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.
```