CPA Quantitative Analysis – April 2026 Past Paper & Answers

Unit: Quantitative Analysis

13 Questions

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Questions

Download CPA Quantitative Analysis April 2026 past paper with detailed answers and marking scheme. This paper is based on KASNEB examination standards and is ideal for revision and exam preparation.

Access the full paper online, download the PDF, or study offline. Each question includes step-by-step solutions to help you understand key concepts in Quantitative Analysis.

Mathematical Techniques

(a) Explain the following terms as used in the quantitative analysis:

(i) Function.

(ii) Domain of a function.

(iii) Matrix.

(iv) Differentiation.

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Mathematical Techniques - Matrix Algebra

A logistics company in Mombasa manages the transportation of two types of goods, A and B to two destinations;

Nairobi and Kisumu.

Matrix A represents the number of truckloads (in tens) allocated to each destination, while matrix B represents cost

adjustment factors (in Sh.“000”) per route due to changes in fuel prices and road conditions.

​\(A = \begin{pmatrix} 4 & 2 \\ 1 & 3 \end{pmatrix} , B = \begin{pmatrix} 2 & 1 \\ 5 & 2 \end{pmatrix}\)​

Management wishes to analyse the combined effect of transportation allocations and cost adjustments.

Required:

(i) Determine the matrix A + B. Interpret the meaning of each element in the resulting matrix.

(ii) Determine the matrix product AB. Explain what the resulting matrix represents in the context of transportation planning.

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Mathematical Techniques - Calculus

A medium-sized manufacturing firm based in Nairobi produces bottled fruit juice for the local and regional market in Kenya, Uganda and Tanzania. The firm operates in a competitive but price-sensitive market where demand is influenced by consumer income and availability of substitutes such as carbonated drinks.

Market research conducted by the firm indicates that the demand for its product is given by:

P = 120 − 0.5Q

Where:

P is the price per unit (in Shillings) and Q is the number of units produced and sold per day.

The firm’s cost structure reflects high fixed costs due to machinery, licensing and compliance with Bureau of Standards, as well as variable costs such as raw materials, labour and electricity. The total cost function is given as follows:

\(TC = 3000 + 30Q + 0.1Q^2\)

Due to space limitations and machinery capacity, the firm can produce a maximum of 15,000 units per day.

Required:

(i) Determine the firm’s profit-maximising level of output and price.

(ii) Compute the level of profit at this level of output.

(iii) Advise management on whether producing at the profit-maximising output is feasible given the firm’s production capacity.

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Mathematical Techniques - Calculus

A manufacturing company produces a commodity whose total cost function (in Shillings “000”) is given by:

\(C(x) = 2x^3 −15x^2 + 36x + 50\)

Where x represents the number of units produced (in hundreds).

Required:

(i) Determine the marginal cost function.

(ii) Calculate the level of output at which the marginal cost is minimised.

(iii) Determine the minimum marginal cost.

(iv) Interpret your results in (a) (ii) and (iii) above in the context of production efficiency.

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Mathematical Techniques - Descriptive Statistics

A retail distribution company recorded the weekly wages (in Shillings “000”) paid to its employees in one of its regional branches. The wage distribution is summarised in the table below:

Weekly wage (Sh.“000”)	Number of employees
10 – 20	6
20 – 30	10
30 – 40	14
40 – 50	20
50 – 60	18
60 – 70	12
70 – 80	8
80 – 90	7
90 – 100	5

Required:

(i) Determine the mode of the wage distribution.

(ii) Compute the median weekly wage.

(iii) Calculate the quartile deviation of the wage distribution.

(iv) Calculate the standard deviation of the weekly wages.

(v) Determine the coefficient of variation. Comment on the consistency of wages in the branch.

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Probability

Explain the following concepts as used in probability:

(i) Mutually exclusive events.

(ii) Independent events.

