the accelerated course and also includes a thorough review of Algebra I. New topics in the three quarters of Algebra include linear inequalities in two variables, higher degree equations and inequalities, complex numbers and logarithms.
Problem solving skills will be emphasized so that the student should be able to examine a given problem and devise a plan of attack. By the conclusion of the Algebra part of the course, students should recognize Algebra as one tool for solving real world problems.
The fourth quarter is devoted to an introduction of Trigonometry. This part of the course is intended to serve two purposes. The first purpose is to acquaint the student with trigonometric notation, definitions of the trig functions and their inverses, use of tables and calculators, and fundamental identities. The second purpose is to make the student aware that there are different approaches to trig depending on the application. The use of the unit circle approach with angle measures in degrees and in radians along with the use of the triangle approach will be stressed. The student will discover applications such as finding the height of a building and investigating rotational motion from physics.
A major goal of this course is to continue to develop a student’s self-discipline and logical thinking. Solving problems through a systematic approach should contribute to the achievement of this goal.
I. At the end of the first semester each student should be able to :
A. Analyze Equations and Inequalities with understanding of Expressions and Formulas, knowledge of the properties of Real Numbers, understanding graphs & measures of central tendencies, be able to solve linear equations and inequalities and have an understanding of Absolute Values with respect to equations and inequalities.
B. Graph linear Relations and Functions, use graphs to estimate solutions, have an understanding of Slope scatter plots special functions and linear inequalities. The student should be able to write linear equations in several forms.
C. Solve Systems of linear inequalities by graphing, using Cramer’s Rule, and graphing calculators. Solve and graph systems of equations in 3 variables.
D. Explore Polynomials and Radical Expressions involving polynomials by factoring, dividing polynomials, and understanding Roots of Real Numbers.
E. Understand radical expressions and be able to solve equations using radicals, complex numbers and be able to simplifying expressions containing Complex Numbers.
F. Understand Quadratic Functions and Inequalities. Be able to solve quadratic equations using graphing, factoring, completing the square, and using the quadratic formula.
G. Use the sum and product of roots rule, understand standard deviation, a normally distributed curve, and the distance and midpoint formula.
II. At the end of the second semester each student should be able to:
A. Have an understanding of polynomial functions, be able to use and understand the Remainder and Factor theorems, be able to graph functions from their zeros and roots.
B. Have a working knowledge of the Rational Zero Theorem, Composition of Functions, and be able to find inverse functions and relations.
C. Be able to recognize and find direct, inverse and joint variations. Be able to multiply, divide, add, and subtract rational expressions.
D. Have an understanding of exponential and logarithmic functions and their graphs. Be able to use the properties of Natural and Common Logs to solve exponential and logarithmic Functions.
E. Have a complete understanding of angles and angle measures in triangles and their relationships to the sides of the triangles. Understand and be able to use trig functions of general angles.
F. Know and use the Law of Sines and Law of Cosines to solve triangle that are not right. Understand circular functions and inverse trig functions and be able to graph them.
G. Be able to verify the trig identities and derive them from another.
H. Be able to use the Sum and Difference of Angles Formulas, the Double Angle and ½ Angle Formulas to solve trig equations.