NO.19 Differentiate f(x) with respect to x, where
A)

B)

C)

D)

NO.20 A basketball squad contains 7 players. The team that lines up on the court tor the start of a match contains 5 ofthe players Calculate how many different teams can be fielded from the squad of 7 players

NO.21 The volume of a cone can be determined by summing up the infinitesimal circular cross-sections of the cone across the length of the cone Consider the function f(x) = x2 for x contained in [0,1].

Now consider an infinitesimal circular cross-sectional element of width dx and radius r = f(x) Determine the volume of the cone enclosedby the function f(x) by considering the volume of each circular cross-sectional element (Recall thatthe sum of infinitesimal elements can be represented as an integral Recall also that the area of a

circle is
A)

B)

C)

D)
1

NO.22 Let X be a continuous random variable with probability density function f(x) that is defined over all real numbers.
DefineE[g(X)]whereg(x)is a continuous function.
A)

B)

C)

D)

NO.23 Express the following using Pi notation:

A)

B)

C)

D)

NO.24 Multiplythe following two matrices together.

A)

B)

C)

D)

NO.25 Identify which of the following values is represented by:

NO.26 Identify which of the following statements is correct.

NO.27 Simplify the expression:

A)

B)

C)

D)

NO.28 Determine which of the following statements is not true about the binomial expansion of (1+x)p, assuming p is real.

NO.29 Identify which of the following statements about statistical measures for a set of data is false.

NO.30 Identify the necessary and sufficient condition under which the quadratic equation ax2+ 2a2x + a3= 0 hasone repeated real root.

NO.31 Identify which of the following statements is correct.

NO.32 Calculate the sum of the following series: 3, -6,12, -24,…, -1.536.

NO.33 Identify which of the following is not true about the population variance of a set of data.

NO.34 Determine the binomial expansion of (2x-X2)3.

NO.35 Calculate the single extreme point of the function: