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Difference of Squares and Consecutive Integers

Difference of Squares and Consecutive Integers

Assessment

Interactive Video

Mathematics

9th - 10th Grade

Hard

Created by

Thomas White

FREE Resource

The video tutorial explains a proof problem from a GCSE past paper, demonstrating how to prove algebraically that the difference between the squares of two consecutive integers equals the sum of those integers. The instructor breaks down the problem, defines key terms, and guides through the algebraic steps to set up and solve the proof. The video concludes with a summary of the proof and encourages viewers to subscribe.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the main objective of the proof question discussed in the video?

To prove that the sum of two integers is greater than their product.

To demonstrate that the product of two integers is equal to their sum.

To prove algebraically that the difference between the squares of two consecutive integers equals the sum of these integers.

To show that the square of a number is always positive.

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What does the term 'difference' refer to in the context of the proof?

Multiplication

Subtraction

Division

Addition

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What does 'consecutive integers' mean?

Integers that are prime

Integers that are equal

Integers that are multiples of each other

Integers that are next to each other

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which algebraic symbols are used to represent the two consecutive integers in the proof?

x and x + 2

a and a + 1

m and m + 2

n and n + 1

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the first step in calculating the difference of squares?

Multiplying the integers

Dividing the integers

Squaring the integers

Adding the integers

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the result of squaring the integer n + 1?

n² + 2

n² + 2n + 1

n² + 1

n² + n + 1

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the simplified form of the difference between the squares of n and n + 1?

2n + 1

2n

n² + 1

n + 1

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