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Morgan County School District Re-3 A.P. Calculus Month August Content and Essential Questions What is the language of algebra? Skills Assessment Graphing real numbers. Comparing and ordering real numbers. Finding absolute value. Simplifying expressions. Homework Basic properties of real numbers. Daily quizzes September How do you solve one variable equations? How do you translate into mathematical phrases? How do you solve and graph inequalities in one variable? Adding, subtracting, multiplying and dividing real numbers. Formal Quizzes after several sections Solve one variable equations. Chapter Test Homework Translate word problems into equations and solve. Formal Quizzes after several sections Solve one step inequalities with integers. Solve multi-step inequalities. How do you solve and graph absolute value equations/inequalities in one variable? Solve combined inequalities. How do you prove theorems in algebra? Solve absolute value equations and inequalities algebraically and graphically. How do you graph linear equations? How do you write the equation of a line? Daily quizzes Write one variable inequalities to solve word problems. Identify and write expressions to demonstrate properties of equality, real numbers, order. Use properties and theorems of real number and of order, to prove algebraic statements. Chapter Test Resources Morgan County School District Re-3 Month Content and Essential Questions A.P. Calculus Skills Assessment Graph lines given the slope and a point. Graph linear equations - using both a chart and slope-intercept form. Find the slope of a line when given two points. October How do you find the range of a function? Writing linear equations when given a y-intercept and a slope, a point and a slope, or two points. Given the domain of a function, determine the range. What is the difference between a function and a relation? Given a function, determine the domain and range. How do you write the equation of a linear function? Determine which relations are functions and which are not. Functions may be a map, a list, a chart or a graph. Homework Daily quizzes How do you solve systems of equations? How do you solve systems of linear inequalities? How do you translate word problems into linear systems of equations and into systems of linear functions? Writing linear functions given a slope and a y-intercept, a point and a slope or two points. Writing linear functions from word problems. Writing systems of linear equations and functions from word problems. How do you add and subtract polynomials? Graph one linear inequality. How do you use the laws of exponents? Graph a system of inequalities. How do you multiply polynomials? Adding, subtracting, multiplying integers. How do you find the LCM and GCF of Formal Quizzes after several sections Chapter Test Resources Morgan County School District Re-3 Month A.P. Calculus Content and Essential Questions Skills algebraic terms? Identify like terms. How do you factor polynomials? Adding and subtracting like terms. Assessment Identify exponents. FOIL Distributive property. Find LCM and GCF of numerical terms. Order exponents from largest to smallest. Multiply polynomials. Factor out a common factor. Factor the sum and the difference of perfect cubes. Factor the difference of perfect squares. November How do you solve polynomial equations? Factor polynomials. Homework Solve equations. Daily quizzes How do you solve word problems using polynomial equations? Identify factors. Formal Quizzes after several sections How do you solve polynomial inequalities? Write polynomial equations from word problems. Chapter Test How do you divide monomials? Solve polynomial equations. How do you use zero and negative exponents? Solve conjunction and disjunction problems. Resources Morgan County School District Re-3 Month Content and Essential Questions How do you use scientific notation? How do you simplify rational expressions? A.P. Calculus Skills Assessment Add, subtract, multiply and divide integers. Use the laws of exponents. Counting places. December How do you simplify, multiply, divide, add and subtract rational expressions? Simplify numerical expressions. Simplify, multiply, divide, add and subtract numerical expressions. Homework Daily quizzes How do you simplify complex fractions? Factor polynomials. Formal Quizzes after several sections Solve polynomial equations. How do you solve equations with rational expressions? Chapter Test Simplify monomial algebraic expressions. Identify a common denominator. January How do you find the roots of real numbers? Identify perfect squares, perfect cubes. Homework Multiply and divide numbers. Daily quizzes How do you simplify radical expressions? Identify, add and subtract like terms. Formal Quizzes after several sections How do you add, subtract, multiply and divide radical expressions? Find the root of a perfect square, perfect cube. Chapter Test How do you solve equations with radical expressions? Rationalize the denominators of fractions. How do you identify rational and irrational numbers? Write the conjugate of a binomial. Multiply conjugates. How do you convert a fraction to a decimal? Identify imaginary numbers. How do you convert a decimal to a fraction? Simplify, add, subtract, multiply and divide radical expressions. Resources Morgan County School District Re-3 Month Content and Essential Questions How do you simplify, add, subtract, multiply and divide imaginary numbers? How do you solve quadratic equations