Entrepreneurship Track Admissions
This track is for students with a strong foundation in mathematics who are inspired to develop their own entrepreneurial projects. Choose the pathway that matches your project’s current stage, submit your booklet, and prepare for a case study exam and an online discussion.
Available for the 3-year program and 2-year Advanced Entry only, not the 4-year program. The mathematics test and written mathematics exam remain part of the admissions process.
Selection Process
Four Steps
- Choose your pathway. Path A is for a developed idea with a prototype. Path B is for an already operating or tested venture.
- Complete and submit your booklet. Download the Candidate Submission Booklet and complete the sections for your chosen pathway for review by the admissions team.
- Case study exam — 60 minutes. Take a case study exam under exam conditions. A preparation guide with typical questions is available in advance; see the preparation sections below.
- Online meeting — 30 minutes. Discuss your project booklet and written responses with the admissions team.
Choose Your Project Pathway
Choose the pathway that reflects where your project actually stands. There is no advantage to overstating its stage: a strong, honest Path A submission with a prototype can stand out just as much as a Path B submission. You are assessed against what is realistic for your stage.
Path A — Developed idea with a prototype
You have a developed idea and an available prototype, together with a presentation, pitch deck or concise written summary/business plan. Revenue is not required.
Complete A0–A3: explain your project’s stage, present the idea, write your Focus Sentence and reflect using Brookfield’s Four Lenses. Submit a pitch deck, presentation or business plan alongside the booklet, or a One-Pager if you do not have a formal deck.
Your deck or plan should cover the problem, solution, target market, business model, team, current challenges and what you have tried to address them. The One-Pager structure covers problem and context, solution and value proposition, target customer, evidence, SWOT highlights and a business model snapshot.
Download the Path A Submission Booklet (PDF, English)- Length: Sections A0–A3 of your booklet should fit on no more than 5 pages. The 5-page limit applies to A0–A3 only. The self-check is not counted. You may attach a pitch deck, presentation, business plan, or sketches or photos of your prototype as an annex. The annex has no page limit.
- Focus Sentence: explain who your product helps, the specific outcome it delivers and the method that makes it distinctive.
- Brookfield’s Four Lenses: reflect from your own perspective, your users’ or customers’ perspective, the perspective of industry peers or mentors, and the perspective of evidence, data or research.
- Complete the self-check for your pathway. Name files clearly, for example Surname_FirstName_ProjectName, and save your submission documents as PDFs.
- If you have used cloud storage such as Google Drive to share photos, videos, etc. and included the link in the booklet, check that anyone with the link can open the folder.
- Complete the declaration with your name, date and signature. It confirms that the work reflects your own thinking and project, and includes consent for TLF to share a project summary and outcomes in admissions and promotional materials, including your name unless you request otherwise.
- Acknowledge everyone who helped and explain their contribution. Include any generative AI tools used and copy the prompts you used.
Path B — Already operating or tested venture
You have already launched something and have real users, data, revenue or funding to report.
Complete B0–B4: explain your project’s stage, write your Focus Sentence, report actual metrics, provide evidence of traction and reflect using Brookfield’s Four Lenses.
Report one key metric and two supporting metrics, explaining why each matters and how it was measured. Include relevant evidence such as active or paying users, revenue, funding, external recognition, how customers find and access your product, and what you have learned from them. Use actual results, not projections; small numbers are welcome when reported honestly.
Download the Path B Submission Booklet (PDF, English)- Length: Sections B0–B4 of your booklet should fit on no more than 5 pages. The 5-page limit applies to B0–B4 only. The self-check is not counted. You may attach a pitch deck, presentation, business plan, or sketches or photos of your prototype as an annex. The annex has no page limit.
- Focus Sentence: explain who your product helps, the specific outcome it delivers and the method that makes it distinctive.
- Brookfield’s Four Lenses: reflect from your own perspective, your users’ or customers’ perspective, the perspective of industry peers or mentors, and the perspective of evidence, data or research.
- Complete the self-check for your pathway. Name files clearly, for example Surname_FirstName_ProjectName, and save your submission documents as PDFs.
