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AP Calculus ABPractice Exam

Calculus ABSection 1, Part ATime - 55 minutesNumber of questions - 28A CALCULATOR MAY NOT BE USED ON THIS PART OF THE EXAMDirections:Solve all of the problems that follow. Available space on the page may be used forscratch work.In this exam:(1)The domain of a function in this exam is assumed to be all real numbers for which thefunction is defined, unless specified otherwise.(2)The inverse notationor the prefix “arc” may be used to indicate an inverse function.For example, the inverse tangent ofCopyright 2015 by Lucid Educationxxmay be written as arcsin( ) or as.

Section 1, Part ACalculus AB1.Using the substitution,the integralis equivalent toA)B)C)D)E)2.Find.A)B)C)D)E)Copyright 2015 by Lucid EducationGo on to the next page

Section 1, Part ACalculus AB3. A line through the point (2, -2) is tangent to functionA) -84.B)-2C)D)f6at the point (-2, 6).E)Grain is pouring out of an opening in the bottom of a grain silo.What isUndefinedThe rate at which the height,h, of the grain in the silo is changing with respect to time, t, is proportional to the square root ofthe height.Which of the following is a differential equation describing this situation?A)B)C)D)E)Copyright 2015 by Lucid Education?Go on to the next page

Section 1, Part ACalculus AB5.Where is the graph ofA)6.concave up?B)C)Shown is a graph of functionAt which value of xA) aB)isD)E)f.f continuous but not differentiable?bCopyright 2015 by Lucid EducationC)cD)dE)eGo on to the next page

Section 1, Part ACalculus AB7.The table shows values of, the derivative of functionreal numbers, only selected values ofxIff.Althoughis continuous over allare shown.-2-101234564.12.31.20-0.6-0.8-201.5has exactly two real zeros, thenfis increasing over which of the following intervals?A)B)C)onlyD)E)8.A)B)C)D)E)Copyright 2015 by Lucid EducationGo on to the next page

Section 1, Part ACalculus AB9. At each point (x,graph offy) on a graph of function f, the graph has a slope equal to.If thegoes through the point (2, 3), thenA)B)C)D)E)10.The derivative of functiong is given by.When isg increasing?A)B)C)D)E)Copyright 2015 by Lucid EducationGo on to the next page

Section 1, Part ACalculus AB11.Functionfis defined asWhich of the following statements is true:I.fis continuous atII.III.exists.fis differentiable atA) None of the statements are true.B)I onlyC)II onlyD)I and II onlyE)I, II, and III12.A)B)Copyright 2015 by Lucid EducationC)D)E)Go on to the next page

Section 1, Part ACalculus AB13.Shown is a graph ofequation, the second derivative of function.The graph of.The curve is given by thehas inflection points at which values ofx?A) b only14.B)c onlyC)a and dD)a and cE)d onlyFunctionfis defined such that for all, the lineis a horizontal asymptote.Which of the following must be true?A)B)is undefined.for all.C)D) All of the above.E)None of the above.Copyright 2015 by Lucid EducationGo on to the next page

Section 1, Part ACalculus AB15.Shown in the diagram is a graph of, the derivative of function.If, then?A)B)C)D)E)16.A)B)Copyright 2015 by Lucid EducationC)D)E)Go on to the next page

Calculus ABSection 1, Part A17.A.B.C.D.E.18.A)B)C)D)E)Copyright 2015 by Lucid EducationGo on to the next page

Section 1, Part ACalculus AB19.fLetgraph offbe the function defined byat.The equation of the line tangent to theisA.B.C.D.E.20.A)B)Copyright 2015 by Lucid EducationC)D)E)2Go on to the next page

Section 1, Part ACalculus AB21. A particle’s position at any time is given by the equationAt what time is the particle at rest?A)22.andB)andC)andD)onlyE)onlyShown is a graph of, the derivative of functionf.Which of the following statements is true?A)B)C)D)E)fffffis not differentiable at.has a local minimum atis increasing from.tois increasing fromtois decreasing fromtoCopyright 2015 by Lucid Education.Go on to the next page