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Hypothesis Testing and Estimation

A large Kenyan logistics company operating across Nairobi, Eldoret and Mombasa employs staff in three departments: Finance, Sales and Operations. The proportions of employees in each department are 45%, 30% and 25% respectively. Historical records show that the probability that an employee is absent on any given day is 0.03 for Finance Department, 0.06 for Sales Department and 0.04 for Operations Department.

The management is concerned about rising staff absenteeism and has also conducted a study on daily output levels.

A random sample of 49 employees recorded an average output index of 54 units with a standard deviation of 14 units. The company’s expected standard output is 50 units.

Required:

(i) Using Bayes’ theorem, determine the probability that an employee belongs to the Sales department given that the employee is absent. Clearly interpret your result in the context of absenteeism.

(ii) Test, at the 5% significance level, whether the average output differs significantly from the expected standard output of 50 units. Clearly state the hypotheses, test statistic and conclusion.

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Correlation and Regression Analysis Time series

Distinguish between the following statistical techniques:

(i) “Correlation analysis” and “regression analysis”.

(ii) “Moving average” and “exponential smoothing”.

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Correlation and Regression Analysis

A car dealership operating in Kampala is analysing the relationship between advertising expenditure and sales performance over several periods. The management intends to use statistical tools to model this relationship and to make short-term forecasts.

The following data were obtained:

Advertising expenditure (Sh. million)	20	40	60	80
Sales (units)	10	14	19	23

Required:

(i) Determine the regression equation of sales on advertising expenditure. Interpret the meaning of the slope coefficient in the context of the business.

(ii) Estimate the expected sales when advertising expenditure is Sh. 50 million. Comment on the reliability of the estimate.

(iii) Giving reasons, explain whether regression analysis or moving average would be more appropriate for forecasting sales in this scenario.

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Time series

A milk processing company has recorded quarterly milk sales (in thousand litres) over two years as shown below:

Quarter	Year 1	Year 2
Q1	120	150
Q2	160	200
Q3	200	240
Q4	180	220

The management intends to analyse both the trend and seasonal variations in sales to improve production and distribution planning.

Required:

(i) Compute the 4-quarter moving averages and centred moving averages.

(ii) Using the ratio-to-moving-average method, compute the seasonal indices for each quarter and adjust them so that their total equals 400.

(iii) Using the seasonal indices obtained in (c) (ii) above, explain how the company can improve its production scheduling and inventory management.

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Linear programming

Highlight FOUR assumptions of linear programming.

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Linear programming

A manufacturing firm located in the Industrial Area, Nairobi produces two products, A and B, using labour and machine resources. Due to increased demand and rising operational costs, the firm seeks to determine the optimal production mix to maximise weekly profit.

Each unit of product A requires:

3 hours of labour
2 hours of machine time

Each unit of product B requires:

2 hours of labour
4 hours of machine time

The total available resources per week are:

Labour: 120 hours
Machine time: 160 hours

The profit contribution per unit is:

Product A: Sh.300
Product B: Sh.400

Required:

(i) Formulate a linear programming model for the above problem, clearly defining the decision variables, objective function and constraints.

(ii) Using the graphical method, determine the optimal production quantities of products A and B. Clearly show the feasible region and all corner points.

(iii) Determine the maximum profit. Interpret the result in the context of the firm’s operations.

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Decision Theory

A manufacturing company is considering expanding its production capacity to meet anticipated demand in the East African market. The management is evaluating two strategies; constructing a large plant or a small plant.

The expected payoffs (in Sh.“000”) under different demand conditions are as follows:

Strategy	High demand	Moderate demand	Low demand
Large plant	800	400	-200
Small plant	500	300	100

The probabilities of demand levels are:

• High demand = 0.5

• Moderate demand = 0.3

• Low demand = 0.2

Required:

(i) Construct a decision tree to represent the above problem, clearly indicating all probabilities and payoffs.

(ii) Compute the Expected Monetary Value (EMV) for each strategy.

(iii) Recommend the most appropriate strategy and justify your answer, considering both return and risk.

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CPA Quantitative Analysis – April 2026 Past Paper & Answers

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CPA Quantitative Analysis – April 2026 Past Paper & Answers

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