- If you have used cloud storage such as Google Drive to share photos, videos, etc. and included the link in the booklet, check that anyone with the link can open the folder.
- Complete the declaration with your name, date and signature. It confirms that the work reflects your own thinking and project, and includes consent for TLF to share a project summary and outcomes in admissions and promotional materials, including your name unless you request otherwise.
- Acknowledge everyone who helped and explain their contribution. Include any generative AI tools used and copy the prompts you used.
What We Assess
The booklet asks you to show where your project stands and how you think, using honest evidence and reflection.
Skills we assess
The case study preparation below develops these useful skills:
- Breaking a big problem into smaller parts.
- Making sensible estimates when exact numbers are unknown.
- Identifying missing information and explaining what details you need to answer the question.
- Reading a table and spotting what matters.
- Doing simple calculations accurately.
- Using everyday observations to solve an unfamiliar problem.
- Applying mathematical tools to business and economics problems, even if you have not practised this in class.
- Distinguishing correlation from causation.
- Making a clear decision and explaining why.
What to focus on when practising
When practising the sample questions, focus on:
- A clear method.
- Assumptions you state and explain.
- Correct arithmetic.
- Conclusions that follow from the facts.
Explain your reasoning as well as your answer. The examples below are preparation material, not a published scoring rubric.
Case Study Preparation Topics
Use the following topics and business tools to prepare for the case study exam.
Mathematics
- Percentages: finding a percentage of a number, percentage increase and decrease, and percentage points. A market share falling from 50% to 45% drops by 5 percentage points, or 10% of its original share.
- Ratios and averages. For example, revenue per customer = total revenue ÷ number of customers.
- Mental arithmetic with large numbers, including millions and billions, and sensible rounding. For example, 1.2 million × 30 ≈ 36 million.
- Units: converting between per day, per week and per year, and keeping units consistent.
- Index numbers and growth: an index rising from 100 to 125 means growth of 25%. Distinguish total growth over five years from growth per year, and identify the correct basis for percentage comparisons.
Statistics and Fair Tests
- Reading tables and charts: spotting trends, the biggest and smallest values, and what changed.
- The mean (average) and why one extreme value can distort it.
- Samples and surveys: using a survey of a few people to estimate the behaviour of many.
- A fair test: change one thing, keep everything else the same and compare against a control group.
- Independent variable: the thing you change on purpose, which may be the cause.
- Dependent variable: the outcome you measure, which may depend on what you changed.
- Control variables: everything else you keep the same so it cannot affect the result.
Example: does a new reading app improve students’ reading? The independent variable is whether a class uses the app. The dependent variable is the reading test score. Control variables include students’ age, the school and the same test for everyone.
Correlation and Causation
Correlation means two things change together; causation means one actually makes the other happen. Ice cream sales and sunburn both rise in summer, but hot weather can cause both. Correlation alone does not prove causation: a hidden third factor may explain the relationship, or the cause may run the other way.
Profit framework
- Profit = revenue − costs.
- Revenue = price × number sold.
- Costs = fixed costs + variable costs.
Fixed costs, such as rent, stay the same however much you sell. Variable costs, such as materials, grow with each item sold. When profit falls, ask whether revenue has fallen, costs have risen, or both; then investigate which part changed.
Simple Business Tools
Use these tools to identify causes, understand the business environment and compare possible solutions.
Fishbone diagram (cause and effect)
Write the problem at the head of the fish. Each bone is a category of possible causes: people, methods, materials, machines, environment and measurement. List possible causes under each category, then check which ones the facts support. This helps you find the root cause rather than settle on the first idea.
STEEPLE
STEEPLE is a checklist of outside forces that affect an organisation:
| Letter | Factor | Example question |
|---|---|---|
| S | Social | Are people’s habits or tastes changing? |
| T | Technological | Is new technology replacing old products? |
| E | Economic | Are people earning or spending more or less? |
| E | Environmental | Are there environmental pressures or climate effects? |
| P | Political | Are governments changing policies? |
| L | Legal | Are new laws or rules coming in? |
| E | Ethical | Is anything seen as unfair or wrong? |
SWOT
SWOT summarises a company’s position:
| Source | Helpful | Harmful |
|---|---|---|
| Inside the company | Strengths | Weaknesses |
| Outside the company | Opportunities | Threats |
How SWOT and STEEPLE fit together
Strengths and weaknesses come from inside the company. Opportunities and threats come from outside, and STEEPLE helps you find them. For each external change, ask whether it helps or harms the business. A trend towards healthy eating is an opportunity for a salad bar but a threat for a fast-food chain. A law limiting plastic packaging may threaten a bottled-water company while creating an opportunity for a maker of reusable bottles.
