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AB Calculus Question Strategies
 

AB Calculus Question Strategies

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A guide to approaching AB Calculus AP Questions

A guide to approaching AB Calculus AP Questions

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    AB Calculus Question Strategies AB Calculus Question Strategies Presentation Transcript

    • When you see… Find the zeros You think…
    • To find the zeros...
    • You think… When you see… Show that f ( x ) is even
    • Even function
    • You think… When you see… Show that f ( x ) is odd
    • Odd function
    • You think… When you see… Show that exists
    • Show exists
      • Show that
    • You think… When you see…
    • Find Limit with calculator
    • You think… When you see…
    • Find limits, no calculator
    • You think… When you see…
    • Find limit with calculator
    • You think… When you see…
    • Find limit, no calculator
    • You think… When you see… Find horizontal asymptotes of f ( x )
    • Find horizontal asymptotes of f(x)
    • You think… When you see… Find vertical asymptotes of f ( x )
    • Find vertical asymptotes of f(x)
    • You think… When you see… Find the domain of f ( x )
    • Find the domain of f(x)
    • You think… When you see… Show that f ( x ) is continuous
    • . f(x) is continuous
    • You think… When you see… Find the slope of the tangent line to f(x) at x = a
    • Slope of tangent line
    • When you see… Find equation of the line tangent to f ( x ) at ( a , b ) You think…
    • Equation of the tangent line
    • You think… When you see… Find equation of the line normal to f ( x ) at ( a , b )
    • Equation of the normal line
    • You think… When you see… Find the average rate of change of f ( x ) at [ a , b ]
    • Average rate of change of f(x)
      • Find
      • f (b) - f ( a)
      • b - a
    • You think… When you see…
    • Intermediate Value Theorem (IVT)
    • You think… When you see… Find the interval where f ( x ) is increasing
    • f (x) increasing
    • You think… When you see… Find the interval where the slope of f ( x ) is increasing
    • Slope of f (x) is increasing
    • You think… When you see… Find the instantaneous rate of change of f ( x ) on [ a , b ]
    • Instantaneous rate of change of f(x)
      • Find f ‘ ( a)
    • You think… When you see… Given s ( t ) (position function), find v ( t )
    • Given position s(t), find v(t)
    • You think… When you see… Find f ’ ( x ) by the limit definition
    • Find f ‘ ( x) by definition frequently asked backwards
    • You think… When you see… Find the average velocity of a particle on [ a , b ]
    • Find the average rate of change on [a,b]
    • You think… When you see… Given v ( t ) , determine if a particle is speeding up at t = k
    • Given v(t), determine if the particle is speeding up at t = k
    • You think… When you see… Given a graph of find where f ( x ) is increasing
    • Given a graph of f ‘(x) , find where f(x) is increasing
    • You think… When you see…
    •  
    • You think… When you see…
    • Relative maximum
    • You think… When you see…
    • Concave Down
    • You think… When you see…
    • Points of Inflection
    • You think… When you see… Show that a piecewise function is differentiable at the point a where the function rule splits
    • Show a piecewise function is differentiable at x=a
    • You think… When you see…
    • Derivative of Inverse Function
    • You think… When you see…
    • Derivative of the inverse of f(x)
    • You think… When you see…
    • Derivative Rules
    • You think… When you see…
    • Implicit Differentiation
    • You think… When you see… Find the derivative of f ( g ( x ))
    • Chain Rule
    • You think… When you see… Find the minimum value of a function
    • Minimum value of a function
    • You think… When you see… Find the minimum slope of a function
    • Minimum slope of a function
    • You think… When you see… Find critical numbers
    • Find critical numbers
    • You think… When you see… Find the absolute maximum of f ( x )
    • Find the absolute minimum of f(x)
    • You think… When you see…
    • Rolle’s Theorem
    • You think… When you see…
    • Mean Value Theorem
    • You think… When you see… Find the range of f ( x ) on [ a , b ]
    • Find the range of f(x) on [a,b]
    • You think… When you see… Find the range of f ( x ) on
    • Find the range of f(x) on
    • You think… When you see…
    • Second Derivative Test
    • You think… When you see…
    • Find inflection points
    • You think… When you see…
    • . y = mx+b is tangent to f(x) at a point
    • You think… When you see…
    • Horizontal tangent line
    • You think… When you see…
    • Vertical tangent line to f(x)
    • You think… When you see… Approximate the value f (0.1) of by using the tangent line to f at x = 0
    • Approximate f(0.1) using tangent line to f(x) at x = 0
    • You think… When you see… Find rates of change for volume problems
    • Rates of Change of Volumes
    • You think… When you see… Find rates of change for Pythagorean Theorem problems
    • Pythagorean Rates of Change
    • You think… When you see…
    • Average value of the function
    • You think… When you see…
    • Average Rate of Change
    • You think… When you see… Given v ( t ) , find the total distance a particle travels on [ a , b ]
    • Given v(t), find the total distance a particle travels on [a,b]
    • You think… When you see… Given v ( t ) , find the change in position of a particle on [ a , b ]
    • Given v(t), find the change in position of a particle on [a,b]
    • You think… When you see…
    • Given v(t) and the initial position of a particle, find the position at t = a .
    • You think… When you see…
    • Fundamental Theorem
    • You think… When you see…
    • Fundamental Theorem, again Chain Rule, too
    • You think… When you see… Find area using left Riemann sums
    • Area using left Riemann sums
    • You think… When you see… Find area using right Riemann sums
    • Area using right Riemann sums
    • You think… When you see… Find area using midpoint rectangles
    • Area using midpoint rectangles
    • You think… When you see… Find area using trapezoids
    • Area using trapezoids
    • You think… When you see… Describe how you can tell if rectangle or trapezoid approximations over- or under-estimate area.
    • Over- or Under-estimates
    • You think… When you see… Given , find
    • Given area under a curve and vertical shift, find the new area under the curve
    • You think… When you see… Given , draw a slope field
    • Draw a slope field of dy/dx
    • You think… When you see… y is increasing proportionally to y
    • . y is increasing proportionally to y
    • You think… When you see… Solve the differential equation …
    • Solve the differential equation...
    • You think… When you see… Given a base, cross sections perpendicular to the x -axis that are squares
    • Semi-circular cross sections perpendicular to the x-axis
    • You think… When you see… Given the value of F ( a ) and the fact that the anti-derivative of f is F , find F ( b )
    • Given F ( a ) and the that the anti-derivative of f is F , find F ( b )
    • You think… When you see… Meaning of
    • Meaning of the integral of f(t) from a to x
    • You think… When you see… Given v ( t ) and s (0) , find the greatest distance from the origin of a particle on [ a , b ]
    • Given v ( t ) and s (0) , find the greatest distance from the origin of a particle on [ a , b ]
    • When you see…
    • You think…
      • the amount of water in
      • the tank at m minutes
    • Amount of water in the tank at t minutes
    • You think… b) the rate the water amount is changing at m
    • Rate the amount of water is changing at t = m
    • You think… c) the time when the water is at a minimum
    • The time when the water is at a minimum
    • You think… When you see…
    • Area between f(x) and g(x) on [a,b]
    • You think… When you see…
    • Volume generated by rotating area between f(x) and g(x) about the x-axis
    • You think… When you see… Given v ( t ) and s (0), find s ( t )
    • Given v(t) and s(0), find s(t)
    • You think… When you see… Find the line x = c that divides the area under f ( x ) on [ a , b ] into two equal areas
    • Find the x=c so the area under f(x) is divided equally OR
    • You think… When you see…
    • Semi-circular cross sections perpendicular to the x-axis