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.

Tags

CCSS.8.F.A.1

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.

Tags

CCSS.8.G.B.7

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.

Tags

CCSS.HSF.TF.A.2

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.

Tags

CCSS.7.SP.A.1

CCSS.HSS.IC.A.1

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.

Tags

CCSS.HSS.IC.B.4