Sample Questions
These eight examples help you practise business case questions. Each includes a sample question and guidance on a good answer.
1. Estimation
Estimate a number you cannot look up, such as how many items are sold in a year. The examiner wants to see your steps, not an exact answer.
Sample question
Estimate how many pizzas are bought in a city of 2 million people in one year. Show each step and state your assumptions.
What a good answer includes
- Give a clear chain of steps before calculating: people → households → how often they buy → pizzas per order.
- State each assumption and give a short reason. For example: “About 2.5 people per household, so 800,000 households. A typical household orders pizza twice a month and gets 2 pizzas each time.”
- Calculate: 800,000 × 2 × 12 × 2 ≈ 38 million pizzas a year. You may also account for restaurant and frozen pizzas.
- Check whether the answer is reasonable: about 19 pizzas per person per year, or one every three weeks.
Tips
- Split people into groups if they behave differently, such as students and families.
- Use round numbers.
- Avoid counting the same thing twice.
2. Structuring a Problem
Explain how you would approach a problem and what information you would ask for before you have any data.
Sample question
A café’s profits have fallen over the last year. What questions would you ask to find out why? Organise your questions clearly.
What a good answer includes
- Use the profit framework: profit = revenue − costs. Split your questions into these two groups.
- Revenue: are fewer customers coming? Does each customer spend less? Have prices or the mix of products people buy changed?
- Costs: has rent gone up? Are coffee, milk or food more expensive? Are staff costs higher?
- External factors: has a new café opened nearby? Are people spending less in general? STEEPLE can help here.
- Start with the most likely causes and explain why you would investigate them first.
3. Reading Data
Read a table or chart and explain what the numbers mean.
Sample question
A bookshop’s sales are shown below. What do you notice, and what might explain it?
| Measure | 2022 | 2023 | 2024 |
|---|---|---|---|
| Printed books sold | 40,000 | 36,000 | 32,000 |
| E-books sold | 5,000 | 8,000 | 12,000 |
| Average price of a printed book | €15 | €16 | €17 |
What a good answer includes
- Identify the trends: printed book sales fall by 4,000 a year (10%, then about 11%), e-book sales more than double, and printed book prices rise.
- Calculate total sales: 45,000, then 44,000, then 44,000. Total demand is roughly steady; the data suggest that customers are switching formats rather than reading less.
- Add a useful calculation: printed book revenue is €600,000, then €576,000, then €544,000. It falls despite higher prices.
- Offer a possible explanation, such as the convenience of reading e-books on phones and tablets. Distinguish this explanation from what the table directly shows.
Tips
- Do not just repeat the numbers. Explain what they mean.
4. Calculations
Use the numbers provided to calculate an answer or compare options.
Sample question
A gym has 1,000 members paying €40 a month. Each member costs the gym €10 a month to serve. The manager wants to cut the price to €30 and expects 1,300 members at the new price. Will the gym’s monthly profit go up or down?
What a good answer includes
- Before fixed costs, the current monthly amount is 1,000 × (€40 − €10) = €30,000.
- After the price cut, it is 1,300 × (€30 − €10) = €26,000 a month.
- If fixed costs stay the same, profit falls by €4,000 a month. On these numbers, the price cut is not worthwhile.
- For an extra step, calculate how many members would keep profit unchanged: €30,000 ÷ €20 = 1,500 members.
Tips
- Explain each step so the examiner can follow it.
- Check units: per month or per year, per person or in total?
- Finish with a sentence that answers the question.
5. Correlation or Causation?
Decide whether two things changing together means that one causes the other.
Sample question
A school notices that students who eat breakfast get better exam results. The head teacher says: “Breakfast makes students do better in exams. Let’s give every student free breakfast and results will rise.”
