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

Slides:

Advertisements

Similar presentations

Copyright © Cengage Learning. All rights reserved.

Advertisements

MATHCOUNTS TOOLBOX Facts, Formulas and Tricks

MATHCOUNTS TOOLBOX Facts, Formulas and Tricks

MATHCOUNTS TOOLBOX Facts, Formulas and Tricks

MATHCOUNTS TOOLBOX Facts, Formulas and Tricks. Lesson 8: Determining the Number of Factors of a Number.

MATHCOUNTS TOOLBOX Facts, Formulas and Tricks

MATHCOUNTS TOOLBOX Facts, Formulas and Tricks

15-5 The Binomial Theorem Pascal’s Triangle. At the tip of Pascal's Triangle is the number 1, which makes up the zeroth row. The first row (1 & 1)

It’s a triangle. A triangle of numbers! Pascal did not create it…. The Chinese did. Blaise Pascal discovered all of the unique patterns in it.

PASCAL’S TRIANGLE. * ABOUT THE MAN * CONSTRUCTING THE TRIANGLE * PATTERNS IN THE TRIANGLE * PROBABILITY AND THE TRIANGLE.

Pascal’s Triangle By: Brittany Thomas.

Chapter 8 Sec 5 The Binomial Theorem. 2 of 15 Pre Calculus Ch 8.5 Essential Question How do you find the expansion of the binomial (x + y) n ? Key Vocabulary:

Notes 9.2 – The Binomial Theorem. I. Alternate Notation A.) Permutations – None B.) Combinations -

BINOMIAL EXPANSION. Binomial Expansions Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 2 The binomial theorem provides a useful method.

Warm Up 2/1/11 1.What is the probability of drawing three queens in a row without replacement? (Set up only) 2.How many 3 letter permutations can be made.

Warm up 1. Write the expression in expanded form, then find the sum. 2. Express the series using sigma notation.

5-7: The Binomial Theorem

Pascal’s Triangle and the Binomial Theorem Chapter 5.2 – Probability Distributions and Predictions Mathematics of Data Management (Nelson) MDM 4U.

Copyright © Cengage Learning. All rights reserved. 8.4 The Binomial Theorem.

The Binomial Theorem.

Copyright © Cengage Learning. All rights reserved. 8 Sequences, Series, and Probability.

Binomial Theorem & Binomial Expansion

Binomial Theorem Binomial Theorem Term 1 : Unit 3

Aim: How do we find probability using Pascal’s triangle? Do Now: If a coin is tossed two times, what is the probability you will get 2 heads?

Learn to find terms in an arithmetic sequence.

13-3 Other Sequences Course 3 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation.

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.

Essential Questions How do we multiply polynomials?

By: Michelle Green. Construction of Pascal’s Triangle ROW 0 ROW 1 ROW 2 ROW 3 ROW 4 ROW ROW 6 ALWAYS.

Section 8.5 The Binomial Theorem. In this section you will learn two techniques for expanding a binomial when raised to a power. The first method is called.

Section 8.5 The Binomial Theorem.

Chapter 12.5 The Binomial Theorem.

Sequences, Series, and Probability

The Binomial Theorem.

The binomial expansions

Copyright © 2014, 2010, 2007 Pearson Education, Inc.

Copyright © Cengage Learning. All rights reserved.

Section 9-5 The Binomial Theorem.

The Binomial Theorem Ms.M.M.

The Binomial Expansion Chapter 7

Day 4: Pascal’s Triangle

The Binomial Theorem Objectives: Evaluate a Binomial Coefficient

10.2b - Binomial Theorem.

Digital Lesson The Binomial Theorem.

Digital Lesson The Binomial Theorem.

Binomial Theorem Pascal’s Triangle

Essential Questions How do we use the Binomial Theorem to expand a binomial raised to a power? How do we find binomial probabilities and test hypotheses?

Patterns, Patterns, and more Patterns!

Find the area of the base, B, times the height

11.9 Pascal’s Triangle.

Blaise Pascal “Man is equally incapable of seeing the nothingness from which he emerges and the infinity in which he is engulfed.” “We are usually convinced.

11.6 Binomial Theorem & Binomial Expansion

LESSON 10–5 The Binomial Theorem.

Digital Lesson The Binomial Theorem.

Binomial Theorem; Pascal’s Triangle

The Binomial Theorem OBJECTIVES: Evaluate a Binomial Coefficient

Digital Lesson The Binomial Theorem.

The binomial theorem. Pascal’s Triangle.

PASCAL'S TRIANGLE FOR CLASS XI BENNY VARGHESE P.G.T MATHS J.N.V PUNE

Copyright © 2014, 2010, 2007 Pearson Education, Inc.

Pascal’s Arithmetic Triangle

Digital Lesson The Binomial Theorem.

Starter – Day November 12 Content Objective: We will use Pascal’s Triangle to expand polynomial expressions faster than calculating them.

Pascal’s Triangle By Marisa Eastwood.

Digital Lesson The Binomial Theorem.

Pascal’s Triangle.

Section 11.7 The Binomial Theorem

pencil, red pen, highlighter, GP notebook, calculator

Presentation transcript:

MATHCOUNTS TOOLBOX Facts, Formulas and Tricks

Lesson 12: Pascal’s Triangle & its uses

Pascal’s Triangle

Pascal’s Triangle Used for Probability

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

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

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

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

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.

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 ( )

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 ( ), 7, 21, and 35 are all divisible by 7.

Hockey Stick Pattern

Triangular Numbers

Points on a Circle.

...

and so on...

Fini?