NGSA Mathematics flashcards
NGSA Mathematics · Build recall with a focused review session.
33 cards. Read the term and the definition here. The deck at the top of this page is optional.
- Order of operations
- The agreed sequence for evaluating expressions: grouping symbols, then exponents, then multiplication and division left to right, then addition and subtraction left to right.
- Greatest common divisor
- The largest positive integer that divides two or more given integers with no remainder. Dividing numerator and denominator by it reduces a fraction to simplest form.
- Least common multiple
- The smallest positive integer that is a multiple of each of two or more given integers. It provides the least common denominator when adding or subtracting fractions.
- Reciprocal
- The multiplicative inverse of a nonzero number; the reciprocal of a/b is b/a, and their product is 1. Dividing by a fraction is the same as multiplying by its reciprocal.
- Percent change
- The ratio of the amount of change to the original amount, expressed as a percent: (new − old)/old × 100%. The original value is always the base.
- Scientific notation
- A way to write numbers as a × 10^n where 1 ≤ |a| < 10 and n is an integer. It simplifies computing with very large or very small quantities.
- Slope formula
- For two points (x₁, y₁) and (x₂, y₂), slope m = (y₂ − y₁)/(x₂ − x₁). It measures vertical change per unit of horizontal change.
- Slope-intercept form
- The equation y = mx + b, where m is the slope of the line and b is the y-coordinate of the point where the line crosses the y-axis.
- Perpendicular line slopes
- Two nonvertical lines are perpendicular exactly when their slopes are negative reciprocals, so the product of the slopes equals −1. Vertical and horizontal lines are also perpendicular.
- Quadratic formula
- For ax² + bx + c = 0 with a ≠ 0, the solutions are x = [−b ± √(b² − 4ac)]/(2a). It solves any quadratic equation, including ones that do not factor.
- Discriminant
- The expression b² − 4ac from the quadratic formula. Positive gives two real roots, zero gives one repeated real root, negative gives no real roots.
- Function
- A relation pairing each input in its domain with exactly one output. On a graph, a relation is a function if no vertical line meets it more than once.
- Direct variation
- A relationship of the form y = kx with constant k ≠ 0, meaning the ratio y/x stays constant. Its graph is a line through the origin.
- Inverse variation
- A relationship of the form y = k/x with constant k ≠ 0, meaning the product xy stays constant. As one quantity increases, the other decreases.
- System of linear equations
- Two or more linear equations solved together. The solution is the ordered pair satisfying all equations, found by substitution or elimination, or shown as the intersection of their graphs.
- Triangle angle sum
- The three interior angles of any triangle add to 180 degrees. This fact lets you find a missing angle when the other two are known.
- Pythagorean theorem
- In a right triangle, the square of the hypotenuse equals the sum of the squares of the legs: a² + b² = c², where c is the side opposite the right angle.
- Circle area and circumference
- For radius r, area A = πr² and circumference C = 2πr = πd. Area is measured in square units; circumference is measured in linear units.
- Similar figures
- Figures with equal corresponding angles and proportional corresponding side lengths. The ratio of their areas equals the square of the scale factor relating their sides.
- Interior angle sum of polygon
- A polygon with n sides has interior angles totaling (n − 2) × 180 degrees. In a regular polygon, each interior angle equals that total divided by n.
- Complementary and supplementary
- Complementary angles have measures summing to 90 degrees; supplementary angles sum to 180 degrees. A linear pair of angles is supplementary.
- Volume of a cylinder
- For a right circular cylinder, V = πr²h, where r is the base radius and h is the height. Volume is expressed in cubic units.
- Mean
- The arithmetic average of a data set, found by adding all values and dividing by the number of values. It is strongly affected by outliers.
- Median
- The middle value when data are ordered from least to greatest; with an even count, it is the mean of the two middle values. It resists outliers.
- Interquartile range
- The difference between the third quartile and the first quartile, IQR = Q₃ − Q₁. It measures the spread of the middle half of the data.
- Theoretical probability
- For equally likely outcomes, P(event) = number of favorable outcomes ÷ total number of outcomes. Every probability lies between 0 and 1 inclusive.
- Complement rule
- The probability that an event does not occur equals 1 minus the probability that it does: P(not E) = 1 − P(E).
- Independent events
- Events whose outcomes do not affect each other. For independent events, the probability that both occur is the product of their individual probabilities.
- Correlation coefficient
- A number r between −1 and 1 describing the strength and direction of a linear association. Values near 0 indicate weak or no linear relationship.
- Unit rate
- A rate expressed per single unit of the second quantity, found by dividing. It allows scaling to any amount by multiplication.
- Average speed
- Total distance traveled divided by total time taken. For trips at different speeds, it is not the simple average of the speeds.
- Combined work rate
- When workers complete a job at rates 1/t₁ and 1/t₂, their combined rate is the sum. The time together is 1 divided by that sum.
- Cross multiplication
- A method for solving proportions a/b = c/d (b, d ≠ 0) by setting ad = bc. It converts a proportion into a linear equation.