# Algebra I Regents Exam - June 2024

High School Math based on the topics required for the Regents Exam conducted by NYSED.
The following are the worked solutions for the Algebra 1 (Common Core) Regents High School Examination June 2024.

Related Pages
Regents Exam Past Papers

### Algebra I Regents New York State Exam - June 2024

Solutions for Questions 1 - 35

1. A ball was launched into the air, and its height above the ground was recorded each second, as shown in the table below.
2. A tour bus can seat, at most, 48 passengers. An adult ticket costs \$18 and a child ticket costs \$12. The bus company must collect at least \$650 to make a profit. If a represents the number of adult tickets sold and c represents the number of child tickets sold, which system of inequalities models this situation if they make a profit?
3. Which equation is always true?
4. The expression -2(x2 - 2x + 1) + (3x2 + 3x - 5) is equivalent to
5. Which sum is irrational?
6. The solution to
7. On an island, a rare breed of rabbit doubled its population each month for two years. Which type of function best models the increase in population at the end of two years?
8. What is the degree of the polynomial 2x - x2 + 4x3?
9. The zeros of the function f(x) = x(x - 5)(3x + 6) are
10. What is the y-intercept of the line that passes through the points (21,5) and (2,21)?
11. Nancy has just been hired for her first job. Her company gives her four choices for how she can collect her annual salary over the first eight years of employment. Each function below represents the four choices she has for her annual salary in thousands of dollars, where t represents the number of years after she is hired.
12. The third term in a sequence is 25 and the fifth term is 625. Which number could be the common ratio of the sequence?
13. The box plot below summarizes the data for the amount of snowfall, in inches, during the winter of 2021 for 12 locations in western New York.
14. Four quadratic functions are represented below.
15. The equation that represents the sequence -2, -5, -8, -11, -14, . . . is
16. The dot plot below shows the number of goals Jessica scored in each lacrosse game last season.
17. The students in Mrs. Smith’s algebra class were asked to describe the graph of g(x) = 2(x - 3)2 compared to the graph of f(x) = x2. Which student response is correct?
18. One Saturday, Dave took a long bike ride. The graph below models computations. his trip.
19. Which expression is equivalent to (x - 5)(2x + 7) - (x + 5)?
20. The functions f(x) and g(x) are graphed on the set of axes below.
21. When babysitting, Nicole charges an hourly rate and an additional charge for gas. She uses the function C(h) = 6h + 5 to determine how much to charge for babysitting. The constant term of this function represents
22. When solved for x in terms of a, the solution to the equation 3x - 7 = ax + 5 is
23. Wayde van Niekerk, a runner from South Africa, ran 400 meters in 43.03 seconds to set a world record. Which calculation would determine his average speed, in miles per hour?
24. Which function has a domain of all real numbers and a range greater than or equal to three?
25. Solve 5(x - 2) ≤ 3x + 20 algebraically
26. Given g(x) = x3 + 2x2 - x, evaluate g(-3).
27. Given the relation R = {(-1,1), (0,3), (-2,-4), (x,5)}. State a value for x that will make this relation a function. Explain why your answer makes this a function.
28. A survey of 150 students was taken. It was determined that 2/3 of the students play video games. Of the students that play video games, 85 also use social media. Of the students that do not play video games, 20% do not use social media. Complete the two-way frequency table.
29. Use the method of completing the square to determine the exact values of x for the equation x2 + 10x - 30 = 0
30. Factor 20x3 - 45x completely
31. Graph the following system of equations on the set of axes below.
32. The table below shows the amount of money a popular movie earned, in millions of dollars, during its first six weeks in theaters. Write the linear regression equation for this data set, rounding all values to the nearest hundredth. State the correlation coefficient to the nearest hundredth. State what this correlation coefficient indicates about the linear fit of the data.
33. Use the quadratic formula to solve the equation 3x2 - 10x + 5 = 0. Express the answer in simplest radical form.
34. Graph the system of inequalities on the set of axes below.
35. Courtney went to a coffee shop to purchase lattes and donuts for her friends. One day she spent a total of \$15.50 on four lattes and two donuts. The next day she spent a total of \$18.10 on three lattes and five donuts. All prices included tax. If x represents the cost of one latte and y represents the cost of one donut, write a system of equations that can be used to model this situation. Courtney thinks that one latte costs \$2.75 and one donut costs \$2.25. Is Courtney correct? Justify your answer. Use your equations to determine algebraically the exact cost of one latte and the exact cost of one donut. Use your equations to determine algebraically the exact cost of one latte and the exact cost of one donut.

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