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Sample Problem Sheet Nicola Talbot July 10, 2017

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Sample Problem Sheet

Nicola Talbot

July 10, 2017

1. Differentiate from first principles f (x) =√x 2. Differentiate the following functions:

(a) y = cos(x2) sin x. (b) y = arccos x.

(c) y = exp(3x + 2) (d) y = x3+ 4x2− x + 3

(e) f (x) = g(x)h(x).

3. Find the gradient of the ellipse given by 4x2+ 3y2= 25.

4. Find the gradient of the unit circle (x2+ y2= 1).

5. Under which of the following functions does S = {a1, a2} become a

prob-ability space?

(a) P (a1) =13, P (a2) = 12 (b) P (a1) = 34, P (a2) =14

(c) P (a1) = 1, P (a2) = 0 (d) P (a1) = 54, P (a2) = −14

6. A coin is weighted so that heads is four times as likely as tails. Find the probability that: (a) tails appears, (b) heads appears

7. Which of the following is the derivative of x sin(x)? (Circle the correct answer.)

A sin(x) B x cos(x)

C sin(x) + x cos(x)

8. Describe what is meant by object-oriented programming.

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Sample Problem Sheet Nicola Talbot July 10, 2017

A coin is weighted so that heads is four times as likely as tails.. Describe what is meant by the term inheritance in object-oriented

EasyProblems Chapter1

A coin is weighted so that heads is four times as likely as tails. Find the probability that: (a) tails appears, (b)