Keystone Algebra: Module 1 Practice

What is the purpose of factoring in algebra?

• To simplify expressions, solve equations, and find roots of polynomials by expressing them as products of simpler expressions.

• To create complex equations that are difficult to solve.

• To convert fractions into decimals for easier calculations.

• To find the maximum value of a polynomial function.

What does it mean for two variables to be directly proportional?

• They are unrelated and do not affect each other.

• They increase or decrease at different rates, leading to a variable ratio.

• They increase or decrease at the same rate, meaning their ratio is constant.

• They are inversely related, meaning one increases while the other decreases.

What is the difference between an expression and an equation?

• An expression is a combination of numbers and variables without an equality sign, while an equation states that two expressions are equal.

• An expression is a statement that can be true or false, while an equation is a mathematical sentence that shows two expressions are equal.

• An expression is always a single number, while an equation can have multiple variables.

• An expression can only contain constants, while an equation can contain both constants and variables.

How do you simplify the expression @@(3x^2 + 2x - 8) - (-x^2 + 6x + 4)@@?

• @@4x^2 - 4x - 12@@

• @@2x^2 + 8x - 4@@

• @@3x^2 + 8x - 12@@

• @@5x^2 - 4x - 8@@

How do you determine if a relation is a function?

• A relation is a function if each input (x-value) corresponds to exactly one output (y-value).

• A relation is a function if it has at least one output for every input.

• A relation is a function if it can be represented as a straight line on a graph.

• A relation is a function if it passes the horizontal line test.

What does it mean for two lines to be parallel?

• They intersect at a right angle.

• They have different slopes and will meet at some point.

• They have the same slope and will never intersect.

• They are always horizontal.

What is the relationship between the coefficients and the roots of a polynomial?

• The coefficients of a polynomial can provide information about the roots, such as their sum and product, according to Vieta's formulas.

• The coefficients determine the degree of the polynomial only.

• The roots of a polynomial are always equal to the coefficients.

• The coefficients have no relationship with the roots of the polynomial.

What is the slope-intercept form of a linear equation?

• @@y = mx + b@@

• @@y = b + mx@@

• @@y = mx - b@@

• @@y = b - mx@@

What is an inequality?

• A mathematical statement that compares two expressions, showing that one is less than or greater than the other.

• A type of equation that always has a solution.

• A statement that two numbers are equal to each other.

• A method of solving for unknown variables.

How do you graph a linear inequality?

• 1. Graph the corresponding linear equation as a solid line (for ≤ or ≥) or dashed line (for < or >). 2. Shade the region that satisfies the inequality.

• 1. Only graph the inequality without the corresponding linear equation.

• 2. Use only dashed lines for all inequalities regardless of the type.

• 3. Shade the entire graph without considering the inequality.