ALGEBRA 2 FINAL EXAM - Sem 1 2024

Front

What is the elimination method in solving systems of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other variable.

Front

How do you solve the equation 4x + 9y = 28 and -4x - y = -28 using elimination?

Back

Add the two equations to eliminate x: 4x + 9y + (-4x - y) = 28 + 28, resulting in 8y = 56, so y = 7. Substitute y back to find x: 4x + 9(7) = 28, leading to x = 7.

Front

What is the result of multiplying 2x^3 by (x^2 - 2x - 3)?

Back

The result is 2x^5 - 4x^4 - 6x^3.

Front

What is the first step in solving the system of equations 2x - 3y = 14 and x + 3y = -11?

Back

The first step is to add the equations to eliminate the y's.

Front

What is the definition of a polynomial?

Back

A polynomial is a mathematical expression consisting of variables, coefficients, and non-negative integer exponents, combined using addition, subtraction, and multiplication.

Front

What is the degree of the polynomial 2x^5 - 4x^4 - 6x^3?

Back

The degree of the polynomial is 5, which is the highest exponent of the variable x.

Front

How do you factor the polynomial x^2 - 5x + 6?

Back

The polynomial factors to (x - 2)(x - 3).

Front

What is the quadratic formula used for?

Back

The quadratic formula is used to find the solutions (roots) of a quadratic equation in the form ax^2 + bx + c = 0, given by x = (-b ± √(b² - 4ac)) / (2a).

Front

What is the difference between a rational and an irrational number?

Back

A rational number can be expressed as a fraction of two integers, while an irrational number cannot be expressed as a simple fraction and has a non-repeating, non-terminating decimal expansion.

Front

What is the process of completing the square?

Back

Completing the square is a method used to solve quadratic equations by rewriting the equation in the form (x - p)² = q, making it easier to solve for x.