Core algebra and problem-solving concepts tuned to PSAT math section question styles, explained conceptually.
34 cards · basic cards · AI-written, checked twice. Edit anything.
- What is the slope of a line, and what does it measure?
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The ratio of vertical change (rise) to horizontal change (run) between two points; measures steepness and direction of a line.- Two lines are perpendicular. If one has slope 3, what is the slope of the other?
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Negative 1/3 (the negative reciprocal).- What does the y-intercept of a line represent?
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The value of y when x equals zero; where the line crosses the y-axis.- Parallel lines have what relationship between their slopes?
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Equal slopes.- What does the discriminant (b^2 - 4ac) tell you about a quadratic equation?
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Whether the equation has two real solutions (positive), one real solution (zero), or no real solutions (negative).- What is the difference between (x + 3)^2 and x^2 + 9?
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(x + 3)^2 = x^2 + 6x + 9; they are not equal. Squaring a binomial requires the middle term.- How do you factor x^2 - 16?
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(x - 4)(x + 4); it is a difference of squares: a^2 - b^2 = (a - b)(a + b).- When you multiply powers with the same base, what do you do with the exponents?
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Add the exponents: a^m * a^n = a^(m+n).- What does a negative exponent mean? Simplify x^(-3).
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A negative exponent means take the reciprocal: x^(-3) = 1/x^3.- Simplify sqrt(72).
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6*sqrt(2); factor out perfect squares: sqrt(36 * 2) = 6*sqrt(2).- What does it mean to rationalize a denominator?
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Rewrite a fraction so the denominator contains no radicals, usually by multiplying by a form of 1.- What is the absolute value of -7, and what does absolute value represent?
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7; absolute value is the distance from zero on a number line (always non-negative).- If you multiply both sides of an inequality by a negative number, what must you do?
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Flip (reverse) the inequality sign.- Solve: |x - 2| = 5. What are the solutions?
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x = 7 or x = -3; absolute value splits into two cases: x - 2 = 5 and x - 2 = -5.- What is function notation, and what does f(3) mean?
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f(x) shows that the output depends on the input x; f(3) means substitute 3 for x and evaluate.
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