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 2019.

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The following are questions from the past paper Regents High School Algebra I January 2019 Exam (pdf). Scroll down the page for the step by step solutions.

Algebra 1 - January 2019 Regents - Questions and solutions 1 - 10

- The scatter plot below shows the relationship between the number of members in a family and the amount of the family’s weekly grocery bill.

The most appropriate prediction of the grocery bill for a family that consists of six members is - The function g(x) is defined as g(x) = -2x
^{2}+ 3x. The value of g(-3) is - Which expression results in a rational number?
- The math department needs to buy new textbooks and laptops for the computer science classroom. The textbooks cost $116.00 each, and the laptops cost $439.00 each. If the math department has $6500 to spend and purchases 30 textbooks, how many laptops can they buy?
- What is the solution to the equation 3/5(x + 4/3) = 1.04?

- The area of a rectangle is represented by 3x
^{2}- 10x - 8. Which expression can also be used to represent the area of the same rectangle? - Which relation does not represent a function?
- Britney is solving a quadratic equation. Her first step is shown below.

Problem: 3x^{2}- 8 - 10x = 3(2x + 3)

Step 1: 3x^{2}- 10x - 8 = 6x + 9

Which two properties did Britney use to get to step 1? - The graph of y = 1/2 x
^{2}- x - 4 is shown below. The points A(-2,0), B(0,-4), and C(4,0) lie on this graph. - Given the parent function f(x) = x
^{3}, the function g(x) = (x - 1)^{3}- 2 is the result of a shift of f(x)

Algebra 1 - January 2019 Regents - Questions and solutions 11 - 20

- If C = 2a
^{2}- 5 and D = 3 - a, then C - 2D equals - Marc bought a new laptop for $1250. He kept track of the value of the laptop over the next three years, as shown in the table below.
- The height of a ball Doreen tossed into the air can be modeled by the function h(x) = -4.9x
^{2}+ 6x + 5, where x is the time elapsed in seconds, and h(x) is the height in meters. The number 5 in the function represents - The function f(x) = 2x
^{2}+ 6x - 12 has a domain consisting of the integers from -2 to 1, inclusive. Which set represents the corresponding range values for f(x)? - Which equation has the same solution as x
^{2}+ 8x - 33 = 0?

- The table below shows the weights of Liam’s pumpkin, l(w), and Patricia’s pumpkin, p(w), over a four-week period where w represents the number of weeks. Liam’s pumpkin grows at a constant rate. Patricia’s pumpkin grows at a weekly rate of approximately 52%.

Assume the pumpkins continue to grow at these rates through week 13. When comparing the weights of both Liam’s and Patricia’s pumpkins in week 10 and week 13, which statement is true? - The function f(x) is graphed below.

The domain of this function is - Which pair of equations would have (–1,2) as a solution?
- Which function could be used to represent the sequence 8, 20, 50, 125, 312.5,…, given that a
_{1}= 8? - The formula for electrical power, P, is P = I
^{2}R, where I is current and R is resistance. The formula for I in terms of P and R is

Algebra 1 - January 2019 Regents - Questions and solutions 21 - 29

- The functions f(x), q(x), and p(x) are shown below.

When the input is 4, which functions have the same output value? - Using the substitution method, Vito is solving the following system of equations algebraically:

y + 3x = -4

2x - 3y = -21

Which equivalent equation could Vito use? - Materials A and B decay over time. The function for the amount of material A is A(t) = 1000(0.5)
^{2t}and for the amount of material B is B(t) = 1000(0.25)^{t}, where t represents time in days. On which day will the amounts of material be equal? - The following conversion was done correctly:

What were the final units for this conversion?

- Solve algebraically for x: 3600 + 1.02x < 2000 + 1.04x
- The number of people who attended a school’s last six basketball games increased as the team neared the state sectional games. The table below shows the data.

State the type of function that best fits the given data. Justify your choice of a function type.

- Solve x
^{2}- 8x - 9 = 0 algebraically.

Explain the first step you used to solve the given equation. - The graph of f(t) models the height, in feet, that a bee is flying above the ground with respect to the time it traveled in t seconds.

State all time intervals when the bee’s rate of change is zero feet per second. Explain your reasoning.

- Graph the function f(x) = 2
^{x}- 7 on the set of axes below.

If g(x) 5 1.5x 2 3, determine if f(x) > g(x) when x = 4. Justify your answer. - Determine algebraically the zeros of f(x) = 3x
^{3}+ 21x^{2}+ 36x.

- Santina is considering a vacation and has obtained high-temperature data from the last two weeks for Miami and Los Angeles.

Which location has the least variability in temperatures? Explain how you arrived at your answer. - Solve the quadratic equation below for the exact values of x.

- Marilyn collects old dolls. She purchases a doll for $450. Research shows this doll’s value will increase by 2.5% each year.

Write an equation that determines the value, V, of the doll t years after purchase.

Assuming the doll’s rate of appreciation remains the same, will the doll’s value be doubled in 20 years? Justify your reasoning.

- The data given in the table below show some of the results of a study comparing the height of a certain breed of dog, based upon its mass.

Write the linear regression equation for these data, where x is the mass and y is the height. Round all values to the nearest tenth.

State the value of the correlation coefficient to the nearest tenth, and explain what it indicates.

- Myranda received a movie gift card for $100 to her local theater. Matinee tickets cost $7.50 each and evening tickets cost $12.50 each.

If x represents the number of matinee tickets she could purchase, and y represents the number of evening tickets she could purchase, write an inequality that represents all the possible ways Myranda could spend her gift card on movies at the theater.

On the set of axes below, graph this inequality.

What is the maximum number of matinee tickets Myranda could purchase with her gift card? Explain your answer.

- One spring day, Elroy noted the time of day and the temperature, in degrees Fahrenheit. His findings are stated below.

At 6 a.m., the temperature was 50°F. For the next 4 hours, the temperature rose 3° per hour.

The next 6 hours, it rose 2° per hour.

The temperature then stayed steady until 6 p.m.

For the next 2 hours, the temperature dropped 1° per hour.

The temperature then dropped steadily until the temperature was 56°F at midnight.

On the set of axes below, graph Elroy’s data.

State the entire time interval for which the temperature was increasing.

Determine the average rate of change, in degrees per hour, from 6:00 p.m. to midnight. - A recreation center ordered a total of 15 tricycles and bicycles from a sporting goods store. The number of wheels for all the tricycles and bicycles totaled 38.

Write a linear system of equations that models this scenario, where t represents the number of tricycles and b represents the number of bicycles ordered.

On the set of axes below, graph this system of equations.

Based on your graph of this scenario, could the recreation center have ordered 10 tricycles? Explain your reasoning.

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