PRE-CALCULUS HONORS (AB/BC) Welcome to Pre-Calculus Honors! Pre-Calculus Honors 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) Algebra a. Can manipulate with ease fractions, decimals and variables in a variety of settings including in equations, expressions, and rational functions b. Comfortable with all forms of factoring including quadratics, sum and difference of cubes, quartics and factoring by grouping c. Add, subtract, multiply and divide radical expressions including rationalizing denominators d. Solve equations and inequalities, including but not limited to i. Polynomial ii. Logarithmic iii. Rational iv. Radical v. Exponential vi. Absolute Value vii. Systems e. Manipulate equations to solve for a single variable f. Know and use the laws of exponents to simplify expressions g. Solve systems of equations h. Identify functions from graphs and tables i. Solve problems involving composition of functions 2) Graphing a. Be familiar with the graphs of linear, absolute value, quadratic, cubic, quartic, logarithmic and exponential functions b. Identify the domain and range of functions i. Be able to determine what value makes a function undefined c. Recognize end behaviors of graphs d. Be familiar with transformations of graphs
3) Trigonometry a. Work with the basic six trig functions including manipulating them to simplify expressions and solve equations by finding all solutions b. Know the trig identities i. Reciprocal ii. Quotient iii. Pythagorean c. Know common values of the six basic trig functions by: i. Memorizing the trig table of values (link for practice) ii. Memorizing the unit circle iii. Finding the values from special right triangles d. Know the graphs of the six basic trig functions including their domain and range e. Convert easily between degrees and radians f. Know the double angle and half angle formulas *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. Graphing Sketch the graph of each function & state the domain and range of each: A) y = x B) y = x 2
II. Factoring Factor each of the following completely or state that it is prime. III. Laws of Exponents
IV. Manipulating Equations For problems 1 4, solve the Linear Equation for the indicated variable. 1) 3m 2n = 4; solve for n 2) 2(g h)+3 = 2h; solve for h 3) ab + 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?
Answer: V. Simplifying Expressions and Solving Equations Simplify. 1) 2) 3) 4)
Simplify. Solve. 1) ln (x-2) = 4 2) -3ln(x+1) = 2 3) ln(x-2) + ln(3)= 5 4) 100 = 200e 0.06x Solve each system. 5) 6)
Solve each equation. Then state which values make the functions undefined. 7) 8) 9) 10) 11) 12) VI. Composite Functions Let f(x) = 2x 1, g(x) = 3x, and h(x) = x 2 + 1. Compute the following: 1. f(g(-3)) 2. f(h(7)) 3. g(h(24)) 4. h(f(x)) 5. g(f(x)) 6. h(g(x)
Write the formula for each transformation. VII. Transformations A) y = x! a translation right four units and up 3 units B) y = x a reflection about the x-axis and a vertical stretch to 3 times its height C) 2 x a reflection about the y-axis and then translate right 3 units D) y = x a translation left 3 units and a horizontal shrink to ¼ its usual size VIII. Identifying Functions Determine whether or not each graph below represents a function.
Identifying Functions from Tables VIII. Trigonometry Trig Facts: You will need to know these as you know your multiplication tables. The values for sin, cos, and tan in Quadrant I should be memorized cold. The other Quadrants values should not take you more than a few seconds to find when quizzed. Fill in the blank: Every trig function takes an angle as input and returns a ratio as output. So, every inverse trig function takes a ratio as input and returns as output.
Fill out the following 16-point unit circle by finding the following: 1) The measures for each angle in radians and in degrees. 2) The coordinate pair for each angle. Converting between radians and degrees. 1. Convert the following angles given in degrees, to radians. Do not use a calculator and give your answers as multiples of π. a) 90 b) 72 c) 45 2. Convert each of the following angles given in radians, to degrees. Give your answers correct to two decimal places. a) 3 radians b) 2.4 radians c) 1 radian
3. Convert each of the following angles given in radians, to degrees. Do not use a calculator. a)!!" b)!! Answers 1. a)! radians, b)!!!! radians, c) radians!!! 2. a) 171.89, b) 137.51, c) 57.30 3. a) 12, b) 36 Double Angle and Half Angle Identities Answers: Answers
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)