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Content
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(file size: 196 KB)
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The concept of derivatives doesn’t exist for students yet, but they are asked to find the slope of the secant line between 2 points on a curve as well as the slope and equation of the tangent line at a point. Also average and instantaneous rate of change at a given time.
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(file size: 153 KB)
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Same as above.
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(file size: 477 KB)
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Look at a graph and determine the limit as x approaches a number as well as positive or negative infinity.
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(file size: 479 KB)
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Find limits as x approaches a number or infinity of algebraic function. Students are required to use problem notation as well as splitting limits into left and right-hand limits.
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Power, product, and quotient rule, as well as finding derivatives by definition. Finding equation of tangent lines too.
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Students are aware that calculators can find derivatives of functions at specific values. This quiz, using tables, tests students on their knowledge of the power, product, quotient, and chain rules where calculators do them little good.
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Emphasizes the basic rules as well as the chain rule and implicit differentiation.
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Same as above.
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Emphasizes the chain rule as used with trig functions. Implicit differentiation at a point or in general tested as well.
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Same as above
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Given a piecewise function, determine whether it is continuous, differentiable, both or neither at a point. Also fund values of constants to make a piecewise function differentiable.
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A 30-question multiple choice exam testing all concepts up through differentiability.
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A seven question related rates exam using problems similar to the ones in the manual.
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Given a position function, find velocity, acceleration and whether the particle is speeding up or slowing down. Also vertical motion problems.
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For the topic of function analysis, students need to be able to examine the derivative of a function and determine whether the function is increasing or decreasing, concave up or down, and to sketch the shape of the function. These problems are given, sometimes all within one week to nail down this difficult concept for students.
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See above.
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See above
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See above
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Given a function, find the absolute maximum or minimum value of the function on an interval.
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A six question optimization exam using problems similar to the ones in the manual.
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I like to give students problems to do over the winter holiday to keep their skills sharp. These are 40 question multiple choice that emphasize max/mins and concavity.
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Just a small exam emphasizing the power rule and trig for integration as well as a differential equation.
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Time to put all their acts together with a big exam. This is a 45 question multiple choice exam testing all concepts through basic integration.
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Basic indefinite integration emphasizing u-substitution.
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Riemann sums as well as the trapezoidal rule. Calculators are needed. This can be given as a take-home exam as each problem as three possibilities so that students can get different versions of the exams.
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Given a piecewise curve, students are asked to find definite integrals between various values utilizing geometric formulas. Also, examine the accumulation function based on this graph.
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Same as above
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Finding definite integrals of algebraic functions, u-substitution and changing the limits, the average value formula as well as the 2nd Fundamental Theorem.
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Same as above
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By the time this topic is taught, time is at a premium. I have a 2-page exam for the concepts with 3 variations for each page. This can be given as a take-home with cheating difficult to accomplish or an in-class exam.
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Derivatives and integrals using the natural log (ln) function as well as the exponential function.
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Same as above
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Find the derivative of the inverse of a function at a point (with and without calculator) as well as the derivative of an inverse trig function and an integral resulting in an inverse trig function.
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Creating a slope field, solving separable DEQ’s as well as solving an exponential growth problem.
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