Algebra C&C Final Exam Fall 2024

Front

What is an arithmetic sequence?

Back

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. This difference is called the common difference.

Front

How do you find the explicit formula for the n-th term of an arithmetic sequence?

Back

The explicit formula for the n-th term of an arithmetic sequence can be expressed as: a_n = a_1 + (n-1)d, where a_1 is the first term and d is the common difference.

Front

What is the common difference in the sequence 16, 13, 10, 7, ...?

Back

The common difference is -3, as each term decreases by 3.

Front

What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities with the same variables. The solution is the set of all points that satisfy all inequalities in the system.

Front

How do you determine if a point is a solution to a system of inequalities?

Back

To determine if a point is a solution, substitute the point's coordinates into each inequality. If the point satisfies all inequalities, it is a solution.

Front

What is the distance formula used for?

Back

Front

Calculate the distance between the points (3, 8) and (-2, -4).

Back

Front

What is standard form in algebra?

Back

Standard form is a way of writing numbers or expressions in a specific format. For polynomials, it is written as: a_nx^n + a_{n-1}x^{n-1} + ... + a_1x + a_0.

Front

Expand the expression (3x + 1)(x + 1).

Back

The expanded form is 3x^2 + 4x + 1.

Front

What does it mean to simplify an expression in radical form?

Back

Simplifying an expression in radical form means to express it in the simplest form possible, often by reducing the radical or combining like terms.