Intro - Fall 2024 Final Part 2

Front

What is the definition of a function in mathematics?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

What is the Pythagorean theorem?

Back

In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. (a² + b² = c²)

Front

Define the term 'derivative' in calculus.

Back

The derivative of a function measures how the function's output value changes as the input value changes. It represents the slope of the tangent line to the graph of the function.

Front

What is the difference between a scalar and a vector?

Back

A scalar is a quantity that has only magnitude, while a vector is a quantity that has both magnitude and direction.

Front

Explain the concept of limits in calculus.

Back

A limit is a value that a function approaches as the input approaches some value. It is fundamental in defining derivatives and integrals.

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the solutions of a quadratic equation ax² + bx + c = 0, given by x = (-b ± √(b² - 4ac)) / (2a).

Front

Define 'asymptote' in the context of graphing functions.

Back

An asymptote is a line that a graph approaches but never touches. It can be vertical, horizontal, or oblique.

Front

What is the principle of mathematical induction?

Back

Mathematical induction is a method of proving that a statement is true for all natural numbers by proving it for the first number and showing that if it holds for an arbitrary number, it holds for the next.

Front

What is the difference between a permutation and a combination?

Back

A permutation is an arrangement of objects in a specific order, while a combination is a selection of objects without regard to the order.

Front

Explain the concept of probability in statistics.

Back

Probability is a measure of the likelihood that an event will occur, expressed as a number between 0 (impossible) and 1 (certain).