MathematicsChapter 7: Mathematical Induction and Binomial Theorem
Inductive Step
Write P(k): the formula with n=k.
Learning objectives
- State the rule or meaning of inductive step in easy words.
- Apply inductive step in a clear step-by-step solution.
- Check the conditions, working, and final answer for accuracy.
Definition
Write P(k): the formula with n=k. For P(k+1), start from the left side, replace using P(k), tidy to the right side of P(k+1). Say 'by IH' when you use P(k).
Formula
n=k. For P(k+1)
Where / symbols
- INDUCTIVE STEP
- Write P(k): the formula with n=k. For P(k+1), start from the left side, replace using P(k), tidy to the right side of P(k+1). Say 'by IH' when you use P(k).
- STEP
- Write P(k): the formula with n=k.
Relationship
- IH = P(k)
Overview
Understand the idea, then apply it:
Main Idea
Write P(k): the formula with n=k. For P(k+1), start from the left side, replace using P(k), tidy to the right side of P(k+1). Say 'by IH' when you use P(k).
Examples Add the next term · Or multiply the next factor · End at the P(k+1) formula
Exam Use
Write the rule first: Write P(k): the formula with n=k. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.
Examples State the central idea · Use one accurate detail · Check the final response
WHAT — INDUCTIVE STEP
Write P(k): the formula with n=k. For P(k+1), start from the left side, replace using P(k), tidy to the right side of P(k+1). Say 'by IH' when you use P(k).
WHY — Why it matters
This rule is a separate learning unit inside principle of mathematical induction. It can be defined, applied, and checked in its own FBISE question.
HOW — How to answer
Write the rule first: Write P(k): the formula with n=k. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.
How to answer a inductive step question
- Read the exact command word and identify what the question asks.
- State the matching idea, rule, or meaning before adding detail.
- Use the unit evidence or mathematical working that directly supports the answer.
- Check accuracy, relevance, and answer length before finishing.
In simple words
You must do both base and step. The step alone does not start the chain.
Key points
- IH = P(k)
- base then step
- assume P(k), prove P(k+1)
- focused answer
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Inductive Step
Sticky Notes · Quick Revision
Core Idea
- Write P(k): the formula with n=k.
What to Know
- Write P(k): the formula with n=k. For P(k+1), start from the left side, replace using P(k), tidy to the right side of P(k+1). Say 'by IH' when you use P(k).
Example or Evidence
- Add the next term
- Or multiply the next factor
- End at the P(k+1) formula
How to Answer
- Write the rule first: Write P(k): the formula with n=k. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.
Common Error
- You must do both base and step. The step alone does not start the chain.
FBISE Exam Check
- State the rule, show the working, and check the answer.
60-second revision
- Write P(k): the formula with n=k.
- Add the next term
- Or multiply the next factor
- State the rule, show the working, and check the answer.
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