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 12

If a and b are odd integers, prove that their product is always odd.

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

Prove that for any integer n, n³ + 2n is always divisible by 3.

Prove that for any integer n, n³ + n² + n is always divisible by 6.

Prove that for any integer n, n⁴ - n² is always divisible by 6.

Prove that for any integer n, n⁵ - n is always divisible by 30.

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

Prove that the product of any four consecutive integers is always divisible by 24.

Prove that the square of any odd integer is always odd.

Prove that the sum of any three consecutive even integers is always divisible by 6.

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.