Algebra 1 Midterm Review

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 nth term of an arithmetic sequence?

Back

The nth term of an arithmetic sequence can be found using the formula: \( a_n = a_1 + (n - 1)d \), where \( a_1 \) is the first term and \( d \) is the common difference.

Front

What is the formula for the nth term of the sequence given by 6 + 5(n - 1)?

Back

The formula for the nth term is \( a_n = 6 + 5(n - 1) \). This can be simplified to \( a_n = 5n + 1 \).

Front

What is the sum of the coefficients in the polynomial (6x + 4x^4 - 3x^2) + (7x^4 + 5x^2 + 8x)?

Back

The sum of the coefficients is 11 (from 4 + 7) + 2 (from -3 + 5) + 14 (from 6 + 8) = 27.

Front

What is the process for adding polynomials?

Back

To add polynomials, combine like terms by adding their coefficients while keeping the variable part the same.

Front

How do you find the slope of a line given two points?

Back

The slope (m) can be calculated using the formula: \( m = \frac{y_2 - y_1}{x_2 - x_1} \), where (x1, y1) and (x2, y2) are the coordinates of the two points.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, meaning the line is descending.

Front

What is the difference between causation and association?

Back

Causation indicates that one event causes another, while association indicates a relationship between two events without implying that one causes the other.

Front

What is direct variation?

Back

Direct variation is a relationship between two variables where one variable is a constant multiple of the other, expressed as \( y = kx \), where k is a non-zero constant.

Front

How do you solve for y in a direct variation problem?

Back

To solve for y in a direct variation problem, use the formula \( y = kx \) and substitute the known values to find k, then use it to find y for other x values.