AP Prep Algebra II Second Semester


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1 AP Prep Algebra II Second Semester Standards 6.A.3 Represent fractions, decimals, percentages, exponents and scientific notation in equivalent forms. 6.A.4 Identify and apply the associative, commutative, distributive and identity properties of real numbers, including special numbers such as pi and square roots. 6.A.5 Perform addition, subtraction and multiplication of complex numbers and graph the results in the complex plane. 6.B.3a Solve practical computation problems involving whole numbers, integers and rational numbers 6.B.5 Identify, represent and apply numbers expressed in exponential, logarithmic and scientific notation using contemporary technology. 6.B.3b Apply primes, factors, divisors, multiples, common factors and common multiples in solving problems. 6.B.3c Identify and apply properties of real numbers including pi, squares, and square roots. 6.C.3a Select computational procedures and solve problems with whole numbers, fractions, decimals, percents and proportions. 6.C.5 Determine the level of accuracy needed for computations involving measurement and irrational numbers. 6.D.3 Apply ratios and proportions to solve practical problems. 6.D.4 Solve problems involving recipes or mixtures, financial calculations and geometric similarity using ratios, proportions and percents. 6.D.5 Solve problems involving loans, mortgages and other practical applications involving geometric patterns of growth. 7.A.4b Apply formulas in a wide variety of theoretical and practical realworld measurement applications involving perimeter, area, volume, angle, time, temperature, mass, speed, distance, density and monetary values. 8.A.3a Apply the basic properties of commutative, associative, distributive, transitive, inverse, identity, zero, equality and order of operations to solve problems. 8.A.4a Use algebraic methods to convert repeating decimals to fractions. 8.A.5 Solve mathematical problems involving recursive patterns and use models that employ such relationships. 8.A.3b Solve problems using linear expressions, equations and inequalities. 8.A.4b Represent mathematical patterns and describe their properties using variables and mathematical symbols. 8.B.3 Use graphing technology and algebraic methods to analyze and predict linear relationships and make generalizations from linear patterns. 8.B.4a Represent algebraic concepts with physical materials, words, diagrams, tables, graphs, equations and inequalities and use appropriate technology. 8.B.5 Use functions including exponential, polynomial, rational, parametric, logarithmic, and trigonometric to describe numerical relationships. 8.B.4b Use the basic functions of absolute value, square root, linear, quadratic and step to describe numerical relationships.
2 8.C.3 Apply the properties of numbers and operations including inverses in algebraic settings derived from economics, business and the sciences. 8.C.4a Analyze and report the effects of changing coefficients, exponents and other parameters on functions and their graphs. 8.C.5 Use polynomial, exponential, logarithmic and trigonometric functions to model situations. 8.D.3a Solve problems using numeric, graphic or symbolic representations of variables, expressions, equations and inequalities. 8.C.4b Apply algebraic properties and procedures with matrices, vectors, functions and sequences using data found in business, industry and consumer situations. 8.D.3a Solve problems using numeric, graphic or symbolic representations of variables, expressions, equations and inequalities. 8.D.4 Formulate and solve linear and quadratic equations and linear inequalities algebraically and investigate nonlinear inequalities using graphs, tables, calculators and computers. 8.D.5 Formulate and solve nonlinear equations and systems including problems involving inverse variation and exponential and logarithmic growth and decay. 8.D.3b Propose and solve problems using proportions, formulas and linear functions. 8.D.3c Apply properties of powers, perfect squares and square roots. Essential Questions What does it mean to raise an expression to a negative exponent? a zero exponent? Why does one use scientific notation? what is the difference between an equation with fractional coefficients and a fractional equation? What makes a fraction complex? How can rational algebra be used to solve shared work or mixture problems? What is the nth root? What is an imaginary Number? What are the properties of the imaginary unit i? What makes a number complex? What makes something a quadratic equation? What are the ways to solve a quadratic equation? How do you create the quadratic formula from a quadratic equation? How do you graph a quadratic equation? How do you apply the distance formula and the midpoint formula? How you you use the pythagorean theorem to find the distance formula?
