WU: S1 Review Day 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

Explain the concept of limits in calculus.

Back

Limits describe the value that a function approaches as the input approaches a certain point. They are fundamental in defining derivatives and integrals.

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 represents the rate at which the function's value changes at a given point, essentially the slope of the tangent line to the curve at that point.

Front

What is the difference between a rational and an irrational number?

Back

A rational number can be expressed as a fraction of two integers, while an irrational number cannot be expressed as a simple fraction and has a non-repeating, non-terminating decimal expansion.

Front

Explain the concept of a quadratic equation.

Back

A quadratic equation is a second-degree polynomial equation in the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What is the significance of the unit circle in trigonometry?

Back

The unit circle is a circle with a radius of one centered at the origin of a coordinate plane, and it is used to define trigonometric functions for all angles.

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 Fundamental Theorem of Algebra?

Back

The Fundamental Theorem of Algebra states that every non-constant polynomial equation has at least one complex root.

Front

Explain the concept of exponential growth.

Back

Exponential growth occurs when the growth rate of a value is proportional to its current value, leading to growth that accelerates over time.