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Sample Questions

 

Calculus I

 

Rate of Change

 

1) What is the rate of change of the circumference of a circle with respect to its radius, r?

 a)  π.
 b)  2 * π.
 c)  π / 2.
 d)  2.0.
 e)  None of the above.



2) What is the rate of change of the circumference of a circle when its radius equals 10.0?

 a)  31.4.
 b)  10 * π.
 c)  5 * π.
 d)  2 * π.
 e)  None of the above.



3) What is the rate of change of the circumference of a circle when its radius equals 6.0?

 a)  31.4.
 b)  18.8.
 c)  2 * π.
 d)  π / 6.
 e)  None of the above.



4) What is the rate of change of the area of a circle with respect to its radius, r?

 a)  2 * π * r.
 b)  2 * π.
 c)  2 * π / r.
 d)  π * r.
 e)  None of the above.



5) What is the rate of change of the area of a circle when its radius equals 5.0?

 a)  2 * π.
 b)  π / 5.
 c)  5 * π.
 d)  10 * π.
 e)  None of the above.



6) What is the rate of change of the area of a circle when its radius equals 8.0?

 a)  16 * π.
 b)  π / 16.
 c)  16 + π.
 d)  8 * π.
 e)  None of the above.



7) What is the rate of change of the volume of a sphere with respect to its radius, r?

 a)  4 * π * r3.
 b)  4/3 * π * r3.
 c)  4 * π * r2.
 d)  4 * π * r3.
 e)  None of the above.



8) What is the rate of change of the volume of a sphere when its radius equals 1.0?

 a)  8 * π.
 b)  4 * π.
 c)  2 * π.
 d)  π.
 e)  None of the above.



9) What is the rate of change of the volume of a sphere when its radius equals 2.0?

 a)  16 * π.
 b)  8 * π.
 c)  4 * π.
 d)  2 * π.
 e)  None of the above.



10) What is the rate of change of the surface area of a cube with respect to its side length, s?

 a)  6 * s2.
 b)  12 * s.
 c)  12 * s2.
 d)  6 * s.
 e)  None of the above.



11) What is the rate of change of the surface of a cube when its side length equals 4.0?

 a)  12.0.
 b)  24.0.
 c)  36.0.
 d)  48.0.
 e)  None of the above.



12) What is the rate of change of the surface of a cube when its side length equals 10.0?

 a)  120.0.
 b)  60.0.
 c)  90.0.
 d)  150.0.
 e)  None of the above.



13) What is the rate of change of the surface area of a sphere with respect to its radius, r?

 a)  8 * π * r2.
 b)  4 * π * r2.
 c)  4 * π * r.
 d)  8 * π * r.
 e)  None of the above.



14) What is the rate of change of the volume of a sphere when its radius equals 2.0?

 a)  8 * π.
 b)  16 * π.
 c)  2 * π.
 d)  20 * π.
 e)  None of the above.



15) What is the rate of change of the volume of a sphere when its radius equals 5.0?

 a)  40 * π.
 b)  20 * π.
 c)  10 * π.
 d)  50 * π.
 e)  None of the above.



16) Let Y = 2 * X3 - 5 * X2 - 4 * X + 10. What is the rate of change of Y with X?

 a)  10 * X - 4.
 b)  2 * X3 - 5 * X2 - 4 * X.
 c)  2 * X2 - 4 * X + 10.
 d)  6 * X2 - 10 * X - 4.
 e)  None of the above.



17) What is the rate of change of Y, in question 16), with respect to X when X = 0?

 a)  0.0.
 b)  -4.0.
 c)  4.0.
 d)  -10.0.
 e)  None of the above.



18) What is the rate of change of Y, in question 16), with respect to X when X = 2?

 a)  0.0.
 b)  -8.0.
 c)  -12.0.
 d)  16.0.
 e)  None of the above.



19) At what rate must the width (W) of a rectangle change, with respect to its length (L), for the area (A) of the rectangle remain constant?

 a)  L / W.
 b)  W / L.
 c)  -W / L.
 d)  -2 * W / L.
 e)  None of the above.



20) What is the rate of change when A = 200, W = 5, and L = 40?

 a)  -0.125.
 b)  -1.25.
 c)  0.125.
 d)  -8.0.
 e)  None of the above.






 

 

 

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