1. The data below shows the weight and index numbers for six commodities in the state of Zambezi:

The weighted index number of the six commodities is 645.6, and the total weight is 300.
Required
a.The weight of commodity C
c.The index number of commodity E

2. TRUE or FALSE: Two events are independent of one another if the probability of the joint event is the product of the probabilities of the separate events, {i.e., if P (A ∩ B) = P (A)P (B)}.

3. In the year 2025, the East African Conference was attended by 570 delegates from Kenya, Uganda, and Tanzania (TZ). The following information relates to the delegates who attended the conference:

Required: Using a Venn diagram to represent the above information, find the:
i. The number of delegates does not represent any of the three countries.
ii. The number of guests who represented only one country.
iii. The number of guests who represented two countries only.
iv. The number of guests who represented at least two countries.

4. Moses is paid 12% interest in the first year,10% in the second year, and 15% in the third year.

Required: The average rate of return using the geometric mean.

5. Tazama East sells two(2) types of hats: Black and Red. The cost of producing 20 black hats and 16 red hats is USD 8,120. The cost of producing 8 black hats and 14 red hats is USD 5,680. Tazama makes a markup of 20% and 30% on queen cakes and black forest, respectively.

Required: Using matrix algebra, determine the cost of producing a black hat and a red hat

6. The total manufacturing cost function of Lawingu East Ltd is quadratic in nature and passes through the following points:

Required: The total manufacturing cost function.

7. TRUE or FALSE: If Laspeyre's price index is 118 and Paasche's price index is 112, Dorbish-Bowley’s Price Index Number = 1.05

8. Given the Venn diagram below, is A U(B∩C) equal to (A ∪ B) ∩ C?

9. Mazuri College has 840 students whose participation in various sports as follows:

Required: Use a Venn diagram to represent the above information and find :
i. The number of students who played at least two of the sports.
ii. The number of students who played one sport only.
iii. The number of students who did not play any of the three sports.

10. From the data below, calculate the Dorbish-Bowley’s Price Index Number.

11. Mathew runs a drinking water business and has determined that the fixed costs add up to USD 2,000, while the variable costs of producing one bottle of drinking water are USD 7 per unit. The selling price per bottle is USD 12. Determine how many units Mathew will need to sell to break even:

12. Tamutamu East Limited manufactures and sells a premium type of cooking oil known as ‘Lamusa’. The marketing department of the company has been monitoring the demand and supply patterns of Lamusa. The following data was compiled for a given period:

The demand and supply functions are linear.

Required: The supply function(Qs)

Lexis East manufactures tires for the local industry. Its cost of production is given by the following function
TC=-6q² + 24q-4
TC=Total Cost
Q=Quantity produced in units
The selling price per unit is USD 10

13. Required: The revenue function(R)

14. Sulumu Soccer Club tickets are based on the seating arrangement. The tickets are sold at USD  140 for the Executive section, USD 120 for the Main, and USD  100 for the Balcony section. The number of tickets sold for the Executive, Main, and Balcony sections,  and the relevant day of the week were as follows for a certain week.

Required: Using matrix algebra, find the total sales made on the relevant days of the week.

15. The table below shows the number of hours worked by three casuals of Ravet Limited in June 2025:

Additional information
a. Normal working hours per month are 240.
b. Overtime is payable for extra hours worked at a rate of 25% above the normal rate.
c. Deductions to be made are:
• PAYE 30% of gross salary
• NSSF –USD 720
• NHIF-USD 400

Required: The net wage for each of the three(3) employees.

