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Determine which of the statements is true about the root(s) of the following equation:

 

A.

There is only one real root which takes a positive value.

B.

There is only one real root which takes a negative value.

C.

There are two real roots, r1 and r2, where r1 is positive and:

r1 = - 0.5 r2

D.

There are two real roots, r1 and r2, where r1 is positive and:

r1 = - 2 r2

Calculate the determinant of the product of the matrices given below:

 

A.

-0.00227

B.

-60

C.

-78

D.

-440

For random variable X, use the following statistics to calculate its coefficient of skewness based on central moments.

E(X) = 3.940

E(X2) = 21.466

skew(X) = E[(X - μ)3] = 6.008

A.

-0.415

B.

0.060

C.

0.415

D.

0.768

Consider the function f(x) = x2-6x+20. This function has a stationary point at x = 3.

 

Determine the nature of this stationary point and how do we know this to be true.

A.

It is a minimum stationary point because the second derivative of the function with respect to x takes the value 2, which is positive.

B.

It is a maximum stationary point because the second derivative of the function with respect to x takes the value 2, which is positive.

C.

It is a maximum stationary point because the value of the function at x = 3 is 11, which is positive.

D.

It is a minimum stationary point because the value of the function at x = 3 is 11, which is positive.

Determine which of the following is the Maclaurin expansion (up to the second order term) of: e2x

A)

B)

C)

D)

A.

Option A

B.

Option B

C.

Option C

D.

Option D

v = f(x, y, z) is a real valued function of 3 variables.

 

Express the partial derivative of v with respect to z in standard mathematical notation.

A)

B)

C)

D)

A.

Option A

B.

Option B

C.

Option C

D.

Option D

Three light bulbs are chosen at random from 15 bulbs of which 5 are known to be defective.

 

Calculate the probability that exactly one of the three is defective.

A)

B)

C)

D)

A.

Option A

B.

Option B

C.

Option C

D.

Option D

The stem and leaf chart below shows the ages of all the pensioners in a small village.

 

 

Identify which of the following is not true.

A.

There are 13 pensioners in the village.

B.

The most common age is 63.

C.

The oldest pensioner is 89.

D.

There is a pensioner aged 70.

Identify the meaning of: | x | > 5

A.

x is greater than 5.

B.

x is greater than or equal to 5.

C.

x is greater than 5 or x is less than -5.

D.

x is greater than or equal to 5, or x is less than or equal to -5.