Day 65 - Summative Exam 2 - 04.21.15

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Bell Ringer
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  • Prerequisites
    • Derivatives
      • Derivative Rules
      • Power Rule
      • Constant Rule
      • Trig Derivatives
  • Antiderivative (video)
    • Indefinite Integral
    • Definition
    • Integral Sign
    • Integrand
    • Variable of Integration
    • Constant of Integration
    • General Solution
    • Basic Integration Rules
  • Summation (Sigma Notation) (video)
  • Area Under a Curve (video 1) (video 2) (video 3)
  • Fundamental Theorem of Calculus
  • Definite Integrals
  • Integration by Substitution (video 1(video 2(video 3)
    • How can integration by substitution be used to solve problems?
          1. Integrate by substitution.
        1. Checkpoints

      • Summative Exam 2

          Exit Ticket
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          Lesson Objective(s)
          • Summative Exam 2
              1. Find critical numbers using differentiation.
              2. Find extrema on a closed interval using differentiation.
              3. Apply understanding of Rolle’s Theorem and the Mean Value Theorem.
              4. Determine intervals on which a function is increasing or decreasing.
              5. Apply the First Derivative Test to find relative extrema of a function.
              6. Determine intervals on which a function in concave upward or downward.
              7. Apply the Second Derivative Test to find inflection points of a function.
              8. Determine horizontal asymptotes using limits.
              9. Determine finite limits at infinity.
              10. Determine infinite limits at infinity.
              11. Determine the conditions that optimize a situation.
              12. Calculate the antiderivative of a function.
              13. Calculating the area under a curve using summation.
              14. Calculate the area under a curve using definite integration.
              15. Integrate by substitution.

                                                              In-Class Help Requests

                                                              • APC.10
                                                                • Use Riemann sums and the Trapezoidal Rule to approximate definite integrals of functions represented algebraically, graphically, and by a table of values and will interpret the definite integral as the accumulated rate of change of a quantity over an interval interpreted as the change of the quantity over the interval
                                                                • Riemann sums will use left, right, and midpoint evaluation points over equal subdivisions.
                                                              • APC.11
                                                                • ​The student will find antiderivatives directly from derivatives of basic functions and by substitution of variables (including change of limits for definite integrals).
                                                              • APC.12
                                                                • ​The student will identify the properties of the definite integral. This will include additivity and linearity, the definite integral as an area, and the definite integral as a limit of a sum as well as the fundamental theorem.
                                                              • APC.13
                                                                • ​The student will use the Fundamental Theorem of Calculus to evaluate definite integrals, represent a particular antiderivative, and facilitate the analytical and graphical analysis of functions so defined.
                                                              • APC.14
                                                                • ​The student will find specific antiderivatives, using initial conditions (including applications to motion along a line). Separable differential equations will be solved and used in modeling (in particular, the equation y' = ky and exponential growth).
                                                              • APC.15
                                                                • ​The student will use integration techniques and appropriate integrals to model physical, biological, and economic situations. The emphasis will be on using the integral of a rate of change to give accumulated change or on using the method of setting up an approximating Riemann sum and representing its limit as a definite integral. Specific applications will include
                                                                  • a)​ the area of a region;
                                                                  • b)​ the volume of a solid with known cross-section;
                                                                  • c)​ the average value of a function; and
                                                                  • d) ​the distance traveled by a particle along a line.

                                                              Past Checkpoints