CPA Quantitative Analysis December 2025 Past Paper with Answers (PDF)

1a

Mathematical Techniques - Descriptive Statistics

Highlight FOUR considerations in determining when to employ a sample in collecting data.

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1b

Probability

The probability of an investor achieving the target profit in a given financial period is 0.12.

Required:

Assuming that the investor makes eight investment trials, determine:

(i) The probability that the investor meets the target profit exactly 4 times.

(ii) The probability that the investor meets the target profit at least once.

(iii) The expected value.

(iv) The variance.

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1c

Mathematical Techniques - Functions

The total revenue function of producing product A is linear in nature.

Th following data shows the number of units of product A sold and the corresponding sales revenue in thousands of shillings:

Sales Revenue (Sh.“000”)	24	37.5
Number of units sold, Q	50	80

The total cost (TC) function is given as TC = 170Q + 5700 (in thousands in shillings.)

Required:

(i) Formulate the revenue function.

(ii) Determine the break even quantity of producing product A.

(iii) Determine the total profit when the number of units sold is 250 units.

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2a

Mathematical Techniques - Matrix Algebra

Boramax Ltd. has won a tender to supply 500 doors, 900 windows and 1,500 metallic cabinets to a housing agency. The management of Boramax Ltd. decided that 300 doors, 400 windows and 700 metallic cabinets could be supplied by supplier A and the balance of the order could be filled from supplier B.

The following details were provided by the suppliers:

1. Production of each door requires 2 hours in welding department, 7 hours in the painting department and 5 hours in the drying department.

2. Production of windows requires 3 hours in the welding department, 5 hours in the painting department and 9 hours in the drying department.

3. Production of metallic cabinet requires 3 hours in the welding department, 5 hours in the painting department and 5 hours in the drying department.

4. The cost per hour in the welding, painting and drying department is Sh.30, Sh,70 and Sh.110 respectively.

Required:

Using the matrix algebra, calculate:

(i) The total number of hours required at each department.

(ii) Calculate the total cost incurred by each supplier.

(iii) The total cost incurred by Boramax Ltd. to supply the order.

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2b

Correlation Analysis Regression Analysis

The number of hours spent studying for an examination by 8 students together with the marks achieved in the examination are given in the table below:

Time (X)	2	3	4	5	6	7	8	9
Marks (Y)	40	38	54	44	54	58	70	80

Required:

(i) Draw a scatter diagram to represent the above data.

(ii) Comment on the nature of the relationship obtained in (b) (i) above.

(iii) Calculate the regression of Y and X.

(iv) Fit the regression equation obtained in (b) (iii) above on the same axis in the scatter diagram in (b) (i) above.

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3a

Regression Analysis

Enumerate FOUR assumptions implied in the application of the linear regression model.

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3b

Mathematical Techniques - Descriptive Statistics

The amounts of profit for 76 companies was recorded as shown below:

Profits (Sh.“000”)	Number of companies
15 – 19	8
20 – 24	10
25 – 29	14
30 – 34	21
35 – 39	11
40 – 44	8
45 – 49	4

Required:

(i) Arithmetic mean profit.

(ii) Modal profit.

(iii) Median profit.

(iv) Standard deviation of the data.

(v) Coefficient of variation of the data.

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3c

Hypothesis Testing and Estimation

The immigration department conducted a survey that revealed the monthly number of tourists that visited a certain country in the first six months of year 2025 from eight countries worldwide as recorded in the table below:

Country of origin	A	B	C	D	E	F	G	H
Monthly number of tourists	252	230	310	360	290	410	380	400

Required:

(i) Test the hypothesis that the number of tourists does not depend on their country of origin at 1% significant level.

(ii) Interpret the result in (c) (i) above.

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4a

Probability

An airline has a regular flight from one airport to another. The airline models the duration of a flight as normally distributed random variables with a mean of 185 minutes and variance of 36 minutes.

Required:

Use this model to calculate the percentage of the flights that are completed in:

(i) Less than 3 hours 11 minutes.

(ii) Less than 3 hours.

(iii) More than 3 and one quarter hours.

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4b

Mathematical Techniques - Integration

The function of a certain curve is given as \(Y = 9x^2 – 10x + 36\)

Required:

Find the integral of the function.

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4c

Decision Theory

CloudTech Limited is considering to launch a new software design. However, demand for the proposed software design is uncertain and the company can either launch the new design immediately or conduct market research before making decision which could either be a favourable or unfavourable outcome. If the research outcome is favourable, CloudTech Ltd. can proceed with the launch. If the research outcome is unfavourable, company has the option to abandon the launch.

