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.
If a and b are integers, which of the following is always true? (1) a + b is an integer, (2) a/b is always an integer, (3) ab is always even, (4) a - b is always positive
If a, b, and c are real numbers, which property is illustrated by a + (b + c) = (a + b) + c? (1) Commutative, (2) Associative, (3) Distributive, (4) Identity
If x is a real number, which of the following is always true? (1) x + 0 = x, (2) x + 0 = 0, (3) x + 0 = 1, (4) x + 0 = x²
If x is a real number, which of the following is always true? (1) x² ≥ 0, (2) x² ≤ 0, (3) x² = x, (4) x² < 0
Fill in the blank: If n is an integer, then n(n+1) is always ________.
Fill in the blank: If n is an integer, then n³ - n is always divisible by ________.
Fill in the blank: The difference between the squares of two consecutive integers is always ________.
Fill in the blank: The product of an even and an odd integer is always ________.
True or False: If a and b are both even, then a + b is even.
True or False: If a and b are both odd, then a - b is always even.
True or False: If a is even and b is odd, then a × b is even.
True or False: If x is a real number, then (x + 1)² = x² + 1.
