Algebra 2 NYS Regents Exam: Question 30 Explained

The Algebra 2 NYS Regents Exam is a challenging test that requires a strong understanding of a wide range of mathematical concepts. Question 30 is often considered to be one of the most difficult questions on the exam, as it typically involves complex algebraic manipulations and problem-solving strategies. In this blog post, we will provide a detailed explanation of question 30 from a recent Algebra 2 NYS Regents Exam, along with a step-by-step solution to help students understand the concepts and techniques involved.

Understanding the Question

Before we dive into the solution, let's take a look at the question itself. Question 30 is usually a multi-part question that requires students to apply their knowledge of various algebraic concepts, such as:

• Polynomial Functions: Working with equations involving variables raised to different powers.
• Rational Functions: Dealing with expressions where one polynomial is divided by another.
• Systems of Equations: Solving multiple equations simultaneously.
• Logarithms and Exponentials: Understanding the relationship between these functions.
• Trigonometry: Applying trigonometric identities and ratios.

The question will often present a real-world scenario or a mathematical problem that requires students to translate it into algebraic expressions and then solve for a specific variable or relationship.

Step-by-Step Solution

Here's a general approach to solving question 30 on the Algebra 2 NYS Regents Exam:

1. Read the Question Carefully: Understand the context of the problem and what it is asking you to find.
2. Identify the Key Concepts: Determine which algebraic concepts are involved in the question.
3. Translate the Problem into Equations: Set up equations based on the information given in the question.
4. Solve the Equations: Use algebraic techniques to solve for the desired variable or relationship.
5. Check Your Answer: Make sure your solution makes sense in the context of the original problem.

Example Problem

Let's consider a hypothetical example of question 30 from the Algebra 2 NYS Regents Exam:

Question: A company manufactures and sells a product. The profit, P(x), in dollars, from selling x units of the product is given by the function P(x) = -0.01x^2 + 10x - 500. Find the maximum profit and the number of units that must be sold to achieve this maximum profit.

Solution:

1. Read the Question Carefully: We are asked to find the maximum profit and the number of units that must be sold to achieve it.
2. Identify the Key Concepts: This problem involves a quadratic function, which represents the profit as a function of the number of units sold. To find the maximum profit, we need to find the vertex of the parabola represented by the function.
3. Translate the Problem into Equations: The equation P(x) = -0.01x^2 + 10x - 500 represents the profit function.
4. Solve the Equations: To find the vertex, we can use the formula x = -b / 2a, where a = -0.01 and b = 10. Substituting these values, we get x = -10 / (2 * -0.01) = 500. This means that the maximum profit is achieved when 500 units are sold. To find the maximum profit, we substitute x = 500 into the profit function: P(500) = -0.01(500)^2 + 10(500) - 500 = $2000.
5. Check Your Answer: The answer makes sense because the profit function is a parabola opening downwards, and the vertex represents the maximum point. Therefore, selling 500 units will result in the maximum profit of $2000.

Tips for Success

Here are some tips to help you succeed on question 30 of the Algebra 2 NYS Regents Exam:

• Practice, Practice, Practice: The more you practice solving similar problems, the more confident you will become.
• Review Key Concepts: Ensure you have a strong understanding of all the algebraic concepts covered in the Algebra 2 curriculum.
• Break Down Complex Problems: Divide complex problems into smaller, more manageable steps.
• Use a Graphing Calculator: A graphing calculator can be a valuable tool for visualizing functions and finding solutions.
• Stay Calm and Focused: Avoid rushing and take your time to read each question carefully.

By following these tips and practicing regularly, you can improve your chances of success on question 30 of the Algebra 2 NYS Regents Exam. Remember, the key to success is understanding the concepts, applying the right techniques, and staying calm under pressure.