**TUESDAY: 6 December 2022. Morning Paper. Time Allowed: 3 hours.**

**Answer ALL questions. Marks allocated to each question are shown at the end of the question. Show ALL your workings.**

**Do NOT write anything on this paper.**

**QUESTION ONE**

1. Describe each of the following sampling techniques:

Cluster sampling. (3 marks)

Stratified sampling. (3 marks)

2. The table below shows the annual maize output for 100 farmers in a certain locality in the month of March 2022:

**Required:**

Compute the:

1. Mean maize output. (3 marks)

2. Modal maize output. (3 marks)

3. Median maize output. (3 marks)

4.Coefficient of variation. (3 marks)

Interpret your results in 4 above. (2 marks)

**(Total: 20 marks)**

**QUESTION TWO**

1. Differentiate between an “identity matrix” and a “vector matrix” giving an example in each case. (4 marks)

2. A manufacturer produces 10 units of product R and 30 units of product S at a total cost of Sh.17,000 in week 1. The

manufacturer also produces 20 units of product R and 40 units of product S at a total cost of Sh.26,000 in week 2.

**Required:**

Determine the cost of producing each unit of product R and each unit of product S using the matrix method. (6 marks)

3. In a bucket, there are 7 red balls and 5 green balls.

Three balls are selected from the bucket without replacement.

**Required:**

1. Represent the above information in a tree diagram. (6 marks)

2. Find the probability that the three balls selected are of the same colour. (4 marks)

**(Total: 20 marks)**

**QUESTION THREE**

1. Compute the value of K in the quadratic equation:

–2k2 + 7k + 4 = 0 (3 marks)

2. Citing an example in each case, describe the following terms in the context of descriptive statistics:

Skewness. (3 marks)

Kurtosis. (3 marks)

3. Distinguish between “simple interest” and “compound interest”. (4 marks)

4. Jane Oluoch intends to deposit money in one of her two accounts; A and B.

If she deposits Sh.400,000 in account A, it earns a simple interest at a rate of 18% per annum for 5 years.

If she deposits Sh.400,000 in account B, it earns interest at a rate of 14% per year compounded quarterly for 5 years.

**Required:**

Calculate the interest earned by depositing in account A. (2 marks)

Calculate the interest earned by depositing in account B. (3 marks)

Citing a reason, advise Jane Oluoch on the most profitable account to invest in. (2 marks)

**(Total: 20 marks)**

**QUESTION FOUR**

1. State four applications of mathematical functions in business. (4 marks)

2. Explain four assumptions of the break even analysis. (8 marks)

3. Hedi Limited has a demand function; 3Q = P – 7 in Sh. “000” where: Q is the quantity of goods produced and sold

and P is the selling price in shillings per unit.

The variable cost per unit of production is Sh.23,000 and the fixed cost is Sh.200,000.

**Required:**

1. Determine the break even point quantity. (6 marks)

2. Determine the profit maximising output. (2 marks)

**(Total: 20 marks)**

**QUESTION FIVE**

1. Find the derivatives of the following functions:

f(x) = x1⁄2 (2 marks)

f(x) = 5×2

(x + 47) (2 marks)

2. Kera Omondi is an employee of Hashina Motors Limited. He received a net pay of Sh.113,536.90 for the month of

May 2022.

The employer had provided him with a house allowance of Sh.20,000 and a medical allowance of Sh.11,000.

The net tax payable in May 2022 was Sh.49,563.10.The monthly personal relief provided was Sh.2,400. Other deductions made on his salary in the month of May were as follows:

Sacco shares Sh.4,000

NSSF Sh.200

Car loan Sh.6,000

NHIF Sh.1,300

The rates of tax are as shown in the table below:

Monthly income Tax rates

First Sh.24,000 10%

Next Sh.8,333 25%

Above Sh.32,333 30%

**Required:**

1. Kera Omondi’s gross salary for the month of May 2022. (3 marks)

2. Net tax payable by Kera Omondi for the month of June if his monthly salary was increased by 15% in June 2022. (3 marks)

3. The following are prices in shillings and quantities in kilogrammes of goods consumed by households in the suburbs

of Nairobi City in the years 2020 and 2021.

**Required:**

1. Laspeyres price index. (3 marks)

2. Paasches price index. (3 marks)

3. Marshalls Edgeworth price index. (3 marks)

4. Interpret the result in 3 above. (1 mark)

**(Total: 20 marks)**