Basics
Who is Pascal’s Triangle named after?
Blaise pascal
What number appears on both edges of the triangle?
1
What kind of expressions does Pascal’s Triangle help expand?
Binomial expressions like (a+b)n
What does Pascal’s Triangle help us find in algebra?
Binomial coefficients / Expanding (a+b)n
What does “binomial” means in the phrase “binomial expansion”?
An expression with two terms (like a+b)
What number is at the very top of Pascal's Triangle
1
Each number inside the triangle is the sum of what?
The two numbers above it
What are the coefficients of (a+b)2?
1,2,1
Using the 5th row of Pascal’s Triangle, what are the coefficients of (a+b)4 ?
1, 4, 6, 4, 1
How many elements are in the 10th row of Pascal’s Triangle?
11 elements
What are the first three rows of Pascal's triangle?
A triangle
What do you notice about the triangle if you add all numbers in each row?
They double each time (1, 2, 3, 8, 16...)
Which row shows the coefficient of (a+b)4?
5th row: 1,4,6,4,1
What row of Pascal´s Triangle gives you the number of ways to flip 3 coins?
4th row (1,3,3,1)
In Pascal’s Triangle, what is the suk of the numbers in 6th row?
64
What are the first three rows of Pascal's triangle?
1;1 1; 1 2 1
What do you notice if you color or mark all the odd numbers in Pascal’s Triangle?
You see a repeating triangle pattern appear.
What are the coefficients for (a+b)5?
1,5,10,10,5,1
What´s the total sum of numbers in the 5th row?
32
True or false: Pascal’s Triangle can br extended infinitely?
True
What year did Blaise Pascal create the triangle named after him?
Around 1654
What do the diagonals of Pascal's Triangle represent?
Counting numbers, triangular numbers, and other sequences.
What is the 7th term (counting from 1) in (a+b)6?
b6 term: 1
If you pick 3 objects out of 5, which Pascal's Triangle number represents that
10 (from row 5, position 3)
Using Pascal’s Triangle, what are the coefficients of the expansion of (x+y)6 ?
1, 6, 15, 20, 15, 6, 1