Understanding Binomial Theorem and Pascal's Triangle

Understanding Binomial Theorem and Pascal's Triangle

Assessment

Interactive Video

Mathematics

9th - 12th Grade

Hard

CCSS
HSA.APR.C.5

Standards-aligned

Created by

Sophia Harris

FREE Resource

Standards-aligned

CCSS.HSA.APR.C.5
The video connects the binomial theorem to combinatorics and Pascal's triangle. It uses the example of expanding (x + y)^3 to explain how terms are chosen using combinatorics, specifically 'three choose two'. The video then relates this to Pascal's triangle, illustrating how different paths in the triangle correspond to choosing terms in the expansion. The explanation includes visualizing paths and expression choices, providing a deeper understanding of the relationship between these mathematical concepts.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the main focus of the video tutorial?

Understanding the quadratic formula

Connecting binomial theorem with combinatorics and Pascal's triangle

Learning about calculus

Exploring the Pythagorean theorem

Tags

CCSS.HSA.APR.C.5

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In the expansion of (x + y)^3, how many expressions are multiplied together?

Two

Five

Three

Four

Tags

CCSS.HSA.APR.C.5

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How many ways can you choose two y's from three expressions in the expansion of (x + y)^3?

Three

Two

Four

One

Tags

CCSS.HSA.APR.C.5

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What real-world analogy is used to explain choosing terms in the binomial expansion?

Selecting fruits from a basket

Picking friends for a car ride

Choosing books from a library

Choosing colors for a painting

Tags

CCSS.HSA.APR.C.5

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What does Pascal's triangle help visualize in terms of binomial expansion?

The variables used

The coefficients of the expansion

The degree of the polynomial

The number of terms

Tags

CCSS.HSA.APR.C.5

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How many ways are there to reach a node in Pascal's triangle?

One

Four

Two

Three

Tags

CCSS.HSA.APR.C.5

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What does each path in Pascal's triangle represent in terms of binomial expansion?

A choice between addition and subtraction

A choice between x and y

A choice between a and b

A choice between multiplication and division

Tags

CCSS.HSA.APR.C.5

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