MATHCOUNTS TOOLBOX Facts, Formulas and Tricks

1. MATHCOUNTS TOOLBOXFacts, 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.

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

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

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

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

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

12. Prime Numbers If the 1st 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 1st 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 1st 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

16. Hockey Stick Pattern

17. Triangular Numbers

18. Triangular Numbers

19. Triangular Numbers

20. Points on a Circle .

21. Points on a Circle . . .

22. Points on a Circle . . . . . . . . .

23. Points on a Circle . . . . . . . . . . . . . . . . . . .

24. Points on a Circle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

25. Points on a Circle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . and so on . . .

26. Fini?