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?
- 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?
- Negative 1/3 (the negative reciprocal).
- What does the y-intercept of a line represent?
- The value of y when x equals zero; where the line crosses the y-axis.
- Parallel lines have what relationship between their slopes?
- Equal slopes.
- What does the discriminant (b^2 - 4ac) tell you about a quadratic equation?
- 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?
- (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?
- (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?
- Add the exponents: a^m * a^n = a^(m+n).
- What does a negative exponent mean? Simplify x^(-3).
- A negative exponent means take the reciprocal: x^(-3) = 1/x^3.
- Simplify sqrt(72).
- 6*sqrt(2); factor out perfect squares: sqrt(36 * 2) = 6*sqrt(2).
- What does it mean to rationalize a denominator?
- 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?
- 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?
- Flip (reverse) the inequality sign.
- Solve: |x - 2| = 5. What are the solutions?
- 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?
- f(x) shows that the output depends on the input x; f(3) means substitute 3 for x and evaluate.