Unit 5 PreAssessment

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What are like terms in algebra?

Back

Like terms are terms that have the same variable raised to the same power. For example, y² and 2y² are like terms because they both contain the variable y raised to the power of 2.

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How do you solve a system of linear equations?

Back

To solve a system of linear equations, you can use methods such as substitution, elimination, or graphing to find the values of the variables that satisfy both equations.

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What is a common difference in an arithmetic sequence?

Back

The common difference in an arithmetic sequence is the constant amount that each term increases or decreases by. For example, in the sequence 3, 7, 11, 15, the common difference is 4.

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What does it mean if a system of equations has no solution?

Back

A system of equations has no solution if the lines represented by the equations are parallel and never intersect, meaning there are no values for the variables that satisfy both equations.

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How do you identify like terms in an expression?

Back

To identify like terms in an expression, look for terms that have the same variable(s) raised to the same power. For example, in the expression 3x² + 5x² - 2x, the like terms are 3x² and 5x².

Front

What is the formula for finding 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, d is the common difference, and n is the term number.

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What is the significance of the slope in a linear equation?

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The slope of a linear equation represents the rate of change of the dependent variable with respect to the independent variable. It indicates how steep the line is and the direction it goes (positive or negative).

Front

How can you determine if two lines are parallel?

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Two lines are parallel if they have the same slope but different y-intercepts. This means they will never intersect.

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What is the difference between a linear equation and a nonlinear equation?

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A linear equation represents a straight line when graphed and has the form y = mx + b, while a nonlinear equation represents a curve and does not have this form.

Front

What is the process of elimination in solving systems of equations?

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The process of elimination involves adding or subtracting equations to eliminate one variable, making it easier to solve for the remaining variable.