NY Regents Algebra I flashcards
NY Regents Algebra I · Build recall with a focused review session.
32 cards. Read the term and the definition here. The deck at the top of this page is optional.
- Rational number
- A number expressible as a fraction of two integers with a nonzero denominator. Its decimal form either terminates or repeats, such as 0.75 or 0.333...
- Irrational number
- A real number that cannot be written as a fraction of integers. Its decimal is non-terminating and non-repeating, for example √2 or π.
- Simplify √(x²)
- The square root of x squared equals the absolute value of x, written |x|, because the principal square root is never negative.
- Negative exponent rule
- A base raised to a negative exponent equals the reciprocal of that base raised to the positive exponent: a^(−n) = 1/a^n for a not equal to zero.
- Scientific notation form
- A number written as a × 10^n where 1 ≤ |a| < 10 and n is an integer. Multiplying numbers adds their exponents; dividing subtracts them.
- Rationalize a denominator
- Rewrite a fraction so no radical remains in the denominator, usually by multiplying numerator and denominator by the radical or conjugate needed to clear it.
- Slope formula
- The slope between points (x₁, y₁) and (x₂, y₂) is m = (y₂ − y₁)/(x₂ − x₁), measuring vertical change per unit of horizontal change.
- Quadratic formula
- For ax² + bx + c = 0 with a ≠ 0, the solutions are x = (−b ± √(b² − 4ac))/(2a). It solves any quadratic equation.
- Discriminant
- The expression b² − 4ac from the quadratic formula. Positive gives two real solutions, zero gives one, and negative gives no real solutions.
- Zero product property
- If a product of factors equals zero, then at least one factor equals zero. This lets you solve factored equations by setting each factor to zero.
- Difference of squares
- The factoring pattern a² − b² = (a − b)(a + b). It applies whenever a binomial is a perfect square minus another perfect square.
- Vertex of a parabola
- For y = ax² + bx + c, the vertex x-coordinate is −b/(2a). The vertex is the maximum or minimum point of the parabola.
- Perpendicular line slopes
- Two nonvertical lines are perpendicular exactly when their slopes are negative reciprocals, so the product of the slopes equals negative one.
- Exponential decay model
- The formula y = a(1 − r)^t models decay, where a is the starting amount, r is the decay rate as a decimal, and t is time periods.
- Vertical line test
- A graph represents a function if and only if no vertical line crosses it more than once, meaning each input has exactly one output.
- Function notation f(x)
- f(x) names the output of function f for input x. To evaluate, substitute the given value for every x in the rule.
- Domain and range
- Domain is the set of all allowed input values; range is the set of resulting output values. For real functions, exclude division by zero and negative radicands.
- Average rate of change
- On the interval from a to b, it equals (f(b) − f(a))/(b − a), the slope of the secant line connecting those two points on the graph.
- Inverse function
- A function that reverses another, swapping inputs and outputs. Its graph reflects over y = x, and it exists only when the original is one-to-one.
- Arithmetic sequence formula
- The nth term is aₙ = a₁ + (n − 1)d, where a₁ is the first term and d is the constant common difference added each step.
- Geometric sequence formula
- The nth term is aₙ = a₁r^(n−1), where a₁ is the first term and r is the constant ratio multiplied between consecutive terms.
- Distance formula
- The distance between two points is √((x₂ − x₁)² + (y₂ − y₁)²), derived from the Pythagorean theorem on the coordinate plane.
- Midpoint formula
- The midpoint of a segment with endpoints (x₁, y₁) and (x₂, y₂) is ((x₁ + x₂)/2, (y₁ + y₂)/2), averaging the coordinates.
- Circle equation
- (x − h)² + (y − k)² = r² describes a circle with center (h, k) and radius r on the coordinate plane.
- 30-60-90 triangle ratios
- A right triangle with angles 30°, 60°, and 90° has side lengths in the ratio 1 : √3 : 2, with the hypotenuse twice the shortest side.
- 45-45-90 triangle ratios
- An isosceles right triangle has side lengths in the ratio 1 : 1 : √2, so the hypotenuse equals a leg times the square root of two.
- Similar figure scaling
- Corresponding sides of similar figures are proportional. Areas scale by the square of the scale factor and volumes by its cube.
- Interquartile range
- The difference between the third quartile and first quartile, IQR = Q3 − Q1. It measures the spread of the middle half of the data.
- Standard deviation shift rule
- Adding the same constant to every data value leaves the standard deviation unchanged; multiplying every value by a constant multiplies it by the absolute value of that constant.
- Residual
- The difference between an observed value and the value predicted by a line of best fit, calculated as actual minus predicted.
- Independent events probability
- When two events do not affect each other, the probability both occur equals the product of their individual probabilities: P(A and B) = P(A)·P(B).
- Conditional probability
- The probability of event A given that B occurred equals P(A and B) divided by P(B), provided P(B) is greater than zero.