subject

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 8
If a = 2 and b = 3, prove that (a + b)² - (a - b)² = 4ab.
If a = 3 and b = 2, prove that (a + b)² = a² + 2ab + b².
If a = 4 and b = 1, prove that (a + b)² - (a - b)² = 4ab.
If a = 5 and b = 2, prove that a² - b² = (a - b)(a + b).
If x + 3 = 7, prove that x = 4.
If x = 2 and y = 5, prove that xy + x + y = (x + 1)(y + 1) - 1.
If x = 3 and y = 4, prove that (x + y)² = x² + 2xy + y².
Prove that for any integer n, n(n + 1) is always even.
Which of the following is a correct algebraic proof for the associative property of multiplication? (1) (ab)c = a(bc), (2) a + b = b + a, (3) a(b + c) = ab + ac
Which of the following is a correct algebraic proof for the commutative property of addition? (1) a + b = b + a, (2) ab = ba, (3) a(b + c) = ab + ac
Which of the following is a correct algebraic proof for the distributive property? (1) a(b + c) = ab + ac, (2) a + b = b + a, (3) (ab)c = a(bc)
Which of the following is a valid algebraic proof for the distributive law? (1) a(b + c) = ab + ac, (2) a + (b + c) = (a + b) + c, (3) ab = ba
Fill in the blank: If n is an odd integer, then n can be written as ______, where k is an integer.
Fill in the blank: The difference of the squares of two consecutive integers is always ______.
Fill in the blank: The product of two consecutive integers is always ______.
Fill in the blank: The product of two odd numbers is always ______.
True or False: If x is a multiple of 10, then x is also a multiple of 5.
True or False: If x is an even number, then x² is also even.
True or False: If x is odd, then x + 1 is even.
True or False: The difference between the squares of two consecutive numbers is always odd.