by completing the square, using the quadratic formula and using the graphing calculator? February How do you use the discriminate to determine what type of roots a quadratic equation will produce? How do you graph a quadratic equation? How do you find the axis of symmetry, the vertex, the x and y intercepts, the range and the domain of parabola's (quadratic equations)? How do you write a quadratic equation when you have been given the roots of the equation? A.P. Calculus Skills Assessment Factor quadratics. Solve quadratics by completing the square. Solve quadratics using the quadratic formula. Determine what the discriminate is. Homework Determine if the discriminate is positive, negative or equal to zero. Daily quizzes Formal Quizzes after several sections Complete the square of a quadratic equation. Chapter Test Find the vertex of a parabola from the equation. Find the axis of symmetry of a parabola from the equation. Find the x and y-intercepts of a parabola from the equation. Find the range and the domain of a parabola from the graph and from the equation. Solve quadratic equations by factoring. Write quadratic equations when given the roots of the equation. March How do you divide one polynomial by another polynomial? Add, subtract and multiply polynomial equations. Homework Daily quizzes Resources Morgan County School District Re-3 Month Content and Essential Questions How do you find factors of polynomials and solve polynomials using the remainder and factor theorems? How do you determine the number, the nature and the roots of a polynomial equation? A.P. Calculus Skills Divide polynomial equations using long division. Divide polynomial equations using synthetic division. Assessment Formal Quizzes after several sections Chapter Test Find the factors of polynomials using the remainder and factor theorems. end of chapter 8 Solve polynomials using the remainder and factor theorems. Determine the number of roots in a polynomial equation. Given one imaginary root, find the other (conjugate) root. April How do you find the distance between two points? How do you find the midpoint? What is the relationship between the center and radius of a circle and the equation of the circle? Find the number of positive and negative roots. Simplify radical expressions. Homework Average coordinates. Daily quizzes Identify the center of a circle from the equation. Formal Quizzes after several sections Chapter Test Complete the square. What is the relationship between the focus, directrix, vertex, and axis of a parabola and the equation of the parabola? Work in the coordinate plane. Write and graph linear equations. What is the relationship between the center, foci, and intercepts of an ellipse and the equation of the ellipse? Using intercepts. What is the relationship between the foci, intercepts, and asymptotes of a hyperbola and the equation of the Find the foci of ellipses, parabola and hyperbola. Understand asymptotes. Resources Morgan County School District Re-3 Month Content and Essential Questions A.P. Calculus Skills Assessment hyperbola? How do you use graphs to determine the number of real solutions of a quadratic system? Use the distance formula to create the equations of conic sections based on their definitions. Graph conic sections. How do you use algebraic methods to find the solutions to a quadratic system? How do you solve systems of linear equations in three variables? end of chapter 9 Substitution method for systems of equations. Understand that the solution to a system of an equation is the point of intersection. end of chapter 9 May How do you extend the meaning of exponents to include rational numbers? How do you extend the meaning of exponents to include irrational numbers and to define exponential functions? How do you find the composite of two given functions and find the inverse of a function? How do you define logarithmic functions and to learn how they are related to exponential functions? How do you apply the basic properties of logarithms? Use laws of exponents. Homework Solve equations. Daily quizzes Define logarithms. Formal Quizzes after several sections Convert rational exponents to radical form. Chapter Test Convert radical form to rational exponents. Use logarithms to solve for an exponent. Evaluate using function notation. Find the inverse of a function. How do you use common logarithms to Resources Morgan County School District Re-3 Month Content and Essential Questions solve equations involving powers and to evaluate logarithms with any given base? How do you use exponential and logarithmic functions to solve growth and decay problems? A.P. Calculus Skills Convert from logarithmic form to exponential form. Convert from exponential form to logarithmic form. Use the laws of exponents to evaluate expressions. Use the law of exponents to solve equations. How do you use degrees to measure angles? Measure angles using degrees. How do you define trigonometric functions of acute angles? Convert from degree, minutes and seconds to decimal form. How do you define trigonometric functions of general angles? Convert form decimal form, to degrees, minutes and seconds. How do you use a calculator or trigonometric tables to find values of trigonometric functions? Identify the values of the six trig functions when given a right triangle or an angle. How do you the fin side and angles of a right triangle? Use trig functions to solve for an unknown. Find the reference angle. Use trig to solve for the missing parts of a right angle. Assessment Resources