About this Flash Card Set
18 Cards
by ryan_mitchell
Plain-language definitions of the core algebra vocabulary and formulas, made for students who want the fundamentals to finally click before tackling harder problems.
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What is a variable?
Back
A letter or symbol that stands in for an unknown or changing number. Example: in 3x + 2, the x is the variable.
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What is a coefficient?
Back
The number multiplied by a variable in a term. Example: in 5y, the coefficient is 5. If a variable has no visible number (like x), its coefficient is 1.
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What is a constant?
Back
A fixed value that does not change — a plain number with no variable attached. Example: in 4x + 7, the constant is 7.
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What is a term?
Back
A single part of an expression separated by + or - signs. It can be a number, a variable, or a product of them. Example: 3x, -2, and 5xy are each one term.
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Expression vs. equation — what's the difference?
Back
An expression is a combination of numbers, variables, and operations with no equals sign (like 2x + 3). An equation sets two expressions equal with an = sign (like 2x + 3 = 11).
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What are like terms?
Back
Terms with the exact same variable(s) raised to the same power, so they can be combined. Example: 3x and 5x are like terms (they add to 8x), but 3x and 3x² are not.
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What is the order of operations (PEMDAS)?
Back
The order for evaluating expressions: Parentheses, Exponents, Multiplication and Division (left to right), then Addition and Subtraction (left to right). Example: 2 + 3 × 4 = 2 + 12 = 14.
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What is the distributive property?
Back
Multiplying a sum means multiplying each term inside the parentheses: a(b + c) = ab + ac. Example: 3(x + 4) = 3x + 12.
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What is slope?
Back
A measure of a line's steepness — the rise over the run, or change in y divided by change in x: m = (y₂ - y₁) / (x₂ - x₁). Example: from (0,1) to (2,5), slope = (5-1)/(2-0) = 2.
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What is slope-intercept form?
Back
y = mx + b, where m is the slope and b is the y-intercept (where the line crosses the y-axis). Example: y = 2x + 3 has slope 2 and crosses the y-axis at 3.
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What is the quadratic formula?
Back
For ax² + bx + c = 0, the solutions are x = (-b ± √(b² - 4ac)) / (2a). It finds the x-values where a quadratic equals zero.
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What is factoring?
Back
Rewriting an expression as a product of simpler factors — the reverse of multiplying out. Example: x² + 5x + 6 factors into (x + 2)(x + 3).
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What is FOIL?
Back
A method for multiplying two binomials: First, Outer, Inner, Last. Example: (x + 2)(x + 3) = x² + 3x + 2x + 6 = x² + 5x + 6.
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What is an inequality?
Back
A statement comparing two expressions using <, >, ≤, or ≥ instead of equals. Example: x + 3 > 5 is true for any x greater than 2.
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What are the basic exponent rules?
Back
Multiply powers with the same base by adding exponents: xᵃ · xᵇ = xᵃ⁺ᵇ. Divide by subtracting: xᵃ / xᵇ = xᵃ⁻ᵇ. A power of a power multiplies: (xᵃ)ᵇ = xᵃᵇ. And x⁰ = 1.
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What is absolute value?
Back
The distance of a number from zero on the number line, always zero or positive. Written with bars: |x|. Example: |-4| = 4 and |4| = 4.
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What is a function?
Back
A rule that assigns exactly one output to each input. Often written f(x). Example: for f(x) = 2x + 1, the input 3 gives f(3) = 7.
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What does 'solving for x' mean?
Back
Rearranging an equation using inverse operations to get x alone on one side. Example: to solve 2x + 3 = 11, subtract 3 (2x = 8), then divide by 2 (x = 4).
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