Name Class/Period Date CUMULATIVE REVIEW (4 th Nine Weeks) Honors Algebra II Essential Question: What algebra skills should I possess when I leave Algebra II Honors? Directions: You will be assigned different sections throughout the 4 th nine weeks. You must show ALL work on notebook paper, LABEL each problem, and you should keep ALL paper in a page protector. All answers should be neatly written on this document (so we can check them quickly). You may work with others, use notes/internet, but all work must be complete and your own work. UNIT TOPIC A-Review Foundations Solve linear equations Solve literal equations Solve inequalities Solve compound equations and inequalities B-Review Linear Find slope Write equations of lines Graphing lines Parallel/Perpendicular C-Review Systems Solve graphically Solve algebraically Solve systems of inequalities Linear programming 1a Polynomials 1.1 Properties of Exponents 1. Add, Subtract, Multiply Polynomials 1.3 Divide polynomials (long/synthetic) 1b Factoring 1.4 Factoring using the GCF 1.5 Factoring by Grouping 1.6 Factoring Trinomials 1.7 Factoring Difference of Squares/Cubes Rational Exponents & Radical Functions.1 Simplifying Radicals. Add/Subtract/Multiply/Divide Radicals/conjugates.3 Rational Exponents.4 Complex Numbers.5 Solving Radical Equations 3a 3b D Solving Quadratics 3.1 Solve x + bx +c = 0 by Factoring 3. Solve ax + bx +c = 0 by Factoring 3.3 Complete the Square 3.4 Use the Quadratic Formula and the Discriminant Graphing Quadratics 3.5 Graph Quadratic Functions in Standard Form 3.6 Graph Quadratic Functions in Vertex or Intercept Form 3.7 Applications of Quadratics Special Functions D.1 Domain & Range D. Operations with Functions/Inverse Functions D.3 Parent Functions D.4 Piecewise Functions D.5 Transformations 4 Rational Functions 4.1 Multiply & Divide Rational Expressions 4. Add & Subtract Rational Expressions 4.3 Solve Rational Equations 5 Exponential & Logarithmic 5.1 Graph Exponential Growth Functions 5. Graph Exponential Decay Functions 5.3 Use Functions Involving e 5.4 Evaluate Logarithms & Graph Logarithmic Functions 5.5 Apply Properties of Logarithms 5.6 Solve Exponential & Logarithmic Equations 5.7 Write & Apply Exponential & Power Functions
Solve Linear Equations Solve Literal Equations Solve Inequalities
Solve Compound Inequalities Find Slope Write Equations of Lines
Graphing Lines Graph each line on the coordinate plane.
Parallel / Perpendicular Solve Systems Graphically
Solve Systems Algebraically Choose any method. Solve Systems of Inequalities Solve each system of inequalities by graphing. Linear Programming
Properties of Exponents
Add, Subtract, Multiply Polynomials Divide Polynomials (synthetic/long) Factoring Simplifying Radicals
Add, Subtract, Multiply, Divide Radicals/Conjugates Rational Exponents
Complex Numbers Solving Radical Equations
Solving Quadratics-Factoring Solving Quadratics-Completing the Square
Solving Quadratics-Quadratic Formula Graphing Quadratics Vertex Concavity Equation of Axis of Symmetry y-intercept Number of Real Zeros and value to the nearest tenth. Two Extra Points Maximum or Minimum Value x 4x 5 = 0 x + x + 5 = 0 -x + 8x 3 = 0 y = -6(x + ) - 1 y = (1/3)(x 1) + y = 4(x+3) + 1
Applications of Quadratics Domain & Range Domain: Range: D: {interval notation} Left to Right R: {interval notation} Bottom to Top Function Operations Let f(x) = 9 x, g(x) = x + x, and h(x) = x. Compute the following: 10. g(f(3)) 11. f(g(4)) 1. h(f(-6)) Inverse Functions How do you solve for the inverse of a function?
How do you check to see if two functions are inverses of each other? 1. What is the inverse of the function: f(x) = x -7 Parent Functions What are the parent functions we discussed? What do their graphs look like? (draw a sketch of each below) What are the domain and range of each of their graphs? (label the D & R on each graph) Piecewise Functions
Transformations
Simplify/Multiply/Divide Rational Expressions Simplify. Identify any x-values for which the expression is undefined. 1. x x + 3x + 3x 4. 4x x 6 4 3. x 3 x x 5x + 3 4. 3 x + x 0x x 16 5. 3x 9x 1 6x + 9x + 3 6. 9 3x 15 x x Multiply. List the undefined values. 7. 4x + 16 x + x 3 i x + 6 x + 4 8. x + 3 x x + 1 i x 1 x + 5x + 6 Divide. Assume all expressions are defined. 6 5x 10x 9. x y y 10. x x 8 x 8x x x 15 x 10x Add/Subtract Rational Expressions Add or subtract. Identify any x-values for which the expression is undefined. 3. x 3 + 4 x 5 x + 1 3x 4. x + 4 x + 4 x 5 x 5 5. x x + 4 x + x 1 x 4 6. 3x 1 x + x 3x 18 x 6 Solve Rational Equations Solve. Check your solution. 11. x + x 1 = 15 x 3 1. x + 8x 10 = 4 x + 14x + 0