Grade 11 Algebra: Expressions and Equations
This worksheet focuses on advanced algebraic expressions and equations, covering topics like solving linear and quadratic equations, simplifying complex expressions, and understanding functions.
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Grade 11 Algebra: Expressions and Equations
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Read each question carefully and provide your answer in the space provided. Show all your work for full credit.
1. Which of the following is equivalent to the expression (x^2 - 4) / (x^2 + 5x + 6)?
(x - 2) / (x + 3)
(x + 2) / (x + 3)
(x - 2) / (x - 3)
(x + 2) / (x - 3)
2. What is the solution set for the equation |2x - 3| = 7?
{5, -2}
{2, -5}
{5, 2}
{-5, -2}
3. The process of finding the value(s) of the variable(s) that make an equation true is called .
4. A equation is an equation that contains one or more rational expressions.
5. Solve the following equation for x: 3(x - 2) + 5x = 4x + 10
6. Simplify the expression: (2x^2 + 7x + 3) / (x + 3)
7. The equation x^2 + 9 = 0 has real solutions.
True
False
8. An extraneous solution is a solution that arises from the process of solving the equation but is not a valid solution to the original equation.
True
False
Match each term on the left with its definition on the right.
9. Polynomial
a. An equation that can be written in the form ax + b = 0, where a and b are real numbers and a ≠ 0.
10. Linear Equation
b. An expression consisting of variables and coefficients, involving only the operations of addition, subtraction, multiplication, and non-negative integer exponents.
11. Quadratic Equation
c. An equation that can be written in the form ax^2 + bx + c = 0, where a, b, and c are real numbers and a ≠ 0.