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.

Which of the following is a correct algebraic proof that the difference of the squares of two consecutive integers is always odd? (1) (n+1)² - n² = 2n+1 (2) (n+1)² - n² = 2n (3) (n+1)² - n² = n+1 (4) (n+1)² - n² = n²+1

Which of the following is a correct proof that the product of two consecutive integers is always even? (1) n(n+1) = 2k (2) n(n+1) = 2k+1 (3) n(n+1) = n²+n (4) n(n+1) = 2m, where m is an integer

Which of the following is a correct proof that the sum of two even integers is always even? (1) 2m + 2n = 2(m+n) (2) 2m + 2n = 2(m+n)+1 (3) 2m + 2n = 2(m+n+1) (4) 2m + 2n = 2(m+n-1)

Which of the following is a correct proof that the sum of two odd integers is always even? (1) (2m+1) + (2n+1) = 2(m+n+1) (2) (2m+1) + (2n+1) = 2(m+n) (3) (2m+1) + (2n+1) = 2(m+n)+2 (4) (2m+1) + (2n+1) = 2(m+n+2)

Fill in the blank: If n is an integer, then n(n+1) is always _______.

Fill in the blank: The difference between the cubes of two consecutive integers is _______.

Fill in the blank: The difference between the squares of any two consecutive integers is _______.

Fill in the blank: The difference between the squares of two numbers a and b is _______.

If n is an integer, is n² - n always even?

If n is an integer, is n³ - n always divisible by 3?

If x and y are both even integers, is x + y always even?

If x is a rational number and y is an irrational number, is x + y always irrational?