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 January 2018.

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The following are questions from the past paper Regents High School Algebra I January 2018 Exam (pdf). Scroll down the page for the step by step solutions.

Algebra 1 - January 2018 Regents - Questions and solutions 1 - 12

- When solving the equation 12x
^{2}- 7x = 6 - 2(x^{2}- 1), Evan wrote 12x^{2}- 7x = 6 - 2x^{2}+ 2 as his first step. Which property justifies this step?

(1) subtraction property of equality

(2) multiplication property of equality

(3) associative property of multiplication

(4) distributive property of multiplication over subtraction - Jill invests $400 in a savings bond. The value of the bond, V(x), in hundreds of dollars after x years is illustrated in the table below.

Which equation and statement illustrate the approximate value of the bond in hundreds of dollars over time in years? - Alicia purchased H half-gallons of ice cream for $3.50 each and P packages of ice cream cones for $2.50 each. She purchased 14 items and spent $43. Which system of equations could be used to determine how many of each item Alicia purchased?
- A relation is graphed on the set of axes below.
- Ian is saving up to buy a new baseball glove. Every month he puts $10 into a jar. Which type of function best models the total amount of money in the jar after a given number of months?
- Which ordered pair would not be a solution to y = x
^{3}- x?

If k is replaced by 1/2 , which statement about these new functions is true? - Last weekend, Emma sold lemonade at a yard sale. The function P(c) = .50c - 9.96 represented the profit, P(c), Emma earned selling c cups of lemonade. Sales were strong, so she raised the price for this weekend by 25 cents per cup. Which function represents her profit for this weekend?
- The product of √576 and √684 is
- Which expression is equivalent to y
^{4}- 100? - The graphs of y = x
^{2}- 3 and y = 3x - 4 intersect at approximately - The expression -24.9t
^{2}+ 50t + 2 represents the height, in meters, of a toy rocket t seconds after launch. The initial height of the rocket, in meters, is - If the domain of the function f(x) = 2x
^{2}- 8 is {-2, 3, 5}, then the range is

If t represents the number of minutes on the treadmill and b represents the number of minutes on the stationary bike, which expression represents the number of Calories that Konnor can burn on the stationary bike?

Algebra 1 - January 2018 Regents - Questions and solutions 13 - 24

- Which polynomial is twice the sum of 4x
^{2}- x + 1 and -6x^{2}+ x - 4? - What are the solutions to the equation 3(x - 4)
^{2}- 27? - A system of equations is shown below.

Equation A: 5x + 9y = 12

Equation B: 4x - 3y = 8

Which method eliminates one of the variables? - The 15 members of the French Club sold candy bars to help fund their trip to Quebec. The table below shows the number of candy bars each member sold.
- Given the set {x| - 2 ≤ x ≤ 2, where x is an integer}, what is the solution of -2(x - 5) < 10?
- If the pattern below continues, which equation(s) is a recursive formula that represents the number of squares in this sequence?
- If the original function f(x) = 2x
^{2}- 1 is shifted to the left 3 units to make the function g(x), which expression would represent g(x)? - First consider the system of equations y = -1/2 x + 1 and y = x - 5.

Then consider the system of inequalities y > 1/2 x + 1 and y < x - 5.

When comparing the number of solutions in each of these systems, which statement is true? - Nora inherited a savings account that was started by her grandmother 25 years ago. This scenario is modeled by the function A(t) = 5000(1.013)
^{t + 25}, where A(t) represents the value of the account, in dollars, t years after the inheritance. Which function below is equivalent to A(t)? - The value of x which makes 2/3(1/4 x - 2) = 1/5(4/3 x - 1) true is
- Which quadratic function has the largest maximum over the set of real numbers?
- Voting rates in presidential elections from 1996-2012 are modeled below

Algebra 1 - January 2018 Regents - Questions and solutions 25 - 37

- On the set of axes below, graph f(x) = |x - 3| + 2.
- Determine all the zeros of m(x) = x
^{2}- 4x + 3, algebraically. - The distance traveled is equal to the rate of speed multiplied by the time traveled. If the distance is measured in feet and the time is measured in minutes, then the rate of speed is expressed in which units? Explain how you arrived at your answer.
- Determine if the point (0,4) is a solution to the system of inequalities graphed below. Justify your answer
- If the zeros of a quadratic function, F, are -3 and 5, what is the equation of the axis of symmetry of F? Justify your answer.
- The formula F
_{g}= GM_{1}M_{2}/r^{2}calculates the gravitational force between two objects where G is the gravitational constant, M_{1}is the mass of one object, M_{2}is the mass of the other object, and r is the distance between them. Solve for the positive value of r in terms of F_{g}, G, M_{1}, and M_{2}. - At Mountain Lakes High School, the mathematics and physics scores of nine students were compared as shown in the table below.

State the correlation coefficient, to the nearest hundredth, for the line of best fit for these data.

Explain what the correlation coefficient means with regard to the context of this situation. - The graph of the function f(x) = ax
^{2}+ bx + c is given below

Could the factors of f(x) be (x + 2) and (x - 3)? Based on the graph, explain why or why not. - 33 Jim is a furniture salesman. His weekly pay is $300 plus 3.5% of his total sales for the week. Jim sells x dollars’ worth of furniture during the week. Write a function, p(x), which can be used to determine his pay for the week.

Use this function to determine Jim’s pay to the nearest cent for a week when his sales total is $8250 - Omar has a piece of rope. He ties a knot in the rope and measures the new length of the rope. He then repeats this process several times. Some of the data collected are listed in the table below.

State, to the nearest tenth, the linear regression equation that approximates the length, y, of the rope after tying x knots.

Explain what the y-intercept means in the context of the problem.

Explain what the slope means in the context of the problem. - The drama club is running a lemonade stand to raise money for its new production. A local grocery store donated cans of lemonade and bottles of water. Cans of lemonade sell for $2 each and bottles of water sell for $1.50 each. The club needs to raise at least $500 to cover the cost of renting costumes. The students can accept a maximum of 360 cans and bottles.

Write a system of inequalities that can be used to represent this situation.

The club sells 144 cans of lemonade. What is the least number of bottles of water that must be sold to cover the cost of renting costumes? Justify your answer. 36. A manager wanted to analyze the online shoe sales for his business. He collected data for the number of pairs of shoes sold each hour over a 14-hour time period. He created a graph to model the data, as shown below.

The manager believes the set of integers would be the most appropriate domain for this model. Explain why he is incorrect.

State the entire interval for which the number of pairs of shoes sold is increasing.

Determine the average rate of change between the sixth and fourteenth hours, and explain what it means in the context of the problem. - Zeke and six of his friends are going to a baseball game. Their combined money totals $28.50. At the game, hot dogs cost $1.25 each, hamburgers cost $2.50 each, and sodas cost $0.50 each. Each person buys one soda. They spend all $28.50 on food and soda. Write an equation that can determine the number of hot dogs, x, and hamburgers, y, Zeke and his friends can buy.

Graph your equation on the grid below.

Determine how many different combinations, including those combinations containing zero, of hot dogs and hamburgers Zeke and his friends can buy, spending all $28.50. Explain your answer.

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