# Algebra I Regents Exam - August 2018

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 August 2018.

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Regents Exam Past Papers

### Algebra I Regents New York State Exam - August 2018

Solutions for Questions 1 - 12

1. The number of bacteria grown in a lab can be modeled by P(t) = 300 • 24t, where t is the number of hours. Which expression is equivalent to P(t)?
2. During physical education class, Andrew recorded the exercise times in minutes and heart rates in beats per minute (bpm) of four of his classmates. Which table best represents a linear model of exercise time and heart rate?
3. David correctly factored the expression m2 - 12m - 64. Which expression did he write?
4. The solution to -2(1 - 4x) = 3x + 8 is
5. The graph of f(x) is shown below
6. If the function f(x) = x2 has the domain {0, 1, 4, 9}, what is its range?
7. The expression 4x2 - 25 is equivalent to
8. Compared to the graph of f(x) = x2, the graph of g(x) = (x 2)2 + 3 is the result of translating f(x)
9. Lizzy has 30 coins that total \$4.80. All of her coins are dimes, D, and quarters, Q. Which system of equations models this situation?
10. Gretchen has \$50 that she can spend at the fair. Ride tickets cost \$1.25 each and game tickets cost \$2 each. She wants to go on a minimum of 10 rides and play at least 12 games. Which system of inequalities represents this situation when r is the number of ride tickets purchased and g is the number of game tickets purchased?
11. Three functions are shown below.
12. Olivia entered a baking contest. As part of the contest, she needs to demonstrate how to measure a gallon of milk if she only has a teaspoon measure. She converts the measurement using the ratios below:
13. If y = 3x3 + x2 - 5 and z = x2 - 12, which polynomial is equivalent to 2(y + z)?
14. An outdoor club conducted a survey of its members. The members were asked to state their preference between skiing and snowboarding. Each member had to pick one. Of the 60 males, 45 stated they preferred to snowboard. Twenty-two of the 60 females preferred to ski. What is the relative frequency that a male prefers to ski?
15. When the function g(x)
16. If f(x) = 2x2 + x - 3, which equation can be used to determine the zeros of the function?
17. Each day, a local dog shelter spends an average of \$2.40 on food per dog. The manager estimates the shelter’s daily expenses, assuming there is at least one dog in the shelter, using the function E(x) = 30 + 2.40x. Which statements regarding the function E(x) are correct?
18. Which point is not in the solution set of the equation 3y + 2 = x2 - 5x + 17?
19. The functions f(x) and g(x) are graphed below.
20. For the sequence -27, -12, 3, 18, …, the expression that defines the nth term where a1 = -27 is
21. The data obtained from a random sample of track athletes showed that as the foot size of the athlete decreased, the average running speed decreased. Which statement is best supported by the data?
22. Which system of equations will yield the same solution as the system below?
23. Which of the three situations given below is best modeled by an exponential function?
24. The length, width, and height of a rectangular box are represented by 2x, 3x + 1, and 5x - 6, respectively. When the volume is expressed as a polynomial in standard form, what is the coefficient of the 2nd term?
25. Explain how to determine the zeros of f(x) = (x + 3)(x - 1)(x - 8). State the zeros of the function.
26. Four relations are shown below.
27. The table below represents the height of a bird above the ground during flight, with P(t) representing height in feet and t representing time in seconds. Calculate the average rate of change from 3 to 9 seconds, in feet per second.
29. The formula for converting degrees Fahrenheit (F) to degrees Kelvin (K) is:
30. Solve the following equation by completing the square:
31. The students in Mrs. Lankford’s 4th and 6th period Algebra classes took the same test. The results of the scores are shown in the following table:
32. Write the first five terms of the recursive sequence defined below.
33. Sarah wants to buy a snowboard that has a total cost of \$580, including tax. She has already saved \$135 for it. At the end of each week, she is paid \$96 for babysitting and is going to save three-quarters of that for the snowboard. Write an inequality that can be used to determine the minimum number of weeks Sarah needs to babysit to have enough money to purchase the snowboard. Determine and state the minimum number of full weeks Sarah needs to babysit to have enough money to purchase this snowboard.
34. A car was purchased for \$25,000. Research shows that the car has an average yearly depreciation rate of 18.5%. Create a function that will determine the value, V(t), of the car t years after purchase. Determine, to the nearest cent, how much the car will depreciate from year 3 to year 4.
35. Graph the following system of inequalities on the set of axes below:
36. Paul plans to have a rectangular garden adjacent to his garage. He will use 36 feet of fence to enclose three sides of the garden. The area of the garden, in square feet, can be modeled by f(w) = w(36 - 2w), where w is the width in feet. On the set of axes below, sketch the graph of f(w).
37. At the present time, Mrs. Bee’s age is six years more than four times her son’s age. Three years ago, she was seven times as old as her son was then. If b represents Mrs. Bee’s age now and s represents her son’s age now, write a system of equations that could be used to model this scenario. Use this system of equations to determine, algebraically, the ages of both Mrs. Bee and her son now. Determine how many years from now Mrs. Bee will be three times as old as her son will be then.

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