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 9

If a and b are both odd numbers, what can you say about their sum?

If a and b are both odd, is ab odd or even?

If a and b are integers and a is even, what can you say about ab?

If x + y is even and x is odd, what can you say about y?

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

Prove that for any integer n, n³ - n is always divisible by 6.

Prove that the product of any three consecutive integers is divisible by 6.

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

Prove that the square of any even number is divisible by 4.

Prove that the sum of any four consecutive integers is 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 the first n even numbers is n(n + 1).

Prove that the sum of the squares of two consecutive integers is always odd.

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