3 How do you use the distance formula to find the equation of a circle? Chapter 10: How do you cancel out an exponent that is a variable? How can you find an unknown exponent if you know the base and the answer? What is a log? How do you use logs? What is e? how can logs and exponential expressions be used in the business world? What is the difference between a sequence and a series? How do you find the nth term of an arithmetic sequence? a geometriuc sequence? How is sigma notation used? How does our work with permutations and combinations apply to the binomial expansion? What does it mean to vary directly vs. jointly or inversely? How is long division related to dividing polynomials? How is synthetic division used to shortcut the method of dividing polynomials? Content Rational Expressions Irrational and Complex Numbers Quadratic Equations and Functions Distance Formula, Midpoint formula, Circles. Chapter 10: Exponential and Logarithmic functions. Sequences and Series Polynomial expansion Direct, inverse, and joint variation. dividing polynomial equations.
4 Skills 1. Simplify quotients using the laws of exponents. 2. Simplify expressions involving the exponent zero and negative integral exponents. 3. Use scientific notation. 4. Simplify rational algebraic expressions. 5. Multiply and divide rational expressions. 6. add and subtract rational expressions. 7. simplify complex fractions. 8. solve equations and inequalities having fractional coefficients. 9. solve and use fractional equations. 10. apply knowledge of rational expressions to solve mixture and shards work problems. 1. Define and work with roots (square, cube, nth) 2. Discuss and work with properties of radicals 3. Work with product and quotient properties of radicals 4. Solve problems including the sums of radicals 5. Work with binomials containing radicals 6. Define and discuss conjugates 7. Solve equations with radicals 8. Define rational and irrational numbers 9. Identify rational and irrational numbers based on properties of numbers 10. Define and discuss the imaginary unit i 11. Define and discuss the complex number system 12. Define complex conjugates 1. Work with completing the sqaure 2. Discuss, derive, and use the quadratic formula 3. Define and discuss the Discriminant and its use in determining the nature of the roots of a quadratic equation 4. Discuss equations in quadratic form 5. Solve quadratic equations using substitution 6. Graph basic quadratic equations using vertex, stretch, and points 7. Put equations in quadratic form by algebraic manipulation and completing the square 8. Discuss minimum and maximum values of a quadratic function 1. Find the distance between any two points and the midpoint of the line segment joining them. 2. learn the relationship between the center and radius of a circle and the equation of a circle.
5 Chapter 10: 1. Extend the understanding of exponents to include rational numbers. 2. Find the composite of two given funcations. 3. find the inverse of a given functions. 4. define a logarithmic function and learn how they are related to exponential functions. 5. apply the basic properties of logarithms. 6. use common logs to solve equations involving powers and evaluate logarithms with any given base. 7. use exponential and logarithmic functions to solve growth and decay problems. 8. define and use the natural logarithm function. 1. determine whether a sequence is arithmetic, geometric, or neither and to supply missing terms of a sequence. 2. find a formula for the nth term of an arithmetic sequence. 3. find a specific term of arithmetic sequences. 4. find a formula for the nth perm of a geometric sequence. 5. find specified terms of geometric sequences. 6. identify series and use sigma notation. 7. find sums of finite arithmetic and geometric series. 8. find sums of infinite goemetric series having ratios with absolute values less than one. 9. expand powers of binomials. 10. use prior knowledge of combinatorics to develop pascal's triangle. 11. derive the binomial theorem. 12. Use the binomial theorem to find a particular term of a binomial expansion. 1. Solve problems involving direct variation. 2. Solve problems involving inverse and joint variation. 3. Divide one polynomial by another polynomial. 4. use synthetic division to divide a polynomial by a first degree binomial. Assessment Homework Quizzes Tests Think, Pair, Share Formal and informal discussions with class
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