Section 1, Part ACalculus AB23.What is the slope the line tangent to the curveA)B)C)at the point (2, 3) ?D)E)24.A)B)C)D)E)Copyright 2015 by Lucid EducationGo on to the next page

Section 1, Part ACalculus AB25.isFunctionfis defined by the equation.Ifand, what?A)B)26.C).A)B)Copyright 2015 by Lucid EducationFindC)D)E)D)E).does not exist.Go on to the next page

Section 1, Part ACalculus AB27.Functionnumbersx.fis a twice differentiable function withIfandA) 728.,B), and9C)12D)13E)x.for all real?, what is a possible value forare all positive for any real numbergraphs could be a graph ofA)and17Which of the following?B)C)D)E)End of Section 1, Part AIf you finish before the time limit for this part, check your work on this part only.Do move on to the next part until you are told to by the test administrator.Copyright 2015 by Lucid Education

Calculus ABSection 1, Part BTime - 50 minutesNumber of questions - 17A GRAPHING CALCULATOR MAY BE REQUIRED TO SOLVE SOME QUESTIONSON THIS PART OF THE EXAMDirections:Solve all of the problems that follow. Available space on the page may be used forscratch work.You may not return to the previous section of the exam.In this exam:(1)The domain of a function in this exam is assumed to be all real numbers for which thefunction is defined, unless specified otherwise.(2)The inverse notationor the prefix “arc” may be used to indicate an inverse function.For example, the inverse tangent of(3)xxmay be written as arcsin( ) or as.The exact numerical answer for a problem may not be listed as one of the given choices.When this is the case, choose the value that is the closest approximation to exact value.Copyright 2015 by Lucid Education

Section 1, Part BCalculus AB76.ofThe derivative of functionff. At what values of xis given bydoes the graphhave an inflection point?A. 077.B.0.382C.0.775D.1.136E.The graph has no inflection point.The region in theof a solid.x-y plane bounded by the lines,Each cross section of the solid perpendicular to the,, andx-axis is a square.is the baseThe volume ofthe solid isA. 3.85B.2.70Copyright 2015 by Lucid EducationC.2.97D.6.70E.5.41Go on to the next page

Section 1, Part BCalculus AB78.Function.fis differentiable andand.FunctionWhat is the equation of the line tangent to functiong atg is defined as.A.B.C.D.E.79.Which could be a graph ofA.D.Copyright 2015 by Lucid Educationfsuch thatB.?C.E.Go on to the next page

Section 1, Part BCalculus AB80.The acceleration of a particle moving along the, the velocity of the particle is 2. At timex-axis is given by?What is the velocity at timeA. -0.44181.B.3.099C.3.178D.4.872E.5.313Shown are selected values for functionsin the closed interval [1, 4].f, g, h, j, and k, all of which are twice differentiableWhich of the functions has a negative first derivative and a positivesecond derivative?A.D.x1234f (x)1412108B.x1234g (x)1413118x1234j (x)891114E.x1234k (x)9111314Copyright 2015 by Lucid EducationC.x1234h (x)141198Go on to the next page

Section 1, Part BCalculus AB82. A particle is moving such that its velocity at any time tWhat is the acceleration of the particle whenis given by.?A. -0.34183.B.-0.568C.-0.947D.1.24E.1.46Functionfis defined asfor.On what interval isfdecreasing?A.B.C.D.E.Copyright 2015 by Lucid EducationGo on to the next page

