Algebra Introduction — Crash Course Review Quiz
7 medium-difficulty multiple-choice questions that reference the video sections. Tests recall and applied reasoning across like terms, polynomials, distribution/FOIL, exponent rules, negative/zero exponents, rational expressions, and complex fraction operations.
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Quiz Questions & Answers
Review every prompt, the correct responses, and helpful context to prep for your own run-through.
Question 1: Which pair of terms can be combined directly as like terms?
3xy and 3x^2y
2 and 2x
5x and 8y
4x^2 and -7x^2
Question 2: Which label best describes 7x - 3x^2 + 5?
Polynomial (trinomial)
Rational expression
Monomial
Binomial
Question 3: When multiplying (2x + 3)(x - 4) by FOIL, which intermediate product must correctly account for sign and yield the outer term?
2x * x = 2x^2
2x * -4 = -8x
3 * x = 3x
3 * -4 = -12
Question 4: Given x^3 * x^-5 * x^2, what exponent rule yields the simplified power of x?
Add exponents: x^(3 + -5 + 2) = x^0 = 1
Subtract exponents sequentially to get x^(3 - 5 - 2) = x^-4
Multiply exponents: x^(3 * -5 * 2) = x^-30
Keep as is since negative exponents are allowed
Question 5: Which manipulation correctly rewrites y^-3 in a simplified final form with only positive exponents?
y^-3 = 1 / y^3
y^-3 = y^(1/3)
y^-3 = 0
y^-3 = -y^3
Question 6: Which first step best simplifies the rational expression (6x^2y)/(15xy^2) before multiplying out numbers?
Use keep-change-flip immediately
Expand numerator to 6x·x·y then distribute into denominator
Cancel common factors: divide 6/15 → 2/5 and remove one x and one y to get (2x)/(5y)
Multiply top and bottom by 2 to eliminate fractions
Question 7: How should you simplify the complex fraction ( (2/3)x ) ÷ ( (4/9)x^2 ) using the video-recommended strategy?
Multiply numerator and denominator by 9 to get rid of denominators then simplify to (18x)/(36x^2) = 1/(2x)
Treat x factors as like terms and combine to x^3
Add fractions across: (2/3 + 4/9) x^(1-2) = (2/3 + 4/9)x^-1
Apply keep-change-flip: (2/3)x * (9/4)x^-2 = (3/2) * x^-1 → (3)/(2x)