Maths Extension 1 Year 11 - Module 4 - Lesson 8
Pascal's Triangle & Its Properties
Name
Date
Class
1. Lesson focus
Pascal triangle and coefficients. Pascal’s triangle begins with row 0=[1]; row n contains the coefficients nCr, and each interior entry is the sum of the two directly above it.
Success criteria
- Apply the lesson method accurately in a routine example.
- Show each algebraic or domain step and check the result.
- Explain why the method and restrictions fit the question.
2. Worked practice
2. Use Pascal’s rule to find 6C2.
3. Find the coefficient of x² in (1+x)^5.
3. Challenge
Use Pascal’s rule to calculate 7C3.
4. Multiple choice
The third entry of Pascal row 5 (starting with 1) is?
A. 10
B. 5
C. 15
D. 20
Worked answer key
Compare each step with your working. Keep stated intervals, domains and restrictions in your final answer.
1. Write the first five entries of Pascal row 4.
1, 4, 6, 4, 1.
2. Use Pascal’s rule to find 6C2.
6C2=5C1+5C2=5+10=15.
3. Find the coefficient of x² in (1+x)^5.
The coefficient is 5C2=10.
Challenge. Use Pascal’s rule to calculate 7C3.
7C3=6C2+6C3=15+20=35.
Multiple choice. The third entry of Pascal row 5 (starting with 1) is?
Correct answer: A. Row 5 is 1,5,10,10,5,1, so the third entry is 10.
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