Mathematical Induction Methods and Concepts

Mathematical Induction Methods and Concepts

Assessment

Interactive Video

Mathematics

11th - 12th Grade

Practice Problem

Hard

Created by

Sophia Harris

FREE Resource

The video tutorial covers advanced mathematical induction in Mathematics Extension 2, focusing on proving statements for values greater than a specific number. It introduces two methods: the assumption approach and the subtraction technique. The tutorial explains how to substitute inequalities into equations and perform algebraic manipulations to simplify expressions. The video concludes with a complete proof and emphasizes the importance of understanding domain restrictions.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is a key difference between mathematical induction in Extension 1 and Extension 2?

Extension 2 starts from n=1.

Extension 2 involves simpler problems.

Extension 2 includes inequalities and starts from n=5.

Extension 2 does not use inequalities.

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In Method 1, what is the initial assumption made?

The statement is true for n=k+1.

The statement is true for n=k.

The statement is false for n=k.

The statement is true for all n.

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the main idea behind Method 2?

Assuming the statement is false.

Subtracting one side from the other to show positivity.

Proving the statement directly.

Using inequalities to prove the statement.

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the equivalent statement when proving that a is greater than b?

a * b is greater than zero.

a - b is less than zero.

a + b is greater than zero.

a - b is greater than zero.

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How can you substitute an inequality into an equation according to Method 2?

By ignoring the inequality.

By adding terms to both sides.

By turning it into an equivalent equation.

By replacing a larger term with a smaller one.

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In the context of Method 2, what does it mean if 2^k is greater than k^2?

k^2 can be replaced with a larger term.

2^k can be replaced with a smaller term.

2^k is less than k^2.

2^k is equal to k^2.

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the result of subtracting the right-hand side from the left-hand side in Method 2?

A negative value.

A positive value.

A value equal to zero.

An undefined value.

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