DP Mathematics: Analysis and Approaches Questionbank

AHL 5.17—Areas under curve onto y-axis, volume of revolution (about x and y axes)
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[N/A]Directly related questions
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20N.1.AHL.TZ0.H_12a:
State the equation of the vertical asymptote on the graph of y=f(x).
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20N.1.AHL.TZ0.H_12b:
State the equation of the horizontal asymptote on the graph of y=f(x).
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20N.1.AHL.TZ0.H_12c:
Use an algebraic method to determine whether f is a self-inverse function.
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20N.1.AHL.TZ0.H_12d:
Sketch the graph of y=f(x), stating clearly the equations of any asymptotes and the coordinates of any points of intersections with the coordinate axes.
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20N.1.AHL.TZ0.H_12e:
The region bounded by the x-axis, the curve y=f(x), and the lines x=5 and x=7 is rotated through 2π about the x-axis. Find the volume of the solid generated, giving your answer in the form π(a+b ln 2) , where a, b ∈ ℤ.
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20N.2.AHL.TZ0.H_3a:
Determine the values of p, q and r.
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20N.2.AHL.TZ0.H_3b:
Hence find the area of the shaded region.
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20N.1.SL.TZ0.S_3a:
Find the value of a.
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20N.1.SL.TZ0.S_3b:
Find the volume of the solid formed when the shaded region is revolved 360° about the x-axis.
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21M.2.AHL.TZ2.11c.i:
Find OA.
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21M.2.AHL.TZ2.11a:
Show that the volume of the solid formed is 15k2π34 cubic units.
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21M.2.AHL.TZ2.11b:
Find the value of k that satisfies the requirements of Pedro’s design.
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21M.2.AHL.TZ2.11d.ii:
State the cross-sectional radius of the bowl at this point.
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21M.2.AHL.TZ2.11c.ii:
Find BC.
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21M.2.AHL.TZ2.11d.i:
By sketching the graph of a suitable derivative of f, find where the cross-sectional radius of the bowl is decreasing most rapidly.
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22M.2.AHL.TZ1.10c.i:
Show that the volume, V m3, of water in the container when it is filled to a height of h metres is given by V=π(13h3+h).
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22M.2.AHL.TZ1.10c.ii:
Hence, determine the maximum volume of the container.
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22M.2.AHL.TZ2.6:
The following diagram shows the curve x236+(y-4)216=1, where h≤y≤4.
The curve from point Q to point B is rotated 360° about the y-axis to form the interior surface of a bowl. The rectangle OPQR, of height h cm, is rotated 360° about the y-axis to form a solid base.
The bowl is assumed to have negligible thickness.
Given that the interior volume of the bowl is to be 285 cm3, determine the height of the base.
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19N.1.AHL.TZ0.H_10c:
Show that 3x+1−1x−1=2x−4x2−1.
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19N.1.AHL.TZ0.H_10d:
The area enclosed by the graph of y=f(x) and the line y=4 can be expressed as lnv. Find the value of v.
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19N.2.AHL.TZ0.H_11b:
Find the area of R.
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19N.2.AHL.TZ0.H_11c:
The region R is now rotated about the y-axis, through 2π radians, to form a solid.
By writing sin3y as (1−cos2y)siny, show that the volume of the solid formed is 2π3.
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19N.2.SL.TZ0.S_8a:
Find the value of p.
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19N.2.SL.TZ0.S_8b.i:
Write down the coordinates of A.
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19N.2.SL.TZ0.S_8b.ii:
Find the equation of the tangent to the graph of f at A.
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19N.2.SL.TZ0.S_8c.i:
Find the coordinates of B.
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19N.2.SL.TZ0.S_8c.ii:
Find the rate of change of f at B.
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19N.2.SL.TZ0.S_8d:
Let R be the region enclosed by the graph of f, the x-axis and the lines x=p and x=b. The region R is rotated 360º about the x-axis. Find the volume of the solid formed.
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18N.2.SL.TZ0.S_10b.i:
Find the value of p and of q.
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18N.2.SL.TZ0.S_10c:
When t = 0, the volume of water in the container is 2.3 m3. It is known that the container is never completely full of water during the 4 hour period.
Find the minimum volume of empty space in the container during the 4 hour period.
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17M.2.AHL.TZ2.H_2b:
Find the volume of the solid formed when the region bounded by the curve, the x-axis for x⩾ and the -axis for is rotated through about the -axis.
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18N.2.SL.TZ0.S_10a:
Find the volume of the container.
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18N.2.SL.TZ0.S_10b.ii:
During the interval < < , he volume of water in the container increases by m3. Find the value of .
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16N.2.SL.TZ0.S_6a:
Use the model to find the volume of the barrel.
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16N.2.SL.TZ0.S_6b:
The empty barrel is being filled with water. The volume of water in the barrel after minutes is given by . How long will it take for the barrel to be half-full?
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17N.2.SL.TZ0.S_5b:
The following diagram shows part of the graph of .
The region enclosed by the graph of , the -axis and the lines and is rotated 360° about the -axis. Find the volume of the solid formed.
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17N.2.SL.TZ0.S_5a:
Find the value of .