NYSED High School Regents Algebra I

Part I

Answer all 24 questions in this part. Each correct answer will receive 2 credits. No partial credit will be allowed. Utilize the information provided for each question to determine your answer. Note that diagrams are not necessarily drawn to scale. For each statement or question, choose the word or expression that, of those given, best completes the statement or answers the question. 

Required

2

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

Required

2

The function g(x) is defined as g(x)= -2x^{2}+3x The value of g(-3) is

Required

2

Which expression results in a rational number?

Required

2

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?

Required

2

What is the solution to the equation \frac{3}{5}\left(x+\frac{4}{3}\right)=1.04?

Required

2

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?

Required

2

Which relation does not represent a function?

Required

2

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?

I. addition property of equality
II. commutative property of addition
III. multiplication property of equality
IV. distributive property of multiplication over addition

Required

2

The graph of y=\frac{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.

Which of these points can determine the zeros of the equation y=\frac{1}{2}x^{2}-x-4?

Required

2

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)

Required

2

If C=2a^{2}-5 and D=3-a, then C-2D equals

Required

2

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.

Which function can be used to determine the value of the laptop for x years after the purchase?

Required

2

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

Required

2

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)?

Required

2

Which equation has the same solution as x^{2}+8x-33=0?

Required

2

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?

Required

2

The function f(x) is graphed below.

The domain of this function is

Required

2

Which pair of equations would have (–1,2) as a solution?

Required

2

Which function could be used to represent the sequence 8, 20, 50, 125, 312.5,..., given that a1=8?

Required

2

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

Required

2

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

When the input is 4, which functions have the same output value?

Required

2

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?

Required

2

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?

Required

2

The following conversion was done correctly:

\frac{3\,\text{miles}} {1\,\text{hour}}\sdot\frac{1\,\text{hour}} {60\,\text{minutes}}\sdot\frac{5280\,\text{feet}} {1\,\text{mile}}\sdot\frac{12\,\text{inches}} {1\,\text{foot}}

What were the final units for this conversion?

Part II 

Answer all 8 questions in this part. Each correct answer will receive 2 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. Utilize the information provided for each question to determine your answer. Note that diagrams are not necessarily drawn to scale. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit.

2

Solve algebraically for x: 3600+1.02x<2000+1.04x

Required

2

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.

Required

2

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

Explain the first step you used to solve the given equation.

Required

2

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.

Required

2

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

If g(x)=1.5x-3, determine if f(x) > g(x) when x=4. Justify your answer.

Required

2

Determine algebraically the zeros of f(x)=3x^{3}+21x^{2}+36x.

Required

2

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.

Required

2

Solve the quadratic equation below for the exact values of x.

4x^{2}-5=75

Part III 

Answer all 4 questions in this part. Each correct answer will receive 4 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. Utilize the information provided for each question to determine your answer. Note that diagrams are not necessarily drawn to scale. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit. 

Required

4

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.

Required

4

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.

Required

4

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.

Required

4

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.

Part IV 

Answer the question in this part. A correct answer will receive 6 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. Utilize the information provided to determine your answer. Note that diagrams are not necessarily drawn to scale. A correct numerical answer with no work shown will receive only 1 credit.

Required

6

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.

NYSED High School Regents Algebra I

Part I

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 \frac{3}{5}\left(x+\frac{4}{3}\right)=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?

The graph of y=\frac{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.Which of these points can determine the zeros of the equation y=\frac{1}{2}x^{2}-x-4?

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)

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. Which function can be used to determine the value of the laptop for x years after the purchase?

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 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 a1=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

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:\frac{3\,\text{miles}} {1\,\text{hour}}\sdot\frac{1\,\text{hour}} {60\,\text{minutes}}\sdot\frac{5280\,\text{feet}} {1\,\text{mile}}\sdot\frac{12\,\text{inches}} {1\,\text{foot}} What were the final units for this conversion?

Part II

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)=1.5x-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.4x^{2}-5=75

Part III

Part IV

Part I

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 \frac{3}{5}\left(x+\frac{4}{3}\right)=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?

The graph of y=\frac{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.Which of these points can determine the zeros of the equation y=\frac{1}{2}x^{2}-x-4?

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)

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. Which function can be used to determine the value of the laptop for x years after the purchase?

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 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 a1=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

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:\frac{3\,\text{miles}} {1\,\text{hour}}\sdot\frac{1\,\text{hour}} {60\,\text{minutes}}\sdot\frac{5280\,\text{feet}} {1\,\text{mile}}\sdot\frac{12\,\text{inches}} {1\,\text{foot}} What were the final units for this conversion?

Part II

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)=1.5x-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.4x^{2}-5=75

Part III

Part IV

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 graph of y=\frac{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.

Which of these points can determine the zeros of the equation y=\frac{1}{2}x^{2}-x-4?

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.

Which function can be used to determine the value of the laptop for x years after the purchase?

The function f(x) is graphed below.

The domain of this function is

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?

The following conversion was done correctly:

\frac{3\,\text{miles}} {1\,\text{hour}}\sdot\frac{1\,\text{hour}} {60\,\text{minutes}}\sdot\frac{5280\,\text{feet}} {1\,\text{mile}}\sdot\frac{12\,\text{inches}} {1\,\text{foot}}

What were the final units for this conversion?

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)=1.5x-3, determine if f(x) > g(x) when x=4. Justify your answer.

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.

4x^{2}-5=75

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 graph of y=\frac{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.

Which of these points can determine the zeros of the equation y=\frac{1}{2}x^{2}-x-4?

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.

Which function can be used to determine the value of the laptop for x years after the purchase?

The function f(x) is graphed below.

The domain of this function is

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?

The following conversion was done correctly:

\frac{3\,\text{miles}} {1\,\text{hour}}\sdot\frac{1\,\text{hour}} {60\,\text{minutes}}\sdot\frac{5280\,\text{feet}} {1\,\text{mile}}\sdot\frac{12\,\text{inches}} {1\,\text{foot}}

What were the final units for this conversion?

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)=1.5x-3, determine if f(x) > g(x) when x=4. Justify your answer.

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.

4x^{2}-5=75