“Pre-Calculus Honors It is the ninth week of school. This Quarter Exam study guide will cover the topics from weeks 3 to 7, with one additional concept added to create Exam 1. The concepts will be slightly more challenging than Tests 1 and 2, which covered weeks 3 to 7. Use the information below to create Test 1 and Test 2 sections, and add the additional concept to the Test 2 section. The student population is 10th-, 11th-, and 12th-grade Pre-Calculus Honors students. Students are encouraged to use their TI-84-Plus CE graphing calculator extensively to check for understanding.   Topics covered on Test 1:   Week 3: ·      A1-3: More Functions Including Piecewise-Defined Functions o   End in Mind §  Understand and use piecewise functions. o   A1-2: Transformation of Functions o   Recognize graphs of common functions. o   Use vertical shifts (up and down) to graph functions. o   Use horizontal shifts (left and right) to graph functions. o   Use reflections (-) example -|2x|to graph functions o   Use vertical stretching (towards the y-axis) and shrinking (compressing towards the x-axis) to graph functions. o   Identify intervals on which a function increases, decreases, or is constant. ·      A1-4: Linear Functions and Slope o   End in Mind §  Calculate a line’s slope. Let students know this brief review will connect to derivatives later. §  Write the point-slope form of the equation of a line, which is used continuously for computation purposes. Week 4 ·      A1-6 Factoring polynomials o   End in Mind ·      Reason for factoring:  In Algebra 1, we learned to factor; in Algebra 2, we learned to factor for two reasons: to simplify rational expressions or to solve. We don’t factor just to factor anymore; if you are asked to put your answer in simplest form, factored form is not simplest form.   ·      We will review three main factoring techniques to prepare for our intro to Calculus lessons, along with using the calculator. o   Factor trinomials. Using the x-method. o   Factor the difference of two squares. o   Factor the sum or difference of two cubes. ·      A2-4 Solve Quadratic Equations Multiple Methods o   End in Mind §  Solve quadratic equations by factoring. §  Solve quadratic equations by the square root property. §  Solve quadratic equations using the quadratic formula. §  Use the discriminant to determine the number and type of solutions. ·      A3-Understanding the behavior of polynomials o   End in Mind §  Identify polynomial functions. §  Recognize characteristics of polynomial functions. §  Determine end behavior.   Topics covered on Test 2: Week 5 ·      T8-2 Solving Trigonometric Equations o   Intro: §  A trigonometric equation is an equation that contains a trigonometric expression with a variable, such as sin (x). The values that satisfy such an equation are its solutions. (Some trigonometric equations have no solution.) When an equation has multiple solutions, the function's period helps ensure we don’t miss any solutions.   o   End in Mind §  Find all solutions of a trigonometric equation; use the unit circle as a guide. §  Solve trigonometric equations in quadratic form. §  Use factoring to separate different functions in trigonometric equations. §  Use identities to solve trigonometric equations. §  Use a calculator to solve trigonometric equations.   ·      Six Techniques to Solve Trig Equations (3 of the six): o   Introduce the Unit Circle, ·      1. The simple Unit Circle equations, a little bit of Algebra 1and 2, Simple no-step [use unit circle] Simple one-step equations (outside and one step inside) [use unit circle] Simple two-step equations (outside only) [use unit circle] ·      2. Take the square root ·      3. Factor out a common factor ·      Six Techniques to Solve Trig Equations   o   1. Factor a trinomial -Trinomial x-method   o   2. Use Pythagorean identity   o   3. Square both sides of the equation   Week 6 ·      A6-3 Logarithmic Functions ·      Definition of the Logarithmic Function o   End in Mind §  Properties of common logarithms. §  Properties of natural logarithms. ·      Note: Use the definition primarily to solve an equation. We now have calculators/computers; we do most of our calculations on them when we are dealing with logs. However, if you need to solve an equation with a variable, the definition will come in handy. ·    Domain [0,  ·    Range (- ·      Use a calculator to show that the x-intercept is 1. o     ·      A6-4 Rules of Logarithms o   End in Mind §  Use the product rule. §  Use the quotient rule. §  Use the power rule. ·      Expand logarithmic expressions (using the three rules) ·      Condense logarithmic expressions (using the three rules) ·      A6-5 Exponential and Logarithmic Equations o   End in Mind §  Use like bases to solve exponential equations. §  Use logarithms to solve exponential equations. §  Use the definition of a logarithm to solve logarithmic equations. Week 7 ·      A5-3 Function Operations o   End in Mind, §  Operation of Functions (Sum, difference, product, quotient) §  Composition of functions ·      A5-4 Inverse relations and functions o   End in Mind §  Verify inverse functions and find the inverse of a function. §  Use the horizontal line test to determine if a function has an inverse function. §  Use the graph of a one-to-one function to graph its inverse function. Use the calculator §  Find the inverse of a function Additional concept ·      A4-2 Simplifying Complex Fractions (rational expressions) o   End in Mind §  Rational expression definition §  Complex rational expression”