Download Math Lesson-2.notebook

Math Lesson­2.notebook
April 30, 2015
Daily Objective
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Students will learn how to determine the value of nCr by using Pascal's Triangle.
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Math Lesson­2.notebook
April 30, 2015
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10.2 Binomial Theorem
Day 2
Pascal's Triangle
The values of nCr in a triangular pattern in which each row corresponds with to a value of n.
Rows
n = 0 (0th)
n = 1 (1st)
n = 2 (2nd)
n = 3 (3rd)
n = 4 (4th)
n = 5 (5th)
Triangle as Combinations
0 C0
1 C 0 1 C 1
2C0 2C1 2C2
3C0 3C1 3C2 3C3
4C0 4C1 4C2 4C3 4C4
5C0 5C1 5C2 5C3 5C4 5C5
Triangle as Numbers
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1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
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Math Lesson­2.notebook
April 30, 2015
Ex. 4: The 6 members of a Model UN club must choose 2 representatives to attend a state convention. Use Pascal's Triangle to find the number of combinations of 2 members that can be chosen as representatives.
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Math Lesson­2.notebook
April 30, 2015
Binomial Theorem
For any positive integer n, the binomial expansion of (a + b)n is:
0 n
n­2 2
n­1 1
n 0
n
(a + b) = nC0a b + nC1a b + nC2a b + ... + nCna b
Ex. 5: Use the Binomial Theorem to write the binomial expansion for (x2 + y)3.
Ex. 6: Use the Binomial Theorem to write the binomial expansion for (a ­ 2b)4.
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Math Lesson­2.notebook
April 30, 2015
Ex. 7: Find the coefficient of x4 in the expansion of (3x + 2)10.
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Math Lesson­2.notebook
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April 30, 2015
YOU PRACTICE
1. In ex. 4, use Pascal's triangle to find the number of combinations of 2 members that can be chosen if the Model UN club has 7 members.
Use the binomial theorem to write the binomial expansion.
2. (x + 3)5
3. (5 ­ 2y)3
4. Find the coefficient of x5 in the expansion of (x ­ 3)7.
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Math Lesson­2.notebook
April 30, 2015
10.2 You Practice is for a Grade!
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