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AP Exam The Final Hours of Test Prep…
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Tonight Dont cram – youve spent a month studying for this exam! Spend a little time reviewing –Practice tests –FRQs –Stand and Deliver Relax Calculator check – good batteries, radians Go to bed early – get a good nights rest
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Tomorrow Morning Get up early Eat a good, healthy breakfast –Avoid sugar or caffeine (its a long test… your blood sugar will spike and drop!) Be confident!
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During the Test Focus on the problems you know Star and come back to other questions later (esp. on FRQs!) READ carefully! MC – eliminate answers, guessing is ok! FRQs –NEAT and ORGANIZED work! –Use proper notation, ( ), dx, units –Start with the questions you know!
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GOOD LUCK!! YOU CAN DO IT! Youve studied and worked soooo hard Be confident!
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When you see… Find equation of the line tangent to f(x) at (a, b) You think…
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Equation of the tangent line
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You think… When you see… Find the interval where f(x) is increasing
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f(x) increasing
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You think… When you see… Find the interval where the slope of f (x) is increasing
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Slope of f (x) is increasing
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You think… When you see… Find the minimum value of a function
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Minimum value of a function
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You think… When you see… Find the minimum slope of a function
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Minimum slope of a function
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You think… When you see… Find critical numbers
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You think… When you see… Find inflection points
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You think… When you see… Show that f(x) is continuous
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. f(x) is continuous
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You think… When you see… Find horizontal asymptotes of f(x)
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You think… When you see… Find the average rate of change of f(x) at [a, b]
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Average rate of change of f(x) Find f (b) - f ( a) b - a
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You think… When you see… Find the instantaneous rate of change of f(x) on [a, b]
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Instantaneous rate of change of f(x) Find f ( a)
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You think… When you see…
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Average value of the function
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You think… When you see… Show that a piecewise function is differentiable at the point a where the function rule splits
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Show a piecewise function is differentiable at x=a
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You think… When you see… Given s(t) (position function), find v(t)
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Given position s(t), find v(t)
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You think… When you see… Given v(t), find how far a particle travels on [a, b]
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You think… When you see… Given v(t) and s(0), find s(t)
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Given v(t) and s(0), find s(t)
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You think… When you see… Show that the Mean Value Theorem holds on [a, b]
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Show that the MVT holds on [a,b]
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You think… When you see… Find f (x) by definition
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You think… When you see… y is increasing proportionally to y
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y is increasing proportionally to y. y is increasing proportionally to y
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You think… When you see…
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Fundamental Theorem
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You think… When you see…
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Fundamental Theorem, again
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You think… When you see… The rate of change of population is …
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Rate of change of a population
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You think… When you see… The line y = mx + b is tangent to f(x) at (a, b)
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y = mx+b is tangent to f(x) at (a,b). y = mx+b is tangent to f(x) at (a,b)
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You think… When you see… Find area using left Riemann sums
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Area using left Riemann sums
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You think… When you see… Find area using right Riemann sums
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Area using right Riemann sums
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You think… When you see… Find area using midpoint rectangles
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Area using midpoint rectangles
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You think… When you see… Find area using trapezoids
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Area using trapezoids
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You think… When you see… Solve the differential equation …
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Solve the differential equation...
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You think… When you see… Meaning of
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Meaning of the integral of f(t) from a to x
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You think… When you see… Given a base, cross sections perpendicular to the x-axis that are squares
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Semi-circular cross sections perpendicular to the x-axis
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You think… When you see… Find where the tangent line to f(x) is horizontal
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Horizontal tangent line
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You think… When you see… Find where the tangent line to f(x) is vertical
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Vertical tangent line to f(x)
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You think… When you see… Find the minimum acceleration given v(t)
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Given v(t), find minimum acceleration
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You think… When you see… Approximate the value f(0.1) of by using the tangent line to f at x = 0
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Approximate f(0.1) using tangent line to f(x) at x = 0
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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)
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Given F(a) and the that the anti-derivative of f is F, find F(b)
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You think… When you see… Given, find
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Given area under a curve and vertical shift, find the new area under the curve
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You think… When you see… Given a graph of find where f(x) is increasing
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Given a graph of f (x), find where f(x) is increasing
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You think… When you see… Given v(t) and s(0), find the greatest distance from the origin of a particle on [ a, b ]
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When you see… Given a water tank with g gallons initially being filled at the rate of F(t) gallons/min and emptied at the rate of E(t) gallons/min on, find
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You think… a)the amount of water in the tank at m minutes
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Amount of water in the tank at t minutes
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You think… b) the rate the water amount is changing at m
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Rate the amount of water is changing at t = m
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You think… c) the time when the water is at a minimum
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The time when the water is at a minimum
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You think… When you see… Given a chart of x and f(x) on selected values between a and b, estimate where c is between a and b.
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You think… When you see… Given, draw a slope field
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Draw a slope field of dy/dx
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You think… When you see… Find the area between curves f(x) and g(x) on [a,b]
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Area between f(x) and g(x) on [a,b]
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You think… When you see… Find the volume if the area between the curves f(x) and g(x) is rotated about the x -axis
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Volume generated by rotating area between f(x) and g(x) about the x-axis
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