Math Facts #1

What does the Pythagorean theorem state?

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.

Formula for the Pythagorean theorem

$$a^2 + b^2 = c^2$$

What is the length of the hypotenuse in the Pythagorean theorem?

$c$ is the length of the hypotenuse.

What are the lengths of the other two sides in the Pythagorean theorem?

$a$ and $b$ are the lengths of the other two sides.

What are some applications of the Pythagorean theorem?

Distance calculations in coordinate geometry and architecture.

What is statistics?

The science of collecting, analyzing, interpreting, presenting, and organizing data.

What are descriptive statistics?

Statistics that summarize data using mean, median, mode, and standard deviation.

What is inferential statistics?

Statistics that make predictions or inferences about a population based on a sample of data.

What is probability?

The measure of the likelihood that an event will occur.

Formula for probability

$$P(A) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$$

What is theoretical probability?

Probability based on reasoning, assuming all outcomes are equally likely.

What is experimental probability?

Probability based on experimental data and actual outcomes.

What are independent events in probability?

Events where the occurrence of one does not affect the probability of the other.

What are dependent events in probability?

Events where the occurrence of one affects the probability of the other.

What defines mutually exclusive events?

Events that cannot occur at the same time.

What are natural numbers?

Counting numbers (1, 2, 3, …).

What are whole numbers?

Natural numbers plus zero (0, 1, 2, …).

What are integers?

Whole numbers including negative numbers (…, -3, -2, -1, 0, 1, 2, 3, …).

What are rational numbers?

Numbers that can be expressed as fractions of integers (e.g., $\frac{1}{2}, -\frac{4}{3}, 0.75$).

What are irrational numbers?

Numbers that cannot be expressed as fractions (e.g., $\sqrt{2}, \pi$).

What are real numbers?

All rational and irrational numbers.

What are complex numbers?

Numbers that have a real part and an imaginary part (e.g., $2 + 3i$ where $i = \sqrt{-1}$).

Why is understanding the number system important?

It's essential for performing operations in algebra, calculus, and beyond, as well as for overall mathematical literacy.