Intro - Fall 2024 Final Part 1

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 permissible outputs, where each input is related to exactly one output.

Front

What is the difference between a linear function and a quadratic function?

Back

A linear function has the form f(x) = mx + b, where m and b are constants, and its graph is a straight line. A quadratic function has the form f(x) = ax² + bx + c, where a, b, and c are constants, and its graph is a parabola.

Front

What is the Pythagorean theorem?

Back

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): c² = a² + b².

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 at a given point.

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. It is used to define the sine, cosine, and tangent functions for all angles.

Front

Explain the concept of limits in calculus.

Back

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

Front

What is the difference between a population and a sample in statistics?

Back

A population is the entire group that you want to draw conclusions about, while a sample is a subset of the population used to represent the whole.

Front

What is the central limit theorem?

Back

The central limit theorem states that the distribution of the sample means approaches a normal distribution as the sample size increases, regardless of the shape of the population distribution.

Front

Define 'hypothesis testing' in statistics.

Back

Hypothesis testing is a method of making decisions using data, where a hypothesis is tested against a null hypothesis to determine if there is enough evidence to reject the null.

Front

What is the purpose of a confidence interval?

Back

A confidence interval is a range of values used to estimate the true value of a population parameter, providing an interval within which we expect the parameter to lie with a certain level of confidence.