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

The Pythagorean theorem states that 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 function's graph 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 an integral in calculus.

Back

An integral represents the accumulation of quantities, such as areas under curves. It is the reverse process of differentiation.

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 difference between a permutation and a combination?

Back

A permutation is an arrangement of items where order matters, while a combination is a selection of items where order does not matter.

Front

Explain the concept of exponential growth.

Back

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