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.
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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.
If n is an integer, which of the following is always even? (1) n² + 1 (2) n² - 1 (3) n² + n (4) n² - n + 1
If x is an even integer, which of the following is always true? (1) x² is odd (2) x² is even (3) x² + 1 is even (4) x² + x is odd
If x is an integer, which of the following expressions is always odd? (1) x² + x (2) x² - x (3) x² + 2x + 1 (4) x² + x + 1
Which of the following is a correct proof that the sum of two odd numbers is even? (1) 2a + 2b = 2(a+b) (2) 2a+1 + 2b+1 = 2(a+b+1) (3) 2a+1 + 2b+1 = 2(a+b+1) (4) 2a+1 + 2b+1 = 2(a+b+1)
Fill in the blank: If n is any integer, then n(n+1) is always _______.
Fill in the blank: If n is any integer, then n² - n is always _______.
Fill in the blank: The difference between the squares of two consecutive integers is always _______.
Fill in the blank: The product of any two consecutive integers is always _______.
True or False: If n is an integer, then n³ - n is always divisible by 6.
True or False: If n is an integer, then n³ + n is always even.
True or False: The difference between the squares of any two consecutive integers is always odd.
True or False: The product of an even and an odd number is always even.
