Math Review: Numbers, Geometry, Data, and Statistics (Lecture Notes)

A set of practice flashcards covering rational numbers, irrational numbers, absolute value, basic arithmetic of fractions, geometry area and perimeter, circle formulas, Pythagorean theorem, polygons and composite figures, data measures (mean, mode, weighted average), and basic number theory (integers, odd/even, primes, percent, and median).

What is a rational number?

A number that can be written as a fraction a/b where a and b are integers and b ≠ 0.

Give an example of an irrational number.

A number whose decimal expansion never repeats, such as π (Pi) ≈ 3.14159…

How is absolute value denoted and what does it measure?

Two vertical lines around a number, |x|; it measures distance from zero on the number line.

What is the absolute value of -5?

5

What are the four operations on fractions?

Addition, subtraction, multiplication, and division.

What does it mean to simplify a fraction?

Reduce to lowest terms by canceling common factors, e.g., 8/24 = 1/3.

What is the area formula for a rectangle?

Area = base × height (length × width).

What is the perimeter of a shape?

The total length around the shape; sum of all side lengths.

How do you calculate the area of a triangle?

Area = (base × height) / 2.

What is the area formula for a circle?

Area = π × r^2 (using π ≈ 3.14).

What is the circumference formula for a circle?

Circumference = 2πr or πd.

What is the relationship between radius and diameter?

Diameter is twice the radius (d = 2r).

What is the Pythagorean theorem and when does it apply?

In a right triangle, a^2 + b^2 = c^2, where c is the hypotenuse.

What is a polygon?

A closed figure made of three or more straight sides.

What is a composite figure?

A shape made of two or more simple shapes; compute its perimeter and area.

How do you compute the perimeter and area of a polygon?

Perimeter: sum of the outside sides; Area: apply polygon area formulas or divide into simpler shapes.

What is the mean (average) of a data set?

Mean = sum of values ÷ number of values.

What is the mode of a data set?

The value(s) that occur most often.

How is a weighted average calculated? Give a sample formula.

Weighted average = (value1 × weight1 + value2 × weight2 + …) ÷ (weight1 + weight2 + …); Example: 80×0.20 + 90×0.30 + 85×0.50 = 85.5.

What are integers?

All whole numbers and their negatives including zero: …, -2, -1, 0, 1, 2, 3, …

What are consecutive integers?

Integers that follow in order with a difference of 1: n, n+1, n+2, …

What are odd numbers?

Numbers not divisible by 2: …, -3, -1, 1, 3, 5, 7, 9, …

What are even numbers?

Numbers divisible by 2: …, -4, -2, 0, 2, 4, 6, …

What are prime numbers?

Numbers greater than 1 with exactly two distinct positive divisors: 2, 3, 5, 7, 11, 13, 17, 19, …

What is percent and how is it written?

Percent is a per-one-hundred value; 40% equals 0.40 or 40/100.

What are hundredths?

The digits to the right of the decimal representing the hundredths place (0.01).

What is the arithmetic mean?

Another term for the mean; sum of values divided by number of values.

What is the median?

The middle value when data are ordered; if even, the average of the two middle values.