Section A (20 Marks)
Write short notes on any four of the following:

Mean Proportional

Preference Shares

Simple Interest (S.I.)

Limit of a Function

Critical Points
Section B (30 marks)
(Attempt any three)

What do you understand by the term equality of ratios? Give example. Write various properties of ratios.

Calculate the present value of an annuity of 3,000 in 6 years at 14%p.a.

If the monthly incomes of A and B are in the ratio of 3 : 2 and those of B and C are in the ratio of 9 : 7, what is the ratio of the monthly incomes of A and C.

What are variations? Explain the different types of variations with worked examples.
Section C (50 marks)
(Attempt all questions. Every question carries 10 marks)
Read the following situations and answer the questions respectively:
Case 1: Geometric Sequence and Common Ratio
Alberta’s crude oil reserves are diminishing by 10% each year. Knowing that 100000 Ml were the initial reserves, show that the crude oil reserves describe a decreasing geometric sequence and find the common ratio for it.
Question 1: Which volume will remain four years later?
Question 2: Plot a graph of the sequence for a period of 20 years.
Case 2: Stocks
Stocks of a company are initially issued at the price of $10. The value of the stock grows by 25% every year.
Question 3: Show that the value of a stock follows a geometric sequence.
Question 4: Calculate the value of the stock ten years after the initial public offering.
Question 5: Plot a graph of the sequence over a period of 10 years after it was issued.