IM3/IM3H Second Semester Final Exam Practice Flashcards

Comprehensive vocabulary flashcards covering probability, statistics, trigonometry, and financial math based on the IM3/IM3H semester final study guide.

Probability

The chance that something will occur, defined as $0 \leq P \leq 1$ or $0\% \leq P \leq 100\%$. For random outcomes, it is calculated as \frac{\text{# of successful outcomes}}{\text{# of total possible outcomes}}.

Independent Events

Two events are independent if the outcome of neither one affects the chances/probability of the other.

Complement of Event E

Read as ‐E prime‑ and denoted by $E'$, it is the set of all outcomes not included in event E. $P(E') = 1 - P(E)$ and $P(E) + P(E') = 1$.

Pascal's Triangle

A mathematical tool useful for solving problems with multiple binary outcomes, such as coin flips.

With Replacement

A process where a first object chosen from a set is put back before the second object is chosen.

Without Replacement

A process where the first object chosen from a set is NOT put back before the second object is chosen.

Frequency Table

A table of data that shows the frequencies observed or associated with possible outcomes, preferably including total rows and columns.

Conditional Probability

The probability that A will occur given that B is true or has already occurred, denoted as $P(A|B) = \frac{P(A \text{ and } B)}{P(B)}$.

Fundamental Counting Principle

If one event occurs in $m$ ways and a second event in $n$ ways, the number of ways the two events can occur in sequence is $m \times n$.

Factorial

A mathematical operation denoted by $n!$ that multiplies a positive integer by all positive integers less than it down to 1. Note: $0! = 1$ and $1! = 1$.

Permutation

An ordered arrangement of objects. The formula for $n$ distinct objects taken $r$ at a time is $nPr = \frac{n!}{(n-r)!}$.

Combination

The number of ways to choose $r$ objects from $n$ objects without regard to order, calculated as $nCr = \frac{n!}{(n-r)!r!}$.

Mean

The weighted average calculated as the sum of the data divided by the number of data points.

Median

The middle of the data; the average of the two middle numbers if there is an even number of data points.

Mode

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

Range

The full spread of data, calculated as the highest value minus the lowest value.

Standard Deviation

The square root of the variance, regarded as the ‐average‑ spread of the data around the mean.

Variance

The average (mean) of the squared distances of each data point from the mean.

Quartiles

Values that separate data into four parts: $Q1$ (25th percentile), $Q2$ (median/50th percentile), and $Q3$ (75th percentile).

Inter-Quartile Range (IQR)

The difference between the third and first quartiles, calculated as $Q3 - Q1$.

Normal Distribution

A symmetric, bell-shaped curve where the mean, median, and mode are at the center and total area adds to $100\%$. Approx. $34\%$ of data falls between $\mu$ and $\mu + \sigma$.

Z-score

A measure of exactly how many standard deviations a data point is above or below the mean.

Pythagorean Theorem

A formula for right triangles ($a^2 + b^2 = c^2$) where $a$ and $b$ are legs and $c$ is the hypotenuse.

SOHCAHTOA

A mnemonic for trig ratios: $\sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}}$, $\cos(\theta) = \frac{\text{Adjacent}}{\text{Hypotenuse}}$, and $\tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}}$.

Triangle Inequality

A rule stating any two side lengths of a triangle must add up to more than the third side, such as $|a - b| < c < a + b$.

Law of Sines

A trigonometric rule for all triangles: $\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}$.

Law of Cosines

A trigonometric rule for all triangles: $c^2 = a^2 + b^2 - 2ab \times \cos(C)$, with variations for sides $a$ and $b$.

Simple Interest

Calculated using $I = Prt$, where $P$ is principal, $r$ is rate, and $t$ is time. Total value is $A = P(1 + rt)$.

Compound Interest

Earning interest on both principal and prior interest, calculated as $A = P(1 + \frac{r}{n})^{nt}$.

Human Capital

The skills, education, and experience that increase an individual's productivity.

Dividends

Profits distributed by a company to its shareholders (owners).

Capital Gains

The profits from selling assets that have increased in value.

Diversification

Spreading investments across different asset types, industries, and regions to reduce the risk of large losses.

Emergency Fund

A set-aside of 3–6 months of living expenses in liquid form to cover unexpected costs.

Hard Inquiry

A check on your credit score or history initiated by seeking new credit.

Deductible

The specific amount an individual must pay toward a claim before an insurance company covers the remaining costs.