Mathematics Assessment Quiz

A function is one-to-one if each element in the domain maps to a unique element in the range. No two distinct elements in the domain map to the same element in the range.

A function is onto if every element in the range has at least one corresponding element in the domain. Every element in the range is 'hit' by the function.

A function is bijective if it is both one-to-one and onto. It perfectly pairs each element in the domain with a unique element in the range.

The order of a matrix is determined by the number of rows and columns. It's represented as (rows x columns).

A continuous function has no breaks or jumps in its graph. You can draw the graph without lifting your pencil.

A function is differentiable at a point if its derivative exists at that point. This means the function has a well-defined tangent line at that point.

The derivative of a function f(x), denoted as f'(x) or df/dx, measures the instantaneous rate of change of the function at a specific point.

The order of a differential equation is determined by the highest order derivative in the equation. The degree is the highest power of the highest order derivative in the equation.

The integrating factor is a function multiplied to both sides of a differential equation to make it easier to solve. It's usually derived from the coefficient of the first order derivative term.

The direction cosines of a line are the cosines of the angles that the line makes with the positive directions of the coordinate axes.

A linear programming problem involves finding the optimal value of a linear objective function subject to various linear constraints. It's used to optimize resources like time, money, and materials.

A feasible solution is a set of values that satisfy all the constraints of a linear programming problem.

The intersection of the lines corresponding to the constraints in a linear programming problem forms the feasible region, which represents all possible solutions satisfying the constraints.

An optimal solution is the feasible solution that maximizes or minimizes the objective function in a linear programming problem.

The corner points of the feasible region are the points at the vertices of the region. The optimal solution often occurs at one of these corner points.

Two events are independent if the occurrence of one event does not affect the probability of the other event occurring. The probability of both events happening is the product of their individual probabilities.

The inverse of a function is another function that 'undoes' the original function. It reverses the mapping between the domain and range.

A matrix is a rectangular array of numbers arranged in rows and columns.

The determinant of a square matrix is a scalar value that represents certain properties of the matrix. It's used in solving systems of linear equations.

The inverse of a matrix is another matrix that, when multiplied by the original matrix, results in the identity matrix.

A system of linear equations is a set of two or more linear equations that share the same variables. Solving the system means finding values for the variables that satisfy all equations simultaneously.

A vector is a quantity that has both magnitude (size) and direction. It's often represented by an arrow.

The dot product of two vectors, also known as the scalar product, is a scalar value that represents the projection of one vector onto the other. It's used to find the angle between vectors and calculate work.

The cross product of two vectors is another vector that is perpendicular to both of the original vectors. It's used to find the area of a parallelogram and the torque of a force.

The magnitude of a vector is its length or size. It's represented by the absolute value symbol (||).

The unit vector in the same direction as a given vector is a vector with a magnitude of 1. It's obtained by dividing the given vector by its magnitude.

The angle between two vectors can be found using the formula cos(q) = (a . b) / (||a|| ||b||), where q is the angle, and a and b are the vectors.

A parallelogram has two pairs of parallel sides. Its area is given by A = ||a x b||, where a and b are the adjacent sides of the parallelogram.

The definite integral of a function f(x) from a to b, denoted as ∫[a, b] f(x) dx, represents the area between the curve of the function, the x-axis, and the vertical lines x = a and x = b.

The fundamental theorem of calculus establishes a connection between differentiation and integration. It states that the derivative of the definite integral of a function is equal to the original function.

A limit in calculus is the value that a function approaches as its input approaches a certain value. It's used to define continuity, differentiability, and other fundamental concepts.