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It also includes Question 4 procedures for inflection points, absolute extrema, and tangents for a derived function g(x)=x 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is the area of region R in Question 1 determined?","Question",{"text":63,"@type":64},"Compute the area of the region enclosed by the given curves and boundaries as required in part (a), using the scoring-guideline setup for the described region.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"What does Question 2 require to decide whether the mosquito population is increasing at an increasing or decreasing rate at t=6?",{"text":68,"@type":64},"Use the model’s derivative information at t=6 to determine the sign of R'(6) and interpret it as increasing with a decreasing rate.",{"name":70,"@type":61,"acceptedAnswer":71},"How do you form the tangent line equation for g(x)=x f(x) at x=2 in Question 4?",{"text":72,"@type":64},"Differentiate g(x)=x f(x) to get g'(x)=f(x)+x f'(x), evaluate at x=2 to find slope, and use point information with the tangent-line form 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B)\n\nQuestion 1  \nLet R be the region enclosed by the graph of y=√x-1,the vertical line x=10,and the x-axis.  \n(a)Find the area of R.  \n(b)Find the volume of the solid generated when R is revolved about the horizontal line y=3.  \n(c)Find the volume of the solid generated when R is revolved about the vertical line x=10.  \n(a)  \n=212.057 or 212.058=407.150  \n# AP®CALCULUS AB2004 SCORING GUIDELINES (Form B)\n\nQuestion 2  \nFor 0≤t≤31,the rate of change of the number of mosquitoes on Tropical Island at time t days ismodeled bymosquitoes per day.There are 1000 mosquitoes on Tropical Island attime t=0.  \n(a)Show that the number of mosquitoes is increasing at time t=6.  \n(b)At time t=6,is the number of mosquitoes increasing at an increasing rate,or is the number ofmosquitoes increasing at a decreasing rate?Give a reason for your answer.  \n(c)According to the model,how many mosquitoes will be on the island at time t=31?Round youranswer to the nearest whole number.  \n(d)To the nearest whole number,what is the maximum number of mosquitoes for 0≤t≤31?Showthe analysis that leads to your conclusion.  \n(a)Since R(6)=4.438>0,the number of mosquitoes is1:shows that R(6)>0increasing at t=6.(b)R'(6)=-1.913  \nSince R'(6)\u003C0,the number of mosquitoes isincreasing at a decreasing rate at t=6.To the nearest whole number,there are 964mosquitoes.  \n(d)R(t)=0 when t=0,t=2.5π,or t=7.5πR(t)>0 on 0\u003Ct\u003C2.5πR(t)\u003C0 on 2.5π\u003Ct\u003C7.5πR(t)>0 on 7.5π\u003Ct\u003C31  \nThe absolute maximum number of mosquitoes occursat t=2.5π or at t=31.1000+  \nThere are 964 mosquitoes at t=31,so the maximumnumber of mosquitoes is 1039,to the nearest wholenumber.  \n# AP®CALCULUS AB2004 SCORING GUIDELINES (Form B)\n\nQuestion 3  \nA test plane flies in a straight line withpositive velocity v(t),in miles perminute at time t minutes,where v is adifferentiable function of t.Selected  \n\n| t(min)   | 0   | 5   | 10   | 15   | 20   | 25   | 30   | 35   | 40   |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| v(t)(mpm)   | 7.0   | 9.2   | 9.5   | 7.0   | 4.5   | 2.4   | 2.4   | 4.3   | 7.3   |\n\nvalues of v(t)for 0≤t≤40 are shown in the table above.  \n(a)Use a midpoint Riemann sum with four subintervals of equal length and values from the table toapproximate)dt.Show the computations that lead to your answer.Using correct units,explain the meaning of)dt in terms of the plane's flight.  \n(b)Based on the values in the table,what is the smallest number of instances at which the accelerationof the plane could equal zero on the open interval 0\u003Ct\u003C40?Justify your answer.  \n(c)The function f,defined by,is used to model the velocity of theplane,in miles per minute,for 0≤t≤40.According to this model,what is the acceleration of theplane at t=23?Indicates units of measure.  \n(d)According to the model f,given in part(c),what is the average velocity of the plane,in miles perminute,over the time interval 0≤t≤40?  \n\n| (a)   | Midpoint Riemann sum is   |  |\n| --- | --- | --- |\n|  | 10·[v(5)+v(15)+v(25)+v(35)]  \u003Cbr>=10·[9.2+7.0+2.4+4.3]=229   |  |\n|  |  |  |\n| The integral gives the total distance in miles that the  \u003Cbr>plane flies during the 40 minutes.   |  |  |\n| (b)   | By the Mean Value Theorem,v'(t)=0 somewhere in  \u003Cbr>the interval(0,15)and somewhere in the interval  \u003Cbr>(25,30).Therefore the acceleration will equal0 for at  \u003Cbr>least two values of t.   |  |\n|  |  |  |\n| (c)   | f'(23)=-0.407 or-0.408 miles per minute²   | 1:answer with units   |\n|  |  |  |\n| (d)   |  | 3:   |\n|  | =5.916 miles per minute   |  |\n\n# AP®CALCULUS AB2004 SCORING GUIDELINES (Form B)\n\nQuestion 4  \nThe figure above shows the graph of f\",the derivative of the function f,on the closed interval-1≤x≤5.The graph of f'has horizontal tangentlines at x=1 and x=3.The function f is twice differentiable withf(2)=6.  \n(a)Find the x-coordinate of each of the points of inflection of the graphof f.Give a reason for your answer.  \n(b)At what value of x does f attain its absolute minimum value on thecl","cbCaihtBXzN0j5f5","https://ap.wps.com/l/cbCaihtBXzN0j5f5","pdf",139000,"English","# Question 1\n## Area and volumes by revolution\n# Question 2\n## Mosquito model, increasing/decreasing rate, maximum\n# Question 3\n## Midpoint Riemann sum, acceleration zero, acceleration at a time, average velocity\n# Question 4\n## Inflection points, absolute extrema, tangent line for g(x)=x f(x)","[{\"question\":\"How is the area of region R in Question 1 determined?\",\"answer\":\"Compute the area of the region enclosed by the given curves and boundaries as required in part (a), using the scoring-guideline setup for the described region.\"},{\"question\":\"What does Question 2 require to decide whether the mosquito population is increasing at an increasing or decreasing rate at t=6?\",\"answer\":\"Use the model’s derivative information at t=6 to determine the sign of R'(6) and interpret it as increasing with a decreasing rate.\"},{\"question\":\"How do you form the tangent line equation for g(x)=x f(x) at x=2 in Question 4?\",\"answer\":\"Differentiate g(x)=x f(x) to get g'(x)=f(x)+x f'(x), evaluate at x=2 to find slope, and use point information with the tangent-line form y=g'(2)(x-2)+g(2).\"}]","AP Calculus AB 2004 Scoring Guidelines (Form B) - Review 8 key | PDF",13]