Algebraic Proofs

Math ⇒ Algebra

Algebraic Proofs starts at 8 and continues till grade 12. QuestionsToday has an evolving set of questions to continuously challenge students so that their knowledge grows in Algebraic Proofs. How you perform is determined by your score and the time you take. When you play a quiz, your answers are evaluated in concept instead of actual words and definitions used.

See sample questions for grade 10

If a and b are both even integers, what can you say about a × b?

If a and b are both odd integers, what can you say about a + b?

If a and b are integers, prove that (a+b)² - (a-b)² is always divisible by 4.

If n is an integer, prove that n² - 1 is always divisible by 8 when n is odd.

If n is an integer, prove that n³ - n is always divisible by 6.

If x is an odd integer, prove that x² is also odd.

Prove that for any integer n, n² + n is always even.

Prove that the difference between the squares of any two consecutive integers is always odd.

Prove that the product of two consecutive integers is always even.

Prove that the product of two odd numbers is always odd.

Prove that the sum of any four consecutive integers is always divisible by 2 but not always by 4.

Prove that the sum of any two even numbers is always even.

Prove that the sum of any two odd numbers is always even.

Prove that the sum of the first n odd numbers is n².

Prove that the sum of three consecutive integers is always divisible by 3.

Show that the sum of the squares of any two odd integers is even.