Assess your understanding of foundational algebraic principles with questions covering equations, expressions, variables, and essential problem-solving skills. This Mathematics Algebra Fundamentals Quiz is designed to help learners practice and reinforce core algebra knowledge in a concise format.
Which pair of terms can be combined because they are like terms in the expression 5x + 3y - 2x + 7?
Explanation: Like terms are those that have the exact same variable(s) raised to the same power, such as 5x and -2x. They can be combined through addition or subtraction. 3y and 7 are not like terms because 7 does not have a variable. 5x and 3y have different variables, while 3y and -2x also do not share the same variable. Only 5x and -2x meet the requirement.
What is the value of x in the equation 3x - 7 = 11?
Explanation: To solve 3x - 7 = 11, add 7 to both sides to get 3x = 18, then divide by 3 to find x = 6. 'x = 4' results from incorrectly adding instead of dividing properly. 'x = -6' comes from misplacing the subtraction. 'x = 18' is what you get before dividing by 3, so only 'x = 6' is correct.
Which expression is equivalent to 4(2x + 5)?
Explanation: Applying the distributive property, multiply 4 by both 2x and 5, resulting in 8x + 20. '8x + 5' ignores multiplying 4 by 5, while '8x + 10x' results from incorrectly distributing and adding variables. '4x + 10' comes from multiplying 4 only by x and 5, not 2x. The correct choice is '8x + 20'.
What are the factored terms of the quadratic expression x² + 7x + 12?
Explanation: To factor x² + 7x + 12, look for two numbers that multiply to 12 and add up to 7. 3 and 4 are such a pair, so (x + 3)(x + 4) is correct. The other options have pairs that either do not add to 7 or do not multiply to 12. For example, 6 and 1 add to 7 but multiply to 6, while 2 and 5 multiply to 10.
In the equation 2y + 9 = 23, what is the coefficient of y?
Explanation: The coefficient is the numerical factor multiplying a variable, which in this case is 2, as it multiplies y in 2y. 9 is a constant added to the expression, not linked directly to y. 23 is the value on the right side of the equation, not a coefficient. 'y' is the variable, not the coefficient.