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MATHCOUNTS TOOLBOX Facts, Formulas and Tricks. Lesson 12: Pascal’s Triangle & its uses.

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Presentation on theme: "MATHCOUNTS TOOLBOX Facts, Formulas and Tricks. Lesson 12: Pascal’s Triangle & its uses."— Presentation transcript:

1 MATHCOUNTS TOOLBOX Facts, Formulas and Tricks

2 Lesson 12: Pascal’s Triangle & its uses

3 Pascal’s Triangle

4 Pascal’s Triangle Used for Probability

5 Remember that the first row is row zero (0). Row 4 is 1 4 6 4 1. This can be used to determine the different outcomes when flipping four coins.

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7 For the Expansion of (a + b) n, use numbers in Pascal’s Triangle as coefficients.

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9 For 2 n, add all the numbers in the n th row. (Remember the triangle starts with row 0.)

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11 Prime Numbers If the 1 st element in a row is a prime number (remember, the 0th element of every row is 1),

12 Prime Numbers If the 1 st element in a row is a prime number (remember, the 0th element of every row is 1), all the numbers in that row (excluding the 1's) are divisible by it.

13 Prime Numbers If the 1 st element in a row is a prime number (remember, the 0th element of every row is 1), all the numbers in that row (excluding the 1's) are divisible by it. Example: in row 7 (1 7 21 35 35 21 7 1)

14 Prime Numbers If the 1 st element in a row is a prime number (remember, the 0th element of every row is 1), all the numbers in that row (excluding the 1's) are divisible by it. Example: in row 7 (1 7 21 35 35 21 7 1), 7, 21, and 35 are all divisible by 7.

15 Hockey Stick Pattern

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17 Triangular Numbers

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20 Points on a Circle.

21 ...

22 .........

23 ...................

24 ..................................

25 .................................. and so on...

26 Fini?


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