Mathematics 11th Grade Practice Flashcards

This set of vocabulary flashcards covers key mathematical definitions from the 11th-grade curriculum, including complex numbers, matrices, sequences, trigonometry, and vector algebra, as presented in the lecture notes.

Complex number

A number composed of a real part and an imaginary part, such as $\text{a+ib}$, where the number $\text{√-1}$ is called a complex or imaginary unit.

Multiplicative inverse of -i

The reciprocal of the complex number $\text{-i}$, which evaluates to $\text{i}$.

Modulus of a complex number

The magnitude of a complex number; for instance, the modulus of $\text{-5i}$ is $5$, and for $\text{a + bi}$ it is $\text{√(a² + b²)}$.

Complex cube roots of unity

The three roots of the equation $\text{x³ = 1}$, denoted as $1, ω, \text{ and } ω²$, where $\text{1+ω+ω² = 0}$.

Into function

A function $\text{f: A → B}$ where the range of the function is a proper subset of the codomain $\text{B}$ ($\text{range f ⊂ B}$).

Surjective function

Also known as an 'onto' function, it occurs when the range of a function equals its codomain ($\text{range f = B}$).

Extraneous roots

Potential solutions to an absolute value or radical equation that must be eliminated because they do not satisfy the original function.

Radical equation

An equation that involves a variable inside a radical expression, such as $\text{√(x+a) + √(x+b) = √(x+c)}$.

Row matrix

A matrix that consists of exactly one row, also referred to as a matrix of order $1 \times n$.

Scalar matrix

A square diagonal matrix in which all the diagonal elements are equal and non-zero.

Singular matrix

A square matrix whose determinant is zero, meaning it does not have a multiplicative inverse.

Proper fraction

A rational expression $\frac{p(x)}{q(x)}$ where the degree of the numerator polynomial $\text{p(x)}$ is strictly less than the degree of the denominator polynomial $\text{q(x)}$.

Arithmetic Progression (A.P)

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

Geometric Mean (G.M)

For any two numbers $\text{a}$ and $\text{b}$, the geometric mean is defined as $\text{±√ab}$.

Allied angles

Angles associated with basic angles, typically expressed as $90^∘ ± θ$, $180^∘ ± θ$, etc.

Periodic functions

Functions that repeat their values in regular intervals, with the smallest positive interval being called the 'period'.

Christian Kramp

The mathematician who introduced the symbolic notation for factorials ($\text{n!}$).

Leibniz, Cauchy, Lagrange, and Newton

Prominent mathematicians cited for introducing various notations for derivatives, such as $\text{f'(x)}$ specifically attributed to Lagrange.

Scalar product (Dot product)

The product of two vectors that results in a scalar, given by $\text{a ⋅ b = |a||b|cos(θ)}$. It is zero if the vectors are perpendicular.

Vector product (Cross product)

The product of two vectors that results in another vector, given by $\text{a × b = |a||b|sin(θ)n}$. It is zero if the vectors are parallel.

Synthetic division

A simplified shorthand process of dividing a polynomial by a linear factor.