FP039-15 Essential Mathematics CW Summative Assessment 2026 | Warwick

FP039 Essential Maths Coursework Assignment Overview

Sections 1- Headlines of Data

Tasks:

1. Locate the total project cost.

a. What is this figure rounded to 3 significant figures?    (1 mark)
b. In the context of this figure, what is the advantage of rounding?    (1 mark)

2. By the end of the project, there were 2 cubic meters of concrete left.

a. What is this as a percentage of the total concrete purchased? Round this value to a suitable degree of accuracy, stating the accuracy clearly. (2 marks)
b. If concrete costs £4.35 per Kg, briefly discuss the impact on the project.    (3 marks)

3. Locate the amount of steel used in the project.

a. How much steel was used to the nearest 1 decimal place?    (1 mark)
b. When planning this project, would rounding this value be useful for the construction company? Explain your answer fully.    (1 mark)

4. By considering rounding boundaries, calculate the potential impact of the adjustments to the foundation.    (4 marks)

[Total 13 marks]

Section 2a – Precedence Tables and Activity Networks

Activities that need completion:

• Surveying the Site: 2 weeks
• Planning and Designing: 5 weeks
• Obtaining Building Permits: 3 weeks
• Clearing the Land: 4 weeks
• Preparing the Foundation: 7 weeks
• Building the Frame: 10 weeks
• Roofing and Walls: 8 weeks
• Installing Electrical and Plumbing: 6 weeks
• Installing Heating and Cooling: 4 weeks
• Installing Doors and Windows: 5 weeks
• Painting and Decorating: 7 weeks
• Landscaping the Surroundings: 4 weeks

Background information on tasks

The following dependency considerations were researched by the project manager:

• Planning and Designing: This task is typically a prerequisite for several subsequent tasks, as it lays the foundation for the project's overall scope and requirements. But the site needs to be surveyed beforehand to see what is possible.
• Obtaining Building Permits: Before proceeding with construction activities, obtaining the necessary permits is often a requirement. The design plans are needed to submit to the relevant authorities to obtain the necessary approvals. Without these permits, construction activities cannot legally begin.
• Clearing the Land: when the flora and debris are cleared from the land in anticipation of building and construction. This task may be dependent on the completion of the surveying process to identify the appropriate areas for clearing.
• Preparing the Foundation: This task generally follows the completion of land clearing and requires a stable and cleared site.
• Building the Frame: This activity relies on having a prepared foundation to support the construction of the frame structure. It also requires building permission.
• Roofing and Walls: This task is typically performed after the frame has been constructed, as it involves enclosing the structure.
• Installing Electrical and Plumbing may depend on the completion of the framing and wall installation, as it involves routing electrical and plumbing systems within the structure.
• Installing Heating and Cooling: This task might follow the completion of electrical and plumbing installations, as it involves integrating heating and cooling systems into the structure.
• Installing Doors and Windows: Before doors and windows can be installed, the basic structure of the building must be completed, particularly the roofing and walls. This ensures that there are defined spaces and openings where the doors and windows can be fitted securely.
• Painting and Decorating: Once the doors and windows are securely in place, the interior spaces are ready to be finished and decorated.
• Landscaping the Surroundings: Landscaping is often one of the final stages of a construction project. It is typically done after most of the interior work, such as painting and decorating, is completed to ensure that the construction and finishing activities do not interfere with the landscaping work.

Tasks:

• Use the information above to arrange the activities into a precedence table, showing the dependencies/precedence clearly. (6 marks)
• Present your precedent table as an activity network (You may do it by hand or in draw.io). (4 marks)

[Total 10 marks]

Section 2b – Floats and Gantt Chart

• Using the activity network in part 2a, draw an Early-Late diagram.  (5 marks)
• Construct a table for total float and state critical activities. State the total float of the network.

(4 marks)

• State the critical path and the total time for the project.    (2 marks)

[Total 11 marks]

Section 2c – Scheduling

The project now needs to be scheduled under the assumption that one job requires 1 working team, and no breaks are needed between jobs. Teams contain 5 people and are paid as a team. When a job is started, it is seen through to completion.

