Quantitative Reasoning and Mathematics Lecture Review

A comprehensive set of vocabulary flashcards covering arithmetic, algebra, geometry, and coordinate geometry concepts from the lecture.

Bow Tie Method

A method used for comparing the size of two fractions.

Zero Product Property

A property stating that if the product of multiple factors is zero, then at least one factor must be zero.

General Form of a Quadratic Equation

An equation in the form $ax^2 + bx + c = 0$.

Quadratic Formula

The formula used to find the roots of a quadratic equation: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.

FOILing

A method for multiplying two binomials by calculating the First, Outer, Inner, and Last terms.

LCM (Least Common Multiple)

The smallest multiple that is shared by two or more numbers.

GCF (Greatest Common Factor)

The largest factor that divides two or more numbers.

Terminating Decimals

Decimals that have a finite number of digits and do not repeat indefinitely.

Power to a Power Rule

An exponent rule stating that $(a^m)^n = a^{m \times n}$.

Negative Exponent Rule

The rule stating that a base raised to a negative exponent is equivalent to the reciprocal of the base raised to the positive version of that exponent: $a^{-n} = \frac{1}{a^n}$.

Profit Equation

The formula used to find financial gain: $\text{Profit} = \text{Revenue} - \text{Cost}$.

Simple Interest Formula

Interest calculated as $\text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time}$.

Compound Interest

Interest calculated on the initial principal and also on the accumulated interest of previous periods.

Converging/Diverging Rate Formula

The formula used when two objects move toward each other or away from each other.

Round-Trip Rate Formula

Used for calculating rate and time when an object travels to a destination and returns over the same distance.

Catch-Up Rate Formula

Used for scenarios where one object starts ahead and another object follows to reach the same position.

Rate-Time-Work Formula

The relationship defined by $\text{Rate} \times \text{Time} = \text{Work}$.

Combined Worker Formula

A formula used to determine the efficiency of two or more workers performing a task together.

Percent Change Formula

The calculation defined as $\frac{\text{New} - \text{Old}}{\text{Old}} \times 100$.

Median

The middle value in a data set; if there is an even number of terms, it is the average of the two middle values.

Mode

The value that appears most frequently in a set of data.

Standard Deviation

A measure of data dispersion calculated by taking the square root of the variance.

Interquartile Range (IQR)

The difference between the third quartile ($Q3$) and the first quartile ($Q1$).

Combinations

A way of selecting items from a larger set where the order of selection does not matter.

Permutations

A way of selecting items from a larger set where the order of selection does matter.

Triangle Inequality Theorem

A theorem stating that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Pythagorean Triples

Sets of three positive integers $(a, b, c)$ that satisfy the equation $a^2 + b^2 = c^2$.

Inscribed Angle

An angle formed by two chords in a circle that have a common endpoint on the circle.

Surface Area of a Cylinder

The total area of the exterior surfaces of a cylinder: $2(\pi r^2) + 2(\pi rh)$.

Volume of a Cylinder

The amount of space inside a cylinder, calculated as $\pi r^2 h$.

Diagonal of a Cube

The length of the segment connecting opposite corners through the center, calculated as $side \sqrt{3}$.

Diagonal of a Rectangular Solid

The length calculated using the formula $\sqrt{L^2 + W^2 + H^2}$.

Slope ($m$)

The steepness of a line determined by the change in $y$ over the change in $x$: $m = \frac{y_2 - y_1}{x_2 - x_1}$.

Slope-Intercept Equation

The equation of a straight line: $y = mx + b$.

Domain

The set of all possible input values ($x$-coordinates) for a function.

Range (Functions)

The set of all possible output values ($y$-coordinates) for a function.

Arithmetic Sequence

A sequence of numbers in which the difference between consecutive terms is constant.

Geometric Sequence

A sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero constant.