Section 1, Part BCalculus AB84.If a circle’s radius is increasing at a constant rate ofarea of the circle when the circle’s circumference is, what is the rate of change of themeters?A.B.C.D.E.85.Function(-1, 3).Iffis continuous on the closed interval [-1, 3] and differentiable on the open intervaland, which of the following statements must be true?A. There exists a number con (-1, 3) such thatB.There exists a numberc on (-1, 3) such thatC.There exists a numberc on (-1, 3) such thatD.There exists a numberc on (-1, 3) such thatE.There exists a numberc on (-1, 3) such thatCopyright 2015 by Lucid Education.for allxGo on to the next page

Section 1, Part BCalculus AB86.For which of the graphs shown does theI.exist?II.III.A) I onlyB)II onlyC)I and II onlyD)III onlyE)I and III only87.interval.A. 2How many relative extrema does functionB.3Copyright 2015 by Lucid EducationC.4D.5have on theE.7Go on to the next page

Section 1, Part BCalculus AB88. A remote control helicopter is launched. During the first 6 seconds of flight, the rate ofchange of the helicopter’s altitude is given by the equation.Which of thefollowing expressions represents the helicopter’s change in altitude during the time that thealtitude is increasing?A.B.C.D.E.89. A potato is baked at a temp of 400EF. At timeEto cool in a 72 F room.it is taken out of the oven and allowedThe rate of change of the potato’s temperature is given by the equationwheret is the time in minutes.What is the potato’s temperature, to thenearest degree, after it has cooled for four minutes?A. 104B.193Copyright 2015 by Lucid EducationC.207D.333E.370Go on to the next page

Section 1, Part BCalculus AB90.The integralis under approximated by a trapezoidal sum and over approximatedby a left Riemann sum.?Which of the following could be a graph ofA.B.D.C.E.91. An object is moving along the x-axis such that its velocity in m/s is given by.A. 25.95What is the average velocity of the object from timeB.26.04Copyright 2015 by Lucid EducationC.27.26D.54.08E.to time?104.17Go on to the next page

Section 1, Part BCalculus AB92. A graph of function1, 2, and 3 respectively.A. 2B.on the interval [-1, 4] is shown. Regions A, B, and C have areas ofWhat is4?C.10D.12E.16End of Section 1, Part BIf you finish before the time limit for this part, check your work on this part only.Do move on to the next part until you are told to by the test administrator.Copyright 2015 by Lucid Education

Calculus ABSection 2, Part ATime - 30 minutesNumber of problems - 2A graphing calculator is required for these problems

Section 2, Part ACalculus AB1. A hot air balloon is launched at timedifferentiable function of time,t.Its altitude in meters is modeled by a twiceFor, the altitudeh at various times is shown inthe table.a)t (min)02356910h (meters)0280330240270420340From the data shown, estimate the rate at whichh is changing at.Show your work.Indicate units of measure.b)Use a trapezoidal approximation with three subintervals to estimate the average height of theballoon during the first five minutes of its flight.c)During the time intervalzero?, what is the least number of times thatmust beJustify your answer.d) A pressurized propane tank supplies propane to the burner. The rate at which propane isdispensed is given by the functionliters per minute.How many liters of propane aredispensed in the first five minutes?Copyright 2015 by Lucid EducationGo on to the next page

Section 2, Part ACalculus AB2.The region W in thex-y plane is bound byandandthey-axis, as shown in the diagram.a)Find the area of region W.b)The horizontal linedivides region W into two sections,for the area of the lower section.c)Consider the region W to be the base of a solid S.perpendicular to thed)x-axis are squares.The cross sections of the solidFind the volume of S.The region W is a top view of an experimental aircraft wing.distancex from the y-axis is given by the functionCopyright 2015 by Lucid EducationWrite an integral expressionDo not evaluate the integral.The thickness of the wing at anyFind the volume of the wing.

End of Section 2, Part AIf you finish before the time limit for this part, check your work on this part only.Do move on to the next part until you are told to by the test administrator.

Calculus ABSection 2, Part BTime - 60 minutesNumber of problems - 4Calculator use is not permitted on these problemsCopyright 2015 by Lucid Education