Introduction to Stating Assumptions

Welcome! In this chapter, we are looking at a vital part of Communicating Reasoning: the ability to state assumptions. When you solve a complex problem, you often have to make certain "leaps" in your logic to reach a solution. Stating these leaps clearly is what separates a good answer from a great one.

Don't worry if the word "assumption" sounds a bit academic. Think of it as being honest about the "fine print" of your solution. By the end of these notes, you will be able to spot these hidden conditions and write them down clearly for your examiner.

What is an Assumption in Problem Solving?

In the context of Problem Analysis and Solution (especially for Paper 3), an assumption is a piece of information that is not explicitly given in the problem but is treated as true so that a solution can be found.

Analogy: Imagine you are planning a picnic and you say, "We will be at the park by \(2\) p.m." You are assuming that it won't rain, that the car will start, and that there won't be a massive traffic jam. You haven't proven those things, but you need them to be true for your plan to work!

In Thinking Skills, you state assumptions to show the examiner that you understand the limits or conditions of your reasoning.

Key Differences to Remember

In this section (Problem Solving), we state assumptions to make our reasoning clear. This is slightly different from Critical Thinking (Paper 2/4), where you identify unstated assumptions that an author has hidden in an argument. Here, you are the one building the logic, so you are responsible for pointing out the assumptions you've made.


Why Do We Need to State Assumptions?

Problems in Paper 3 are often "models" of real-world situations. Real life is messy, so models have to simplify things. You state assumptions because:

  • Information might be missing: You might need a value (like a speed or a cost) that isn't provided, so you assume a reasonable one to move forward.
  • To simplify the calculation: You might assume a rate remains constant (e.g., "I assume the worker's speed does not drop during the \(8\)-hour shift").
  • To choose between options: If a problem has multiple paths, you might assume one condition is more important than another (e.g., "I assume the goal is to minimize cost rather than time").

Common Types of Assumptions in Reasoning

When you are asked to state assumptions, look for these common categories:

1. The "Constant Rate" Assumption

If you are calculating how long a task takes, you often assume the speed stays the same.
Example: "I assume the machine produces \(10\) units every hour without breaking down or slowing."

2. The "No External Change" Assumption

You assume that factors outside the problem don't change unexpectedly.
Example: "I assume the price of fuel stays at \(\$1.50\) per litre for the entire duration of the trip."

3. The "Inclusion/Exclusion" Assumption

You define exactly what is being counted.
Example: "I assume that the 'weekend' mentioned in the text only refers to Saturday and Sunday, excluding Friday evening."

4. The "Simplification" Assumption

Ignoring small details to make the math possible.
Example: "I assume the time taken to switch between tasks is \(0\) minutes."


How to Identify and State Assumptions: Step-by-Step

If a Paper 3 question asks you to "State any assumptions you have made," follow these steps:

Step 1: Look at your final answer. Ask yourself: "Under what circumstances would this answer be wrong?"

Step 2: Trace back your steps. Did you use a number that wasn't in the text? Did you treat a changing value as if it were fixed?

Step 3: Write it clearly. Use the phrase "I have assumed that..." followed by a specific, logical condition.

Example Scenario:
You are asked to find the minimum number of buses needed to transport \(200\) students. Each bus holds \(50\) people. You calculate \(200 \div 50 = 4\) buses.
Possible Assumption: "I assume all \(200\) students arrive at the same time and are ready to board." or "I assume no buses break down."


Common Mistakes to Avoid

  • Being too vague: Don't just say "I assumed some things about the timing." Be specific: "I assumed each transition takes exactly \(5\) minutes."
  • Stating the obvious: Don't assume something the syllabus or prompt already told you. If the prompt says "The price is \(\$10\)," you don't need to assume the price is \(\$10\).
  • Confusing assumptions with working: Your working shows the math; your assumption explains the "rules" you followed to do that math.

Quick Review: Key Takeaways

Key Term: Assumption — A condition accepted as true without proof to allow a problem to be solved.

Where it appears: Mostly in Paper 3 (Problem Analysis and Solution) under the topic "Communicating Reasoning."

Quick Tip: If you find yourself thinking "The question doesn't say if..." but you decide to do the calculation anyway, you have just made an assumption! Write it down.


Checklist for your Exam:

1. Is my assumption necessary for the solution?
2. Is my assumption reasonable (not a wild guess)?
3. Is my assumption clearly stated in words (not just hidden in numbers)?

Note: For more on how to present your full solution, see the chapters on "Explain reasoning" and "Justify the solution to a problem with logical reasoning."