Algebraic Proofs
Math ⇒ Algebra
Algebraic Proofs starts at 8 and continues till grade 12.
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See sample questions for grade 9
If a and b are both odd numbers, what can you say about their sum?
If a and b are both odd, is ab odd or even?
If a and b are integers and a is even, what can you say about ab?
If x + y is even and x is odd, what can you say about y?
If x is an odd integer, prove that x² is also odd.
Prove that for any integer n, n³ - n is always divisible by 6.
Prove that the product of any three consecutive integers is divisible by 6.
Prove that the product of two consecutive integers is always even.
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 (4) a + (b + c) = (a + b) + c
Which of the following is a correct expansion of (a + b)(a - b)? (1) a² - b² (2) a² + b² (3) a² - 2ab + b² (4) a² + 2ab + b²
Which of the following is a correct expansion of (a + b)²? (1) a² + 2ab + b² (2) a² - 2ab + b² (3) a² + b² (4) a² - b²
Which of the following is a correct step in proving that (a - b)² = a² - 2ab + b²? (1) (a - b)² = (a - b)(a - b) (2) (a - b)² = a² - b² (3) (a - b)² = a² + 2ab + b² (4) (a - b)² = a² - ab + b²
Fill in the blank: If n is an integer, then n² - n is always _______.
Fill in the blank: If n is an odd integer, then n + 1 is _______.
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 _______.
If a and b are both even, is a + b always even?
If a number is divisible by both 2 and 3, is it always divisible by 6?
If x is an even integer, is x² always even?
If x is an integer, is x(x+1) always even?
