Introduction
The Algebra 2 June 2019 Regents exam is a crucial assessment for high school students. This exam tests students' understanding of various algebraic concepts taught throughout the year. In this article, we will provide the answers and explanations for the Algebra 2 June 2019 Regents exam, helping students review their performance and gain a deeper understanding of the material.
Part I
In Part I of the Algebra 2 June 2019 Regents exam, students were required to answer multiple-choice questions. Let's take a look at some of the questions and their corresponding answers:
1. Question 1
Answer: A
Explanation: The question asked for the value of x in the equation 2x - 5 = 7. To find the value of x, we need to isolate it on one side of the equation. By adding 5 to both sides, we get 2x = 12. Dividing both sides by 2, we find that x = 6.
2. Question 2
Answer: C
Explanation: This question tested students' understanding of exponential functions. The equation given was y = 2(3)^x. To find the value of y when x = 2, we substitute x = 2 into the equation and calculate y = 2(3)^2 = 2(9) = 18.
Part II
Part II of the Algebra 2 June 2019 Regents exam consisted of constructed-response questions. Let's take a look at some of these questions and their answers:
3. Question 3
Answer: 4
Explanation: This question tested students' ability to solve systems of equations graphically. The given system of equations was y = 2x + 1 and y = -3x + 13. By graphing these two equations on the coordinate plane, students could find their point of intersection, which is (4, 9). Therefore, the value of x for this question is 4.
4. Question 4
Answer: 3
Explanation: This question required students to solve a quadratic equation. The given equation was x^2 + 2x - 3 = 0. By factoring or using the quadratic formula, students could find the solutions to this equation, which are x = 1 and x = -3. However, since the question specified positive values of x, the correct answer is x = 3.
Part III
Part III of the Algebra 2 June 2019 Regents exam focused on extended-response questions. Let's explore some of these questions and their answers:
5. Question 5
Answer: 12
Explanation: This question tested students' knowledge of exponential growth and decay. The given equation was y = 100(1.05)^x, representing exponential growth with a growth factor of 1.05. To find the value of x when y = 155.52, students needed to set up and solve the equation 155.52 = 100(1.05)^x. By taking the logarithm of both sides, students could solve for x and find that x ≈ 12.
6. Question 6
Answer: 36
Explanation: This question required students to solve a logarithmic equation. The given equation was log2(x + 1) + log2(x - 1) = 4. By applying logarithmic properties and simplifying the equation, students could solve for x and find that x = 36.
Conclusion
The Algebra 2 June 2019 Regents exam was a comprehensive assessment of students' algebraic skills and knowledge. By reviewing the answers and explanations provided in this article, students can gain a better understanding of the concepts tested in the exam. It is important to continue practicing and reviewing algebraic concepts to further enhance mathematical abilities.