Updated November 12, 2014 MATH FLOW CHART Grade 6 Grade 7 Grade 8 Grade 9 Grade 10 Grade 11 Grade 12 Calculus Advanced Advanced Advanced Math AB or BC Algebra II Algebra I Geometry Analysis MAP GLA-Grade 8 MAP EOC-Algebra I MAP - ACT AP Statistics College Calculus Algebra/ Algebra I Geometry Algebra II AP Statistics MAP GLA-Grade 8 MAP EOC-Algebra I Trigonometry MAP - ACT Math 6 Pre-Algebra Statistics Extension Extension MAP GLA-Grade 6 MAP GLA-Grade 7 or or Algebra II Math 6 Pre-Algebra Geometry MAP EOC-Algebra I College Algebra/ MAP GLA-Grade 6 MAP GLA-Grade 7 MAP - ACT Foundations Trigonometry of Algebra Algebra I Algebra II Geometry MAP GLA-Grade 8 Concepts Statistics Concepts MAP EOC-Algebra I MAP - ACT Geometry Algebra II MAP EOC-Algebra I MAP - ACT Discovery Geometry Algebra Algebra I Algebra II Concepts Concepts MAP - ACT MAP EOC-Algebra I Additional Full Year Courses: General Math, Applied Technical Mathematics, and AP Computer Science. Calculus III is available for students who complete Calculus BC before grade 12. MAP GLA – Missouri Assessment Program Grade Level Assessment; MAP EOC – Missouri Assessment Program End-of-Course Exam Mathematics Objectives Calculus Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. Linear and Nonlinear Functions • Write equations of linear and nonlinear functions in various formats. • Graph linear and nonlinear functions. • Solve linear and nonlinear functions using a variety of methods. • Apply functions to solve real world problems. The Derivative • Show that the difference quotient represents the average rate of change, the slope of the secant line, and the average velocity. • Demonstrate that the derivative can represent the instantaneous rate of change, the slope of the tangent line, and the instantaneous velocity. • Calculate the derivative of several types of functions. • Identify critical points, concavity, and increasing and decreasing intervals using graphs and derivatives. • Investigate and use applications of the second derivative to solve problems. • Use the derivative for business applications, implicit differentiation, related rates, and linear approximation. • Find the derivatives of trigonometric functions and use them to analyze a variety of applications. Integration • Use the Fundamental Theorem of Calculus to find the antiderivative. • Use the anitderivative to find the area under a curve. • Find integrals using integration by parts. • Find the volume of a solid using the definite integral. • Find the integrals of trigonometric functions. Multivariable Calculus • Use multivariable calculus to find maxima and minima and to explore three-dimensional space. Honoring Tradition ~ Continuing Excellence Pending Board Approval, May 13,2015 Mathematics Objectives Advanced Placement Calculus AB Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. Functions, Graphs, and Limits Analysis of Graphs • Construct slope fields and interpret slope fields as visualizations of various equations. • Solve problems in which a rate is integrated to find the net change over time in a variety of applications. • Use integration to calculate areas of regions in a plane. • Use integration to calculate volumes of solids. • Find limits of indeterminate forms using L’Hopital’s Rule. • Use limits to evaluate improper integrals. • Use the direct comparison test and the limit comparison test to determine the convergence or divergence of improper integrals. • Differentiate, integrate, or substitute into a known power series in order to find additional power series representations. Limits of Functions • Use properties of limits to find the limit of a sequence. • Find limits of indeterminate forms using L’Hopital’s Rule. • Evaluate indefinite and definite integrals by the method of substitution. • Use properties of limits to find the limit of a sequence. • Determine whether a sequence converges or diverges. • Find limits of indeterminate forms using L’Hopital’s Rule. • Use limits to evaluate improper integrals. • Use the direct comparison test and the limit comparison test to determine the convergence or divergence of improper integrals. • Differentiate, integrate, or substitute into a known power series in order to find additional power series representations. • Construct slope fields and interpret slope fields as visualizations of various equations. Asymptotic and Unbounded Behavior • Use limits to evaluate improper integrals. • Use the direct comparison test and the limit comparison test to determine the convergence or divergence of improper integrals. • Solve problems involving exponential growth and decay. Continuity as a Property of Functions • Use Euler’s Method for approximating points for a solution to an initial value problem. • Solve problems in which a rate is integrated to find the net change over time in a variety of applications. • Use integration to calculate areas of regions in a plane. • Use integration to calculate volumes of solids. • Use limits to evaluate improper integrals. • Use the direct comparison test and the limit comparison test to determine the convergence or divergence of improper integrals. Honoring Tradition ~ Continuing Excellence Pending Board Approval, May 13, 2015 Derivatives Concept of the Derivative • Construct antiderivatives using the Fundamental Theorem of Calculus. • Solve initial value problems. • Construct slope fields and interpret slope fields as visualizations of various equations. Derivative at a Point • Construct slope fields and interpret slope fields as visualizations of various equations. Derivative as a Function • Construct slope fields and interpret slope fields as visualizations of various equations. • Solve initial value problems. Second Derivatives • Find derivative and second derivatives of parametrically defined functions. Applications and Computation of Derivatives • Calculate lengths of parametrically defined curves. • Use vectors to solve problems involving the velocity, acceleration, speed, and distance traveled. • Construct slope fields and interpret slope fields as visualizations of various equations. • Solve problems involving exponential growth and decay. • Evaluate indefinite and definite integrals by the method of substitution. Integrals Interpretations and Properties of Definite Integrals • Solve problems in which a rate is integrated to find the net change over time in a variety of applications. • Use integration to calculate areas of regions in a plane. • Use integration to calculate volumes of solids. Applications of Integrals • Solve problems in which a rate is integrated to find the net change over time in a variety of applications. • Use integration to calculate areas of regions in a plane. • Use integration to calculate volumes of solids. • Calculate lengths of parametrically defined curves. • Use vectors to solve problems involving the velocity, acceleration, speed, and distance traveled. • Calculate slopes and areas of regions in the plane determined by polar curves. Fundamental Theorem of Calculus • Construct antiderivatives using the Fundamental Theorem of Calculus. Techniques and Applications of Antidifferentiation • Construct antiderivatives using the Fundamental Theorem of Calculus. • Solve initial value problems. • Evaluate indefinite and definite integrals by the method of substitution. • Use integration by parts to evaluate indefinite and definite integrals. • Solve problems involving logistic population growth. • Solve problems in which a rate is integrated to find the net change over time in a variety of applications. • Use integration to calculate areas of regions in a plane. • Use integration to calculate volumes of solids. • Solve problems involving exponential growth and decay. Numerical Approximations to Definite Integrals • Solve problems in which a rate is integrated to find the net change over time in a variety of applications. • Use integration to calculate areas of regions in a plane. • Use integration to calculate volumes of solids. Honoring Tradition ~ Continuing Excellence Pending Board Approval, May 13, 2015 Mathematics Objectives Advanced Placement Calculus BC Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. Functions, Graphs, and Limits Analysis of Graphs • Construct slope fields and interpret slope fields as visualizations of various equations. • Solve problems in which a rate is integrated to find the net change over time in a variety of applications. • Use integration to calculate areas of regions in a plane. • Use integration to calculate volumes of solids. • Find limits of indeterminate forms using L’Hopital’s Rule. • Use limits