16. Mwala East Micro-finance issued the following unsecured loans to various clients:

Required
Using a frequency distribution table of the data with a USD  200 thousand class interval, find the total of fx^2

17. In an exam revision session, four students from Diamond Academy were given a quiz. The chances for the four(4) students will pass the quiz were 1/3,1/7,1/2 and 1/ 5 respectively

Required
i. The probability that all 4 students failed the quiz
ii. The probability that all 4 students passed the quiz

18. The data below shows the number of bicycles sold by Matawi Limited for 30 days:

Complete the frequency table below, beginning with the 110-114 class limit:

19. Ruth, a Nairobi Book vendor, sold 75 Business Mathematics revision e-books and 25 Cost Accounting revision e-books for USD 175 to Tezo College of Accountancy in July 2023. Later in the same month, she sold 125 Business Mathematics revision e-books and 50 cost accounting books for USD 300 to the Meza Institute of Finance and Accounting.

Required
Use matrix algebra to compute the price of a Business Mathematics revision e-book and the price of a cost accounting revision e-book.

20. The following are the indices of Madex country for the years 2017-2021:

Required
The constant indices using 2017 as the base year (2017=100).

21. If y = e^x, then y increases:

A machine produces rods of expected length 50 mm. A sample rod measures 49.2 mm.
What is the percentage error?

23. TRUE or FALSE: The expression 7x – 14 can be factorized as 7(x – 2).

24. The antilog₁₀(2.5) equals:

25. TRUE or FALSE: ln(xy) = ln(x) + ln(y).

26. Sum of first n terms of an AP is:

27. To accumulate USD 200,000 in 5 years at 6% per year, the annual deposit R is:

28. If C(x) = 4x^2 + 20x + 100 , the marginal cost is:

29. Compute using integration by parts: ∫xe^xdx

30. Given profit P(x) = -2x^2 + 40x, Maximum profit occurs at:

31. A trader marks goods at USD 5,000 but allows a 10% trade discount. The selling price after discount is:

32. A merchant bought goods for USD 50,000 and sold them at a mark-up of 40%. SP is:

33. If interest earned is USD 6,000, rate is 10% p.a., and time is 2 years, the principal is:

34. A sum of 5,000 earns compound interest at 8% p.a. compounded annually. The CI after 2 years is:

35. TRUE or FALSE: Sum of the Year’s Digits(SYD) results in LOWER depreciation in early years.

36. An employee earns USD 300 per hour an,d overtime is paid at 1.5 times the hourly rate. If he works 40 hours regular time and 6 hours overtime, what is his total wage?

37. A salesperson earns a monthly salary of USD 20,000 plus 10% commission. If her total income was USD 50,000, what were her sales?

38. A Z-chart is used mainly to:

39. Given speeds: 2400 km/h and 6200 km/h, find the harmonic mean.

40. The coefficient of variation (CV) is given by:

41. If U = {1, 2, 3, 4, 5}, A = {1, 2}, what is Aʹ (complement of A)?

42. A business has customer groups: Event A: Purchased product A (30 customers), Event B: Purchased product B (20 customers). If both bought A & B = 10, total customers = 50. What’s the probability that a customer bought either A or B?

43. In a population, 80% like product X, 55% like product Y, 40% like both. What’s the probability a person likes X or Y?

44. TRUE or FALSE: An event is any subset of a sample space.

45. In the experiment of rolling a die, what is the probability of getting an even number?

46. TRUE or FALSE: P(A ∩ B) = P(A|B)P(B) only when A and B are independent.

47. If a product defect is 2% overall and machine A produces 5% defective while machine B produces 1%, Bayes’s Theorem helps to:

48. Lajengo West Limited sells building materials, whose data for the two years is shown below:

Assume that the price, variable cost per unit, and fixed costs are the same in the two periods.

Required:The break-even point in sales revenue for year 2

Farida West Enterprises sells chocolates, and each dozen consists of two varieties, namely Dark and White chocolates. Dark chocolates cost USD 150 each, whereas White chocolates cost USD 300 each. The selling prices for dark chocolates and white chocolates are USD 210 and USD 350 each, respectively
49. Additional information
 The daily cost per dozen of the dark chocolates is USD 2,400.
 8 dark chocolates and 4 white chocolates should be packed in each dozen.

Required: The daily profit earned from each dozen chocolates.

50. TRUE or FALSE: An Ogive curve never goes upward, because cumulative frequencies only decrease.