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Core Content and Skills
Math Calculus 1/SUPA 295
2008-2009
BOE Approved

Functions and Graphs  Content   Skills  Functions and Mathematical Modeling Graphs of Equations and Functions Types of Functions Interval Notation Calculator Programs   define functions find domain and range of relations identify dependent and independent variables identify equations of circles, parabolas, etc. use vertical line test to identify functions use interval notation to express domains and ranges     Prelude to Calculus  Content   Skills  Derivative by Definition Tangent Lines and Normal Lines Idea of the Limit Numerical Investigation into the Limit Limit Laws Indeterminate Forms Limit Approaching Infinity Limit Definition Trigonometric Limits One-Sided Limits   use slope predictors to identify tangent lines write equations of tangent lines and normal lines find the derivative by definition evaluate limits using limit laws find limits approaching infinity find limits from the left and right find limits of trigonometric function

Prelude to Calculus Continued  Content   Skills  Infinite Limits Concept of Continuity Intermediate Value Theorem More Limits   identify points of discontinuity and the type of discontinuity use the IVT to find zeroes of functions     The Derivative  Content   Skills  Basic Derivative Rules Product Rule Quotient Rule Chain Rule Derivatives of Trigonometric Functions   find the derivative using power rules find the derivatives using product rules find the derivative using quotient rules find the derivative using the chain rule find the derivative using combinations of the derivative rules     Derivative Applications  Content   Skills  Velocity and Acceleration Absolute Max and Min Local Max and Min Applied Max/Min Problems   find the average rate of change of a function find the instantaneous rate of change of a function use the derivative to see the relationship between position, velocity, and acceleration find the local and absolute maximum or minimum of a function solve applied maximum/minimum problems using a four-step process

Derivative Applications continued  Content   Skills  Derivative of Natural Logarithms and e Implicit Differentiation Related Rates Presentations Newton’s Method   find the derivative of natural logarithm functions find the derivative of functions involving e find the derivative implicitly use the derivative to solve related rates problems present solutions of derivative application problems to classmates and defend results use Newton's method of approximation to find solutions to functions

Additional Applications of the Derivative  Content   Skills  Linear Approximations Differentials Intervals of Increase and Decrease Rolle’s Theorem Mean Value Theorem 1st Derivative Test   approximate functions using differentials and the linear approximation methods find intervals of increase and decrease of functions using the 1st derivative test identify extrema and zeroes of functions using Rolle's theorem and the Mean Value Theorem     Graphing  Content   Skills  Steps to Graphing Concavity and Inflection Points Asymptotes   be able to graph complex functions including asymptotes, intervals of increase and decrease, maximums and minimums, intervals of concavity, inflections points and limits without the use of a calculator

Polar Coordinates and Plane Curves/The Integral  Content   Skills  Graphing ln x, e^x Parabolas Hyperbolas Ellipses Polar Coordinates   be able to graph natural logarithm equations and functions involving e identify and graph conic sections including parabolas, ellipses, and hyperbolas convert polar coordinates to rectangular and vice versa graph polar functions

The Integral Continued  Content   Skills  Antiderivatives U-substitution Antiderivatives with ln, e, and Trigonometric Functions Initial Value Problems Motion Problems   find antiderivatives of basic functions use u-substitution to find anti-derivatives find antiderivatives of functions with trig, natural logarithms, or with e find the specific solutions for the antiderivatives using initial values to identify the constant solve problems involving acceleration, velocity, and position

Applications of the Integral  Content   Skills  Summation Rules Area under the Curve Riemann Sums Definition of the Integral Average Value   find area under curves using inscribed and circumscribed rectangular polygons use Riemann sums associated with a partition find the definite integral from a to b find the average value of a function     More Applications of the Integral  Content   Skills  Fundamental Theorem of Calculus Area between Curves Riemann, Trapezoid, and Simpson Calculator Programs   use the First Fundamental Theorem of Calculus to evaluate integrals find the area between 2 curves use the Trapezoid rule and Simpson's rule for approximating integrals

More Applications of the Integral  Content   Skills  Volume by Disks Volume by Cylindrical Shells Volume by Slicing Arc Length Surface Area of a Solid of Revolution Work Elastic Springs   find the volume of a solid of revolution using disks, cylindrical shells, and washers find the volume of solids through slicing find the length of an arc of a function from a to b find the surface area of a solid of revolution find the work done against gravity find the work done in filling or emptying a tank find the work done in stretching or compressing a spring     Applications continued  Content   Skills  Work Done in Filling or Emptying a Tank Fluid Pressure Presentations   find work done with fluids find the fluid pressure given the shape of a "trough" or a dam face express solutions and defend work to classmates of various work problems

Review and Take Final Exam  Content   Skills  Start Calculus 2 Topics (Techniques of Integration)   if time we begin finding the integral of more advanced functions