All solutions here are SUGGESTED. KS will hold no liability for any errors. Comments are entirely personal opinions.

Numerical Answers (click the questions for workings/explanation)

Question 1:

Question 2:

Question 3:

Question 4:

Question 5:

Question 6:

Question 7:

Question 8:

Question 9:

Question 10:

let depth of water be cm.

When

Comments/Explanations: This is easy. Just don’t make careless mistake with the .

(ai)

(aii)

.

(b)

Comments/Explanations: The integration by parts can be really tedious. so just be careful. As for the part, it can be both -1 or 1, depending on what n is. So we have two values of a.

(i)

(ii)

(iii)

Equation of Normal:

At E,

At F,

Area

Comments/ Explanations:

(a)

(i)

Note: Half line do not cut the center of the circle!

(ii)

Equation of Circle:

Equation of Bisector:

Solving, and

(b)

(ii)

For is purely imaginary and positive (lies on positive imaginary axis)

For to be imaginary,

For to be positive,

Comments/ Explanations:

(i)

Required probability

(ii)

Required probability

(iii)

Required probability

Comments/ Explanations:

(i)

(a)

Required answer

(b)

Required answer

(ii)

The sample collected will be representative of the employee’s gender and department, instead of their age. Thus, it will not be suitable as it is not representative.

(iii)

Let be the age of employees.

Let be the population mean age of employees

Under approximately by Central Limit Theorem.

Since is rejected,

(iv)

For to be not rejected,

Comments/Explanations:

(i)

Number of ways

(ii)

Number of ways

(iii)

Required Probability

(iv)

Required Probability

Comments/ Explanation:

(i)

[graph to be inserted]

is the outlier.

(ii)

The scatter diagram shows a curvilinear relationship between x and y variables. Thus, a linear model is not appropriate.

(iii)

d is positive since it represent the maximum efficiency obtained as the power increases.

c is negative since the scatter show an increasing trend.

(iv)

Using GC,

(v)

When

The estimate would be reliable since it is within the data range. The value is close to 1 which shows a strong linear relationship.

Comments/Explanations:

(i)

(b)

Using GC,

(c)

Let W denote the number of guesses that George made correctly, out all 100.

Since is large ,

approximately

by continuity correction

Comments/Explanations:

(i)

The mean number of a particular type of weed that grow on the field is a constant.

A particular type of weed growing on the field is independent of another particular type of weed growing on the field.

(ii)

Let X be the number of dandelion growing per .

(iii)

(iv)

Since approximately

by continuity correction

(v)

Let Y denote the number of daisies per .

Using GC,

Comments/ Explanation: