CPA › Quantitative Analysis › August 2026

CPA Quantitative Analysis – August 2026 Past Paper & Answers

Unit: Quantitative Analysis

15 Questions

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Questions

Download CPA Quantitative Analysis August 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.

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1a

Mathematical Techniques - Matrix Algebra

Explain the following terms as used in matrix algebra:

(i) Determinant of a square matrix.

(ii) Inverse of a matrix.

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1b

Mathematical Techniques - Matrix Algebra

Zimele Ltd, a Kenyan edible oil processor, supplies two wholesalers in Nairobi and Kisumu. Let x and y represent the weekly quantities, in hundreds of cartons, of Brand A and Brand B respectively. The dispatch requirements are represented by the following simultaneous equations:

3x + 2y = 46

5x + 4y = 82

Required:

Using the determinant method:

(i) Compute the determinant of the coefficient matrix and state whether the system has a unique solution.

(ii) Determine the weekly quantities of Brand A and Brand B to be dispatched.

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1c

Mathematical Techniques - Differentiation

Ruku Ltd, a dairy processing company, produces packets of yoghurt for supermarkets and retail shops. The company's production manager has estimated that the total daily cost function, in shillings "000", is given by:

\(C(x) =\) \(x^3 - 18x^2 +\)\(120x + 500\)

Where x represents the number of packets produced per day, in thousands. The management wishes to determine the production level at which the rate of increase in total cost is lowest.

Required:

(i) Determine the marginal cost function.

(ii) Using differentiation, determine the production level at which marginal cost is minimised.

(iii) Compute the minimum marginal cost.

(iv) Interpret the result obtained in (c) (ii) and (c) (iii) above for the company's production planning decision.

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2a

Mathematical Techniques - Descriptive Statistics

Differentiate between “grouped data” and “ungrouped data” as used in descriptive statistics.

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2b

Mathematical Techniques - Descriptive Statistics

Boda Limited, a courier company, recorded delivery times, in minutes, for parcels delivered within Nairobi during

one week as follows:

Delivery time (minutes)	Number of parcels
10 – 20	10
20 – 30	30
30 – 40	120
40 – 50	120
50 – 60	30
60 – 70	10

Required:

(i) Compute the mean delivery time.

(ii) Determine the median delivery time.

(iii) Calculate the standard deviation of the delivery times.

(iv) Determine the coefficient of variation.

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2c

Mathematical Techniques - Descriptive Statistics

The company considers delivery performance consistent where the coefficient of variation is below 25%. Evaluate whether the delivery times are sufficiently consistent.

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3a

Hypothesis Testing and Estimation

Distinguish between “a null hypothesis” and “an alternative hypothesis” as used in statistics.

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3b

Probability

Zuma Limited, a retail chain company, receives customer orders through three channels: online, telephone and walk-in orders. The proportions of orders received through the three channels are 50%, 30% and 20% respectively.

Historical records show that the probabilities of late delivery are 0.04, 0.06 and 0.03 respectively.

Required:

(i) Determine the probability that a randomly selected order is delivered late.

(ii) Interpret the result in (b) (i) above for service monitoring.

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3c

Hypothesis Testing and Estimation

Mzima Water company claims that the average content of its bottled water is not more than 500 ml. A random sample of 36 bottles has a mean content of 503 ml. The population standard deviation is known to be 9 ml.

Required:

Test, at the 5% significance level, whether the average content is significantly above the stated level. Clearly state the hypotheses, test statistic and conclusion.

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4a

Regression Analysis

Differentiate between “interpolation” and “extrapolation” in the context of regression forecasting.

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4b

Correlation and Regression Analysis

Consult Limited, a training firm, recorded the number of training hours attended by six staff members and their performance scores as follows:

Staff member	1	2	3	4	5	6
Training hours (X)	4	6	8	10	12	14
Performance score (Y)	48	55	63	68	74	80

Required:

(i) Compute the Pearson correlation coefficient between training hours and performance score.

(ii) Interpret the strength and direction of the relationship.

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4c

Time series

Yala Limited, a retail outlet recorded annual sales, in Sh. million, as follows:

Year	2021	2022	2023	2024	2025
Sales (Sh. million)	42	47	53	58	65

Required:

(i) Fit a least-squares linear trend equation to the sales data using 2023 as the time origin.

(ii) Using the trend equation obtained in (c) (i), forecast the outlet’s sales for the year 2026 and interpret the forecast in the context of the outlet’s sales performance.

(iii) Evaluate ONE limitation of using the forecast obtained in (c) (ii) for the outlet’s planning decisions.

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5a

Linear programming

Explain the following terms as used in linear programming:

(i) Slack variable.

(ii) Binding constraint.

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5b

Linear programming

Jane Bakers, produces cakes and loaves of bread. Each cake requires 3 kg of flour and 2 hours of oven time. Each loaf requires 2 kg of flour and 1 hour of oven time. The bakery has 120 kg of flour and 70 oven hours available per week. The contribution per cake is Sh.500 and per loaf is Sh.300.

Required:

(i) Formulate the linear programming model.

(ii) Using the graphical method, determine the optimal production mix.

(iii) Compute the maximum weekly contribution.

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5c

Montel Limited, an export company, is considering three export strategies. The estimated profits, in Sh.“million”, under different market conditions are as follows:

Strategy	Strong market	Stable market	Weak market
Expand cold storage	18	10	-3
Use contracted storage	12	8	2
Maintain current capacity	8	6	4

Required:

(i) Determine the best strategy using the maximin criterion.

(ii) Determine the best strategy using the minimax regret criterion.

(iii) Recommend a strategy, giving reasons for your recommendation.

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Unlock Solution

CPA: Quantitative Analysis — August 2026

The computation for this specific sitting involves adjusting the net profit for non-allowable expenses...

Step-by-Step Workings:

Net Profit1,800

Add: Non-Deductible13,000

Adjusted Profit14,800

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