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 2024.

**Related Pages**

Regents Exam Past Papers

Algebra I Regents New York State Exam Questions January 2024 (pdf)

Solutions for Questions 1 - 24

- The graph below represents a dog walker’s speed during his 30-minute walk around the neighborhood
- Given the relation: {(0,4), (2,6), (4,8), (x,7)} Which value of x will make this relation a function?
- The Speedy Jet Ski Rental Company charges an insurance fee and an hourly rental rate. The total cost is modeled by the function R(x) = 30 + 40x. Based on this model, which statements are true?
- The eleventh term of the sequence 3, 26, 12, 224, …, is
- Which situation represents exponential growth?
- The expression (-x
^{2}+ 3x - 7) - (4x^{2}+ 5x - 2) is equivalent to - If f(x) = x
^{2}, which function is the result of shifting f(x) 3 units left and 2 units down? - An equation used to find the velocity of an object is given as
v
^{2}= u^{2}+ 2as, where u is the initial velocity, v is the final velocity, a is the acceleration of the object, and s is the distance traveled. When this equation is solved for a, the result is - Mrs. Smith’s math class surveyed students to determine their favorite flavors of soft ice cream. The results are shown in the table below.
- If f(x) = x
^{2}+ 2x + 1 and g(x) = 3x + 5, then what is the value of f(1) - g(3)? - Which function has the largest y-intercept?
- Two texting plans are advertised. Plan A has a monthly fee of $15 with a charge of $0.08 per text. Plan B has a monthly fee of $3 with a charge of $0.12 per text. If t represents the number of text messages in a month, which inequality should be used to show that the cost of Plan A is less than the cost of Plan B?
- The function f(x) is graphed on the set of axes below
- What is the degree of the polynomial 5x - 3x
^{2}- 1 + 7x^{3}? - The product of (x
^{2}+ 3x + 9) and (x - 3) is - The solution to 2/3(3 - 2x) = 3/4 is
- If f(x) = 2x + 6 and g(x) = |x| are graphed on the same coordinate plane, for which value of x is f(x) = g(x)?
- What is the solution to the inequality 2x - 7 > 2.5x + 3?
- Three expressions are written below.
- Joe deposits $4000 into a certificate of deposit (CD) at his local bank. The CD earns 3% interest, compounded annually. The value of the CD in x years can be found using the function
- When factored completely, -x
^{3}+ 10x^{2}+ 24x is - When the temperature is 59°F, the speed of sound at sea level is 1225 kilometers per hour. Which process could be used to convert this speed into feet per second?
- The zeros of a polynomial function are -2, 4, and 0. What are all the factors of this function?
- What is the range of the function f(x) = (x - 4)
^{2}+ 1? - Student scores on a recent test are shown in the table below
- State whether 2 √3 + 6 is rational or irrational. Explain your answer.
- The table below shows data from a recent car trip for the Burke family.
- On the set of axes below, graph the equation 3y + 2x = 15.
- Using the quadratic formula, solve 3x
^{2}- 2x - 6 = 0 for all values of x. Round your answers to the nearest hundredth - The piecewise function f(x) is given below.
- Express the equation x
^{2}- 8x = -41 in the form (x - p)^{2}= q. - Factor 36 - 4x
^{2}completely - While playing golf, Laura hit her ball from the ground. The height, in feet, of her golf ball can be
modeled by h(t) = -16t
^{2}+ 48t, where t is the time in seconds. - The table below shows the number of SAT prep classes five students attended and the scores they received on the test.
- Julia is 4 years older than twice Kelly’s age, x. The product of their ages is 96.

Write an equation that models this situation.

Determine Kelly’s age algebraically.

State the difference between Julia’s and Kelly’s ages, in years. - On the set of axes below, graph the following system of inequalities:
- Jim had a bag of coins. The number of nickels, n, and the number of quarters, q, totaled 28 coins.

The combined value of the coins was $4.

Write a system of equations that models this situation.

Use your system of equations to algebraically determine both the number of quarters, q, and the number of nickels, n, that Jim had in the bag.

Jim was given an additional $3.00 that was made up of equal numbers of nickels and quarters.

How many of each coin was he given? Justify your answer.

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