- Why might the data not prove that breakfast causes better results?
- Suggest another explanation.
- How could the school test whether breakfast really helps?
What a good answer includes
- The two things are correlated, but students who eat breakfast may differ from those who do not in other ways.
- A hidden third factor could cause both. More organised home routines, more sleep or more parental support may make students more likely to eat breakfast and study well.
- Suggest a fair test: offer free breakfast to a randomly chosen half of similar classes for a term. Compare their results with the other half’s, keeping other conditions the same.
Tips
- Ask whether something else could cause both.
- Consider whether the cause could run the other way.
- A good test changes one thing and compares against a control group.
6. Finding the Root Cause
Use clues given one at a time to find the most likely reason for a problem.
Sample question
A bakery’s profits have fallen. You find out:
- Prices and the number of loaves sold are unchanged.
- The cost of flour, butter and staff per loaf is unchanged.
- Customers now ask for more types of bread, so the bakers make 15 varieties instead of 5.
- Each variety needs the ovens to be cleaned and reset before baking.
What is the most likely cause of the falling profits?
What a good answer includes
- Rule out the changes the facts do not support: prices, sales volume and the stated per-loaf costs have not changed.
- Spot the key clue: more varieties mean more oven changeovers. Investigate the extra cleaning time, downtime and staff hours; these can increase total costs without producing more bread.
- Suggest a fix: cut the least popular varieties, bake similar breads in the same batch or charge more for special breads.
Tips
- A fishbone diagram can help you list possible causes before choosing one. Consider people, methods, materials, machines and environment.
7. Generating Ideas
Suggest ways to grow a business, create new products or cut costs, and explain why they could work.
Sample question
A small bicycle shop in a busy city wants to earn more money. Suggest at least four ideas and explain why each might work.
What a good answer includes
- Offer varied ideas with reasons. Repairs and servicing could bring repeat business because people use their bikes for years. Rentals could serve tourists visiting the city.
- Consider selling helmets, lights and locks with bikes, offering monthly maintenance plans or selling electric bikes. Explain why each idea fits the customers.
- Link your ideas to the shop’s location, staff skills and existing customers.
- Use SWOT: opportunities such as more tourists or more cycling, together with strengths such as expert staff, help identify realistic ideas.
Tips
- Four well-explained ideas earn more marks than ten ideas without reasons.
8. Trade-offs and Decisions
Choose between options and explain the trade-off: getting more of one thing may mean getting less of another.
Sample question
A cinema can charge €6 or €12 for a ticket. At €6 it is usually full; at €12 it is about half full. Which price would you choose? Explain the trade-off and use a real-life example.
What a good answer includes
- Make a clear choice. For example: “I would charge €12 on Friday and Saturday evenings and €6 on weekday afternoons.”
- Explain the trade-off: a higher price earns more per ticket but fills fewer seats. A lower price fills the room but earns less per ticket. Popcorn and drink sales also depend on attendance.
- Use simple numbers: with 200 seats, €6 × 200 = €1,200 and €12 × 100 = €1,200. Ticket revenue is the same, so higher attendance may bring more snack sales.
- Give a real-life example: airlines and trains charge more at busy times and less at quiet times.
- Discuss risks, such as customers feeling that the higher price is unfair.
Tips
- Make a clear decision and explain the trade-off; “it depends” alone does not explain your reasoning.
Preparation and Exam Tips
- Read the whole case first. Identify the key numbers and the actual question.
- Plan before answering. Sketch a structure in your notes: revenue and costs, a chain of steps or a fishbone diagram.
- State your assumptions. “I assume…” is better than an unexplained number.
- Explain every step so that someone else can follow your reasoning, even if they reach a different estimate.
- Round sensibly. For an estimate, 1,960 × 49 is close to 2,000 × 50.
- Check whether your answer makes sense in real life.
- Answer the question with a clear conclusion: “So profit falls by €4,000” or “I recommend…”.
- Match the detail to the marks available. A 2-mark question needs two clear points, not a lengthy explanation.
- Use new information. When a case introduces extra facts, include them in your next answer.