The probabilities and pay offs were given as below:

Option 1: Launch immediately

Probability of high demand will be 50% with a project profit of Sh.1,200,000.
Probability of low demand will be 30% with a project loss of Sh.400,000.
Probability of no demand will be 20% with zero pay off.

Option 2: Conduct market research at cost of Sh.300,000

Probability of favourable research outcome is 60%.
Probability of unfavourable research outcome is 40%.
If the research outcome is favourable, the demand will be 70% with a project profit of Sh.800,000.
Probability of low demand will be 30% with a projected loss of Sh.200,000.
If research outcome is unfavourable, the company can choose to abandon the launch incurring only the Sh.300,000 research costs.

Required:

(i) Construct a decision tree based on the given probability and outcomes.

(ii) Calculate the expected monetary value for each option.

(iii) Recommend the best investment decision for the company.

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5a

Probability

A total of 1,232 students in Elimu College have taken a course in Spanish, 879 students have taken a course in French and 114 students have taken a course in Russia. Further 103 students have taken a course in both Spanish and French, 23 students have taken a course in both Spanish and Russia and 14 students have taken courses in both French and Russia.

Required:

If 2,092 students have taken at least one of the three courses:

(i) Present the above information in a venn diagram.

(ii) Determine the number of students that have taken a course in all the three languages.

(iii) Determine the number of students that have taken at least two of the three languages.

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5b

Probability

The probabilities that a sportsman makes a certain dangerous journey by car, motor bike or on foot are 1/2, 1/6 and 1/3 respectively. Probabilities of an accident occurring using a car, motorbike or on foot are 1/5, 3/5 and 1/10 respectively.

Required:

(i) Draw a tree diagram to represent the above information.

(ii) Determine the probability of an accident occurring using any of the three means.

(iii) If it is known that the sportsman had an accident, find the probabilities of him having travelled by car, motorbike or on foot.

(iv) If is known that the sportsman arrived safely, find the probabilities of him having travelled by the car, motor bike or on foot.

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6a

Mathematical Techniques - Integration

Find the value of the following integral:

\(\int (2x^3 + 7x – 2)\)dx for an interval between x = 0 and x = 3.

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6b

Mathematical Techniques - Descriptive Statistics

Enumerate FOUR disadvantages of using mode as measure of central tendency.

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6c

Linear programming

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6d

Linear programming

After a couple of iterations, the simplex method produced the following mid iteration table in (c) above:

\(\begin{array}{l|cccc|c} \text{Basis} & \text{A} & \text{B} & \text{S}_1 & \text{S}_2 & \text{Z} \\ \hline \text{S}_1 & 0 & 2 \frac{2}{3} & 1 & -\frac{2}{3} & 26 \frac{2}{3} \\ \text{A} & 1 & \frac{2}{3} & 0 & \frac{1}{3} & 36 \frac{2}{3} \\ \hline \text{Z} & 0 & -3 \frac{1}{3} & 0 & 13 \frac{1}{3} & 1,466 \frac{2}{3} \end{array}\)

Required:

(i) Produce the final simplex tableau.

(ii) State the optimal production plan.

(iii) Find the slack for each constraint.

(iv) Give the shadow price for labour and raw material.

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7a

Mathematical Techniques - Descriptive Statistics

Explain the following terms:

(i) Mean absolute deviation.

(ii) Mean square error.

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7b

Correlation and Regression Analysis

The table below shows the number of hours that 8 students spent revising for an accounting test and the corresponding marks(Y) they obtained:

Time (Hours)	2	3	5	5	6	7	8	9
Marks (%)	40	38	54	44	54	58	70	80

Required:

(i) Calculate the Spearman’s rank correlation coefficient between hours studied and marks obtained.

(ii) Interpret the meaning of the value (R) in relation to the association between study time and performance.

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7c

Time series

A retail company recorded the monthly sales in units of one of its best-selling products over the past 6 months of the year 2025:

Month	Sales (units)
June	420
July	440
August	415
September	430
October	425
November	445

Required:

(i) Forecast the sales for the month of December 2025 using the exponential smoothing method with a smoothing constant α = 0.2.

(ii) Calculate three months moving average forecast for December 2025.

(iii) Forecast the sales for December 2025 using the 3 months weighted moving averages with weights of 0.5, 0.3 and 0.2 starting with the most recent time period and backwards.

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CPA Quantitative Analysis – December 2025 Past Paper & Answers

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CPA Quantitative Analysis – December 2025 Past Paper & Answers

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