Algebra: Concepts and Connections EOC Review 1

What is the definition of an irrational number?

• A number that can be expressed as a simple fraction.

• A number that can be written as a ratio of two integers.

• A number that cannot be expressed as a simple fraction; it cannot be written as a ratio of two integers.

• A number that is always a whole number.

How can you verify if your answer to a quadratic equation is correct?

• By substituting it back into the original equation to see if it holds true.

• By graphing the equation and checking the intersection points.

• By using the quadratic formula to recalculate the roots.

• By checking if the discriminant is positive.

What is the process for simplifying square roots?

• To simplify square roots, factor the number under the root into its prime factors and pair them to take them out of the root.

• To simplify square roots, add the number under the root to the square of the root.

• To simplify square roots, multiply the number under the root by its square root.

• To simplify square roots, subtract the number under the root from the square of the root.

What does it mean for a function to be in standard form?

• A quadratic function is expressed as f(x) = ax^2 + bx + c.

• A linear function is expressed as f(x) = mx + b.

• A cubic function is expressed as f(x) = ax^3 + bx^2 + cx + d.

• A function is in standard form if it has no variables.

What is the significance of the intersection point of two lines in a graph?

• It indicates the slope of the lines.

• It represents the solution to the system of equations represented by the two lines.

• It shows the distance between the two lines.

• It determines the angle between the two lines.

How do you convert the quadratic function f(x)=x^2+8x+3 into vertex form?

• (x+4)^2 - 13

• (x+4)^2 + 13

• (x-4)^2 - 13

• (x-4)^2 + 13

What is the importance of understanding inequalities in real-world applications?

• Inequalities help model situations where quantities are limited or constrained, such as budgets or resource allocations.

• Inequalities are only used in theoretical mathematics and have no real-world applications.

• Inequalities are primarily used to solve equations without any constraints.

• Inequalities are irrelevant in financial planning and resource management.

How do you determine if two lines are perpendicular?

• Two lines are perpendicular if the product of their slopes is -1.

• Two lines are perpendicular if they intersect at a right angle.

• Two lines are perpendicular if their slopes are equal.

• Two lines are perpendicular if they are parallel.

What inequality represents the total value of d dimes and q quarters being less than $14.75?

• 0.1d + 0.25q < 14.75

• 0.1d + 0.25q > 14.75

• 0.1d + 0.25q = 14.75

• 0.1d + 0.25q ≤ 14.75

What is the definition of a rational number?

• A rational number is any number that can be expressed as the quotient or fraction of two integers.

• A rational number is a number that cannot be expressed as a fraction.

• A rational number is any whole number or its negative.

• A rational number is a number that has a non-repeating decimal representation.