Introduction
Algebra 2 is a challenging subject for many students, and the June 2017 Regents exam was no exception. This standardized test assesses students' understanding and application of algebraic concepts, and can be a daunting task for even the most diligent learners. In this article, we will provide the answers and explanations for the Algebra 2 June 2017 Regents exam, helping students to review and understand the material covered in the test.
Part 1: Multiple Choice
The June 2017 Regents exam consisted of multiple-choice questions, which required students to select the correct answer from a set of options. Let's take a look at some of the questions and their answers:
Question 1
The first question on the exam asked students to solve the equation 2x + 5 = 15. The correct answer is x = 5, as subtracting 5 from both sides of the equation yields 2x = 10, and dividing both sides by 2 gives x = 5.
Question 2
Question 2 tested students' knowledge of quadratic equations. The question asked for the solution to the equation x^2 + 4x - 12 = 0. Factoring the equation gives (x - 2)(x + 6) = 0. Therefore, the solutions are x = 2 and x = -6.
Part 2: Constructed Response
In addition to multiple-choice questions, the Algebra 2 June 2017 Regents exam also included constructed response questions, where students had to show their work and explain their reasoning. Let's explore some of these questions and their answers:
Question 3
Question 3 asked students to solve the system of equations:
2x + 3y = 7
4x - 5y = 6
To solve this system, one possible method is to use the method of substitution. By solving the first equation for x, we get x = (7 - 3y)/2. Substituting this expression for x in the second equation gives:
4((7 - 3y)/2) - 5y = 6
Simplifying the equation gives 14 - 6y - 5y = 6. Combining like terms gives -11y = -8, and dividing both sides by -11 yields y = 8/11. Substituting this value of y into the first equation gives x = (7 - 3(8/11))/2, which simplifies to x = 9/11.
Question 4
Question 4 tested students' knowledge of exponential functions. The question asked for the value of y when x = 3 in the equation y = 2(3)^x. Plugging in x = 3 gives y = 2(3)^3 = 2(27) = 54.
Part 3: Extended Response
The final part of the Algebra 2 June 2017 Regents exam consisted of extended response questions, which required students to provide a more detailed explanation of their solution. Let's dive into some of these questions and their answers:
Question 5
Question 5 asked students to graph the equation y = -2|x - 3| + 4. To graph this equation, we can start by finding the vertex. The vertex form of the equation is y = a|x - h| + k, where (h, k) represents the coordinates of the vertex. In this case, h = 3 and k = 4. Therefore, the vertex is (3, 4).
Next, we can find some additional points to plot on the graph. By substituting different values of x into the equation, we can find corresponding values of y. For example, when x = 2, y = -2|2 - 3| + 4 = -2(1) + 4 = 2. This gives us the point (2, 2). Similarly, when x = 4, y = -2|4 - 3| + 4 = -2(1) + 4 = 2. This gives us the point (4, 2).
Plotting these points and connecting them with a smooth curve, we get the graph of the equation y = -2|x - 3| + 4.
Question 6
Question 6 tested students' understanding of logarithmic functions. The question asked for the value of x when log(x) = 2. To solve this equation, we can rewrite it in exponential form as 10^2 = x. Therefore, x = 100.
Conclusion
The Algebra 2 June 2017 Regents exam was a comprehensive test that challenged students' understanding and application of algebraic concepts. By reviewing the answers and explanations provided in this article, students can gain a better understanding of the material covered in the exam and improve their performance in future assessments. Remember, practice and perseverance are key to mastering algebraic concepts. Good luck!