Morgan County School District Re-3 A.P. Calculus August What is the language of algebra? Graphing real numbers. Comparing and ordering real numbers. Finding absolute value. 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? How do you solve and graph absolute value equations/inequalities in one variable? How do you prove theorems in algebra? How do you graph linear equations? How do you write the equation of a line? Simplifying expressions. Basic properties of real numbers. Adding, subtracting, multiplying and dividing real numbers. Solve one variable equations. Translate word problems into equations and solve. Solve one step inequalities with integers. Solve multi-step inequalities. Solve combined inequalities. Solve absolute value equations and inequalities algebraically and graphically. 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.
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? What is the difference between a function and a relation? 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. Given a function, determine the domain and range. How do you write the equation of a linear function? How do you solve systems of equations? How do you solve systems of linear inequalities? Determine which relations are functions and which are not. Functions may be a map, a list, a chart or a graph. Writing linear functions given a slope and a y-intercept, a point and a slope or two points. How do you translate word problems into linear systems of equations and into systems of linear functions? How do you add and subtract polynomials? Writing linear functions from word problems. Writing systems of linear equations and functions from word problems. Graph one linear inequality. How do you use the laws of exponents? Graph a system of inequalities. How do you multiply polynomials? How do you find the LCM and GCF of Adding, subtracting, multiplying integers.
algebraic terms? How do you factor polynomials? Identify like terms. Adding and subtracting like terms. 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? How do you solve word problems using polynomial equations? How do you solve polynomial inequalities? How do you divide monomials? How do you use zero and negative exponents? Factor polynomials. Solve equations. Identify factors. Write polynomial equations from word problems. Solve polynomial equations. Solve conjunction and disjunction problems.
How do you use scientific notation? How do you simplify rational expressions? 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? How do you simplify complex fractions? How do you solve equations with rational expressions? Simplify numerical expressions. Simplify, multiply, divide, add and subtract numerical expressions. Factor polynomials. Solve polynomial equations. Simplify monomial algebraic expressions. Identify a common denominator. January How do you find the roots of real numbers? How do you simplify radical expressions? Identify perfect squares, perfect cubes. Multiply and divide numbers. Identify, add and subtract like terms. How do you add, subtract, multiply and divide radical expressions? Find the root of a perfect square, perfect cube. How do you solve equations with radical expressions? Rationalize the denominators of fractions. How do you identify rational and irrational numbers? How do you convert a fraction to a decimal? Write the conjugate of a binomial. Multiply conjugates. Identify imaginary numbers. How do you convert a decimal to a fraction? Simplify, add, subtract, multiply and divide radical expressions.
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? Factor quadratics. Solve quadratics by completing the square. Solve quadratics using the quadratic formula. 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? Determine what the discriminate is. Determine if the discriminate is positive, negative or equal to zero. Complete the square of a quadratic equation. 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.
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? end of chapter 8 Divide polynomial equations using long division. Divide polynomial equations using synthetic division. Find the factors of polynomials using the remainder and factor theorems. 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? Find the number of positive and negative roots. Simplify radical expressions. Average coordinates. What is the relationship between the center and radius of a circle and the equation of the circle? What is the relationship between the focus, directrix, vertex, and axis of a parabola and the equation of the parabola? Identify the center of a circle from the equation. Complete the square. 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. Understand asymptotes. 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.
hyperbola? How do you use graphs to determine the number of real solutions of a quadratic system? 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 Use the distance formula to create the equations of conic sections based on their definitions. Graph conic sections. 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? Use laws of exponents. Solve equations. Define logarithms. Convert rational exponents to radical form. Convert radical form to rational exponents. Use logarithms to solve for an exponent. How do you apply the basic properties of logarithms? How do you use common logarithms to Evaluate using function notation. Find the inverse of a function.
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? How do you use degrees to measure angles? How do you define trigonometric functions of acute angles? How do you define trigonometric functions of general angles? How do you use a calculator or trigonometric tables to find values of trigonometric functions? How do you the fin side and angles of a right triangle? 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. Measure angles using degrees. Convert from degree, minutes and seconds to decimal form. Convert form decimal form, to degrees, minutes and seconds. Identify the values of the six trig functions when given a right triangle or an angle. Use trig functions to solve for an unknown. Find the reference angle. Use trig to solve for the missing parts of a right angle.