Algebra rules and equation-solving shortcuts commonly tested on the GMAT quant section. Front: the concept or rule. Back: definition or formula with a brief usage note.
33 cards · basic cards · AI-written, checked twice. Edit anything.
- Distributive property: a(b + c) = ?
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ab + ac. Use to expand products and factor expressions.- FOIL method: (a + b)(c + d) = ?
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ac + ad + bc + bd. First, Outer, Inner, Last.- Difference of squares: a^2 - b^2 = ?
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(a + b)(a - b). Factors as sum times difference.- Perfect square trinomial: (a + b)^2 = ?
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a^2 + 2ab + b^2. First squared, double product, last squared.- Sum of cubes: a^3 + b^3 = ?
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(a + b)(a^2 - ab + b^2). Factor as sum times a special trinomial.- Difference of cubes: a^3 - b^3 = ?
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(a - b)(a^2 + ab + b^2). Factor as difference times a special trinomial.- Quadratic formula: x = ?
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(-b +/- sqrt(b^2 - 4ac)) / 2a for ax^2 + bx + c = 0.- Completing the square: what is the goal?
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Rewrite ax^2 + bx + c as (x + p)^2 + q to solve or analyze the quadratic.- When you multiply or divide an inequality by a negative number, what happens to the sign?
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The inequality sign flips. If a < b and c < 0, then ac > bc.- For a quadratic ax^2 + bx + c with roots r and s, the sum r + s = ?
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-b/a. The sum of roots equals negative b divided by a.- For a quadratic ax^2 + bx + c with roots r and s, the product rs = ?
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c/a. The product of roots equals c divided by a.- What is an extraneous solution?
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A value that satisfies the transformed equation but not the original equation, often from squaring both sides.- Fraction addition: a/b + c/d = ?
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(ad + bc) / bd. Find a common denominator, add numerators.- Fraction subtraction: a/b - c/d = ?
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(ad - bc) / bd. Find a common denominator, subtract numerators.- Fraction multiplication: a/b * c/d = ?
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ac / bd. Multiply numerators together, multiply denominators together.
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