Grade 11 Mathematics Tutorial Vocabulary

Vocabulary flashcards reviewing core mathematical concepts, theorems, and definitions from the Grade 11 Summer Special Tutorial Program curriculum.

AA Similarity Theorem

A similarity criterion stating that if two angles of one triangle are respectively congruent to the two corresponding angles of another triangle, then the triangles are similar.

SSS Similarity Theorem

A similarity criterion stating that if the corresponding three sides of two triangles are proportional to each other, then the triangles are similar.

SAS Similarity Theorem

A similarity criterion stating that if the corresponding two sides of two triangles are proportional and their included angles are congruent, then the two triangles are similar.

Function

A relation such that no two different ordered pairs have the same first-coordinates and different second-coordinates.

Functional Value

For a function $f: A \rightarrow B$, for any $x \in A$, the image of $x$ under $f$, denoted as $f(x)$, is called the functional value of $f$ at $x$.

Composition of Functions

For functions $f: A \rightarrow B$ and $g: B \rightarrow C$, the function $h$ defined by $h(x) = g(f(x))$ for $x \in A$ where $f(x)$ is in the domain of $g$, denoted as $g \circ f$.

Vertical Line Test

A test used to determine whether a graph of a curve is a function; if any vertical line cuts the curve at more than one point, then the curve is not a function.

One-to-One Function (Injective Function)

A function $f: A \rightarrow B$ where each element in the domain has a distinct image in the co-domain, such that for all $x, y \in A$, $f(x) = f(y)$ implies $x = y$.

Horizontal Line Test

A test used to determine whether a graph of a function is one-to-one, satisfied if every horizontal line crosses the graph at most once.

Onto Function (Surjective Function)

A function $f: A \rightarrow B$ in which each element in the co-domain has at least one pre-image in the domain, meaning the range of $f$ is equal to $B$.

One-to-One Correspondence (Bijective Function)

A function $f: A \rightarrow B$ that is both one-to-one (injective) and onto (surjective).

Invertible Function

A function $f$ that is one-to-one, possessing an inverse function denoted by $f^{-1}$.

Identity Function

The function defined by $I(x) = x$.

Power Function

A function of the form $f(x) = ax^n$, where $a$ and $n$ are real numbers and $a \neq 0$.

Signum Function

A function denoted by $f(x) = \text{sgn}(x)$, defined as $1$ if $x > 0$, $0$ if $x = 0$, and $-1$ if $x < 0$.

Greatest Integer Function

A function $f(x) = \lfloor x \rfloor$ that yields the greatest integer that is less than or equal to $x$, also called the floor or step function.

Polynomial Remainder Theorem

A theorem stating that if a polynomial $f(x)$ of degree greater than or equal to $1$ is divided by $(x - c)$, then the remainder is $f(c)$.

Polynomial Factor Theorem

A theorem stating that for a polynomial $f(x)$ of degree greater than or equal to $1$, $(x - c)$ is a factor of $f(x)$ if and only if $f(c) = 0$.

Exponential Function

A function denoted by $f(x) = a^x$, where base $a > 0$, $a \neq 1$, and $x$ is any real number.

Natural Exponential Function

The exponential function $f(x) = e^x$ with base $e$, where $2 < e < 3$.

Logarithmic Function

The inverse function of an exponential function $f(x) = a^x$ (where $a > 0$ and $a \neq 1$), denoted by $f^{-1}(x) = \log_a(x)$.

Quadrantal Angles

Angles in standard position whose terminal sides lie on the $x$-axis or $y$-axis.

Co-terminal Angles

Angles that have the same terminal sides, expressible as $\theta \pm n \times 360^\circ$ or $\theta \pm n \times 2\pi$ for any integer $n$.

Reference Angle

The acute angle $\theta_R$ formed by the terminal side of an angle $\theta$ and the $x$-axis.