• Draw a Gantt chart to represent the activities.    (4 marks)
• Calculate a lower bound estimate for the number of teams needed to complete the project in the minimum time. Show your work along with any relevant interpretations. (2 marks)
• Schedule the activities, clearly stating the number of worker groups needed.    (3 marks)

[Total 9 marks]

Section 3 – Modelling Risk

The following report was produced by the CEO of the company, David Tapp.

To: Site Manager on Project

From: David Tapp, CEO

Subject: Company Accident Rate Report

Dear Construction Site Manager,

I hope you are well.

I am pleased to present to you the official Company Accident Rate Report, which highlights the accident rates observed among our employees based on their years of experience with the company. The data presented below has been meticulously collected and analysed, and we hope that this report will provide valuable insights into the safety performance of our workforce and provide a useful starting point for scheduling your project. The average cost of an accident to the company is approximately
£3250.

Employees with Nine Years of Experience:

Employees with nine years of experience exhibit a significantly lower accident rate, with an average of 1 accidents every 9 years. This finding demonstrates that our most experienced employees have been maintaining a high level of safety performance.

Newly Employed Workers with One Year of Experience:

Newly employed workers with one year of experience face an average accident rate of 5.5 accidents per year. This is a
concerning observation, indicating that safety awareness and training measures should be reinforced for new employees to reduce their accident rate.

Employees with Three Years of Experience:

Employees with three years of experience have an average accident rate of 22 accidents every 5 years. It is essential to closely monitor this group to identify potential safety improvement opportunities.

Employees with Five Years of Experience:

Employees who have worked for the company for five years have a rate of 4 accidents every 2 years. This suggests that the safety performance of employees with five years of experience is better than those with three years of experience, with a reduced average accident rate.

Employees with Seven Years of Experience:

Employees who have worked for the company for seven years have an average accident rate of 12 accidents every 10 years. This data suggests a moderate accident rate, indicating room for potential safety improvements in this experience bracket.

Should you have any questions or require further clarification, please do not hesitate to reach out. 

Thank you for your attention to this matter.

Sincerely,

David Tapp

CEO, Milburn Engineering and Construction

Tasks:

• Using the data from the report, draw a scatter diagram where 𝑇 represents the years of experience, and 𝑅 is the yearly rate of accident. (5 marks)
• Explain how you know that a linear model would be appropriate here.    (1 mark)
• Using the data above, define an equation in the form 𝑅 = 𝑎𝑇 + 𝑏. Where 𝑎 and 𝑏 are constants to be found, rounded to 1 decimal place. (5 marks)
• Interpret the values of the coefficients 𝑎 and 𝑏.    (2 marks)
• How realistic is the model in part 3?    (1 mark)
• According to the model produced in part 3, how many accidents could be expected from an employee who has 4 years of experience?    (1 mark) [Total 15 marks]

Section 4 – Optimising Business Constraints

Milburn Engineering and Construction are able to offer different types of classroom option when constructing the school. The maximum cost allocated for construction of the classrooms is £405,000. There are two types of classroom available, and each has its own requirements:

As the builders, you are tasked with deciding the optimal amount of each classroom in order to maximise profit for the company. The number of each type of classroom that can be fitted into the school is dependent on the number of resources available locally and the budget given by the local council. The school needs at least 10% of classrooms to be Smart and at least 10% to be Traditional. Milburn Engineering and Construction has been able to acquire 36 projector screens and 27 radiators.

The revenue for every traditional classroom is £35,000 and for every smart classroom its £45,000. By formulating this as a linear programming problem, define the design that will maximise the profit.

Marks will be awarded as follows:

• Introduction and overview of the situation, defining decision variables. (2 marks)
• Formulating the objective function and constraints correctly. (4 marks)
• A diagram to represent the problem with region of feasibility, labelled F. (6 marks)
• Optimal solution calculated and presented with interpretation. (7 marks)

[Total 19 marks]
 
Section 5 – Statistics

Below shows a list of possible workers for the project.

Tasks:

• Produce a summary of statistics for the variables Experience and Weekly Rate.

(4 marks)

• Use the relevant information in section 3 and the two variables in the list above to best choose the workers you will need for your project. You must give reasons and state any assumptions. (10 marks)

[Total 14 marks]