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 11

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

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 if n is an integer, then n² + n is always even.

Prove that if n is an integer, then n³ - n is always divisible by 3.

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

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

Prove that the square of any integer is either of the form 4k or 4k+1 for some integer k.

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

Prove that the sum of the cubes of two consecutive integers is always an odd number.

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

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

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