Mathematics Advanced Year 11 - Module 3 - Lesson 2
Limits
1. Key Ideas
What happens to a function as its input gets closer and closer to a particular value? Sometimes the answer is obvious. Sometimes it is hidden behind a division by zero that needs to be untangled. The concept of a limit is the key that unlocks all of calculus — and in this lesson, you will learn how to find it.
- The meaning of limit notation $\lim_{x \to a} f(x)$
- Why a limit can exist where a function is undefined
2. Success Criteria
By the end, you should be able to:
- The meaning of limit notation $\lim_{x \to a} f(x)$
- How to evaluate limits by substitution
- How to evaluate limits by factor-and-cancel
3. Key Terms
4. Activity: Build the Lesson Map
Use the lesson to complete the table. Keep answers brief but specific.
| Prompt | Your answer |
|---|---|
| Main concept | |
| Important example | |
| Common mistake to avoid | |
| How this links to the next lesson |
5. Short Answer Questions
1. Explain this lesson goal in your own words: "The meaning of limit notation $\lim_{x \to a} f(x)$". Use one specific example from the lesson.
2. Apply this idea to a new example: "How to evaluate limits by substitution". Show your reasoning clearly.
3. Analyse why this idea matters for understanding Limits: "How to evaluate limits by factor-and-cancel".
6. Extend: Apply the Idea
A student gives a memorised answer about Limits but does not use evidence or reasoning.
Improve the answer by writing a stronger response that uses accurate terminology, a relevant example and a clear explanation.
7. Multiple Choice
1. What is the best first step when answering a question about Limits?
A. Identify the key concept being tested
B. Write every fact from memory
C. Ignore the command word
D. Skip examples and evidence
2. Which answer would show stronger understanding of Limits?
A. An answer with accurate terms and reasoning
B. A copied definition only
C. A single-word response
D. An answer with no example
3. What should you do if a question asks you to explain?
A. Link the idea to a reason or cause
B. List unrelated facts
C. Only draw a diagram
D. Write the shortest possible answer
8. Success Criteria Proof
Finish with evidence that you can do each success criterion.