Honors Algebra II Spring 2016 Final Exam Format

Transcription

1 Honors Algebra II Spring 2016 Final Exam Format 40 questions, all multiple choice 16 questions from Units 1 4B, 24 questions from Units 5A 6 Can use graphing calculator for entire test May 23 9:38 AM Unit 1: Statistics 1. Standard Deviation Calculate and understand calculation 2. Normal Distribution Know the Empirical Rule and how to apply it to a given situation 3. Z Scores Calculate and understand calculation 4. Margin of Error Understand concept and simple calculation 5. Central Limit Theorem Understand concept and what a confidence interval means 6. Sampling Methods Be able to identify type of sampling method in a certain scenario 1

2 Unit 3: Polynomial Operations, Compositions, and Inverses 1. Naming Polynomials Name by degree and number of terms, find the leading coefficient, and identify whether the function is even/odd. 2. Polynomial Operations Add, subtract, multiply, and divide using long division 3. Binomial Expansion How to use Pascal's triangle to expand a binomial in the form (ax + by) n 4. Factoring Polynomials Sum/Difference of Cubes + all methods learned in previous courses 5. Composition How to create a composition of functions and simplify using order of operations 6. Inverses Definition of inverse to be a function (one to one), finding an inverse, and effect of finding the inverse on the parent function's characteristics. Unit 4A: Polynomial Graphs 1. Characteristics Based on L.C. and degree, maximum number of turns and end behavior 2. Graphs Shape of graph through the x axis based on the multiplicity of roots 3. Function Symmetry Even/Odd/Neither symmetry based on both algebraic and graphical definitions 4. Transformations How different transformations affect the points of an original parent function 5. Systems of Equations What a solution to a system of equations looks like graphically 2

3 Unit 4B: Solving Polynomials 1. Solving by Factoring Set equal to zero and factor. Set each factor equal to zero and solve for roots. 2. Synthetic Division How it's done and when you can use it. 3. Remainder Theorem What a remainder means after dividing a polynomial by a linear binomial 4. Fundamental Theorem of Algebra Number of solutions to a polynomial is the same as the degree 5. Rational Roots Theorem Any rational solutions to the polynomial will be the ratio of factors of the constant over factors of the leading coefficient AFTER the GCF is removed 6. Irrational Roots/Complex Numbers Theorem All irrational roots or complex roots always come in pairs 7. Polynomial inequality How to solve algebraically or graphically Unit 5A: Rational Functions 1. Simplifying Factor and simplify 2. Characteristics Asymptotes (Vertical, Horizontal, and Slant), Holes, and X and Y Intercepts. 3. Rational Operations Add, subtract, multiply, and divide rationals 4. Solving Rational Equations Solve and remember to check for extraneous solutions 5. Solving Rational Inequalities Solve and check your intervals. Remember that any excluded value should be included as an excluded endpoint to the intervals. 6. Rational Inverses How to find the inverse and its characteristics 3

4 Unit 5B: Radical, Absolute Value, Piecewise, and Step Functions 1. Radical Operations Add, Subtract, Multiply, and Divide 2. Solving Radical Equations and Inequalities Check for extraneous solutions and additional constraint on even index radicals 3. Radical Characteristics Square root and cube root graphs 4. Radical Transformations How to apply given transformations to a parent graph and how they affect the characteristics 5. Radical Inverses Find the radical inverse and its characteristics (domain restriction...) Unit 5B: Radical, Absolute Value, Piecewise, and Step Functions (continued) 6. Solving Absolute Value Equations and Inequalities Isolate AV and set equal to both + and solutions 7. Graphing Absolute Value Functions Based on transformations 8. Evaluating Piecewise Functions 9. Graphing Piecewise Functions continuous versus discontinuous based on transition points in domain and finding domain/range 10. Evaluating Greatest Integer Functions 11. Graphing Greatest Integer Functions Based on transformations 4

5 Unit 6: Exponential and Logarithmic Functions 1. Geometric Series How to evaluate a series in sigma notation and write an equation for a series 2. Characteristics of Exponential Graphs Graph based on transformations and decide whether the function is growth or decay 3. Switching between Exponential and Logarithmic Forms 4. Properties of Logarithms Expand and Condense 5. Solving Exponentials/Logarithmic Equations Use properties to solve. Check for extraneous solutions on logarithms. 6. Solving Exponential/Logarithmic Inequalities Remember to apply extra constraint to logarithmic inequalities. 7. Exponential/Logarithmic Inverses Find the inverse and its characteristics 8. Word Problems Set up an exponential equation and solve using any method (logarithm or change of base) 5