Math TSA Tech Bowl Study Guide

Sections: Algebra, Geometry, Calculus

i

Defined as the solution to the equation x²=-1. It allows for the solution of equations that have no real number solutions, forming complex numbers when combined with real numbers.

𝜋

An irrational, transcendental constant representing the ratio of any circle's circumference to its diameter, approximately 3.141593. It is central to geometry and trigonometry.

𝑒

A mathematical constant approximately equal to 2.71828. It is the base of the natural logarithm and defines the rate of continuous growth (e.g., compound interest, population growth).

Logarithm

The inverse function of exponentiation. If b^y=x, then log_b(x)=y. It answers the question: "To what power must the base 𝑏 be raised to equal 𝑥?".

Natural logarithm

denoted as $\text{ln}(x)$, is the logarithm to the base $e$ (approximately $2.71828$). It answers the question: "To what power must $e$ be raised to obtain $x$?".

Graph

a visual representation of data or mathematical functions. It typically displays relationships between variables, using a coordinate system.

Slope of a line

measures its steepness and direction. It is calculated as the change in the y-coordinate divided by the change in the x-coordinate (rise over run).

y-intercept

the point where a line crosses the y-axis. It represents the value of y when x equals zero.

Ray

a part of a line that starts at a specific point and extends infinitely in one direction.

Tangent

a line that touches a curve at a single point without crossing it. In trigonometry, this function relates the angle of a right triangle to the ratio of the opposite side to the adjacent side.