Flashcard on the standard AII.1 - AII.12 - 1O,4O- Dec 13 2024

Front

What is the common difference in an arithmetic sequence?

Back

The common difference is the constant amount that each term in the sequence increases or decreases by. For example, in the sequence 29, 21, 13, 5, the common difference is -8.

Front

How do you calculate permutations for awarding prizes?

Back

To calculate the number of ways to award first, second, and third prizes among 6 organizations, use the formula for permutations: P(n, r) = n! / (n - r)!. Here, n = 6 and r = 3, so P(6, 3) = 6! / (6 - 3)! = 120.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce. For example, if a function has a range of [1, ∞), it means the output values start from 1 and go to infinity.

Front

What does 8! (8 factorial) represent?

Back

8! represents the product of all positive integers from 1 to 8. It is calculated as 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 40320.

Front

When is a function considered to be increasing?

Back

A function is considered to be increasing on an interval if, for any two points in that interval, the function's value at the second point is greater than at the first point. For example, the function is increasing on the interval (-3, 3).

Front

What is an arithmetic sequence?

Back

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. For example, 2, 5, 8, 11 is an arithmetic sequence with a common difference of 3.

Front

How do you find the common difference in an arithmetic sequence?

Back

To find the common difference, subtract any term from the subsequent term. For example, in the sequence 10, 7, 4, the common difference is 7 - 10 = -3.

Front

What is the formula for calculating permutations?

Back

The formula for permutations is P(n, r) = n! / (n - r)!, where n is the total number of items, and r is the number of items to arrange.

Front

What does the notation [1, ∞) mean in terms of range?

Back

The notation [1, ∞) indicates that the range includes all values starting from 1 and extending to infinity, including 1 but not including infinity.

Front

What is the significance of factorial in mathematics?

Back

Factorial, denoted by n!, is the product of all positive integers up to n. It is used in permutations, combinations, and other areas of mathematics.