Regents Review Stations

1

The prices of seven race cars sold last week are listed in the table.

What is the mean value of these race cars, in dollars?

1

The prices of seven race cars sold last week are listed in the table.

What is the median value of these race cars, in dollars?

1

The prices of seven race cars sold last week are listed in the table.

State which of these measures of central tendency best represents the value of the seven race cars.

Explain your answer.

1

The heights, in feet, of former New York Knicks basketball players are listed.

Using the heights given, complete the frequency table.

1

The heights, in feet, of former New York Knicks basketball players are listed.

Using the heights given, complete the frequency table.

1

Solve the following system of inequalities on the grid and label the solution S.

3x + 4y > 20
x < 3y - 18

Is the point (3, 7) in the solution set?

Explain your answer.

1

Edith babysits for x hours a week after school at a job that pays $4 an hour. She has accepted a job that pays $8 an hour as a library assistant working y hours a week. She will work both jobs. She is able to work no more than 15 hours a week, due to school commitments. Edith wants to earn at least $80 a week, working a combination of both jobs.

Write one inequality that can be used to represent the situation.

1

Edith babysits for x hours a week after school at a job that pays $4 an hour. She has accepted a job that pays $8 an hour as a library assistant working y hours a week. She will work both jobs. She is able to work no more than 15 hours a week, due to school commitments. Edith wants to earn at least $80 a week, working a combination of both jobs.

Write the other inequality that can be used to represent the situation.

1

Edith babysits for x hours a week after school at a job that pays $4 an hour. She has accepted a job that pays $8 an hour as a library assistant working y hours a week. She will work both jobs. She is able to work no more than 15 hours a week, due to school commitments. Edith wants to earn at least $80 a week, working a combination of both jobs.

Graph these inequalities on the set of axes.

Determine and state one combination of hours that will allow Edith to earn at least $80 per week while working no more than 15 hours.

1

Let f be the function represented by the graph shown.

Let g be the function such that

Determine which function has the larger maximum value.

Justify your answer.

1

An Air Force pilot is flying at a cruising altitude of 9000 feet and is forced to eject from the aircraft. The function h(t) = -16t 2 + 128t + 9000 models the height, in feet, of the pilot above the ground, where t is the time, in seconds, after she is ejected from the aircraft.

Determine and state the vertex of h(t). Explain what the second coordinate of the vertex represents in the context of the problem.

After the pilot was ejected, what is the maximum number of feet she was above the aircraft's cruising altitude. Justify your answer.

1

An Air Force pilot is flying at a cruising altitude of 9000 feet and is forced to eject from the aircraft. The function h(t) = -16t 2 + 128t + 9000 models the height, in feet, of the pilot above the ground, where t is the time, in seconds, after she is ejected from the aircraft.

Explain what the second coordinate of the vertex represents in the context of the problem.

1

An Air Force pilot is flying at a cruising altitude of 9000 feet and is forced to eject from the aircraft. The function h(t) = -16t 2 + 128t + 9000 models the height, in feet, of the pilot above the ground, where t is the time, in seconds, after she is ejected from the aircraft.

After the pilot was ejected, what is the maximum number of feet she was above the aircraft's cruising altitude.

Justify your answer.

1

The vertex of the parabola represented by f(x) = x 2 - 4x + 3 has coordinates (2, -1).

Find the coordinates of the vertex of the parabola defined by g(x) = f (x - 2) .

1

The vertex of the parabola represented by f(x) = x 2 - 4x + 3 has coordinates (2, -1).

If g(x) = f (x - 2) , explain how you arrived at your answer.

1

Let f(x) = -2x 2 and g(x) = 2x - 4 .

On the set of axes, draw the graphs of y = f(x) and y = g(x) .

Using this graph, determine and state all values of x for which f(x) = g(x) .

1

The volume of a large can of tuna fish can be calculated using the formula

Write an equation to find the radius, r, in terms of V and h.

1

The volume of a large can of tuna fish can be calculated using the formula

Determine the diameter, to the nearest inch, of a large can of tuna fish that has a volume of 66 cubic inches and a height of 3.3 inches.

1

The formula for the area of a trapezoid is

Express b1 in terms of A, h, and b2 .

1

The formula for the area of a trapezoid is

The area of a trapezoid is 60 square feet, its height is 6 feet and one base is 12 feet.

Find the number of feet in the other base.

1

Solve the inequality below to determine and state the smallest possible value for x in the solution set.

1

Solve for x algebraically:

1

The number of carbon atoms in a fossil is given by the function y = 5100(0.95) x , where x represents the number of years since being discovered.

What is the percent change each year?

1

The number of carbon atoms in a fossil is given by the function y = 5100(0.95) x , where x represents the number of years since being discovered.

Explain how you arrived at your answer.

1

Rhonda deposited $3,000 in an account in the Merrick National Bank, earning 4.2% interest, compounded annually. She made no deposits or withdrawals.

Write an equation that can be used to find B, her account balance after t years.

1

Jackson is starting an exercise program. The first day he will spend 30 minutes on a treadmill. He will increase his time on the treadmill by 2 minutes each day.

Write an equation for T(d) , the time, in minutes, on the treadmill on day d.

1

Jackson is starting an exercise program. The first day he will spend 30 minutes on a treadmill. He will increase his time on the treadmill by 2 minutes each day.

Find T (6), the minutes he will spend on the treadmill on day 6.

1

Determine and state whether the sequence 1, 3, 9, 27, ... displays exponential behavior.

Explain how you arrived at your decision.

1

Central High School had five members on their swim team in 2010. Over the next several years, the team increased by an average of 10 members per year. The same school had 35 members in their chorus in 2010. The chorus saw an increase of 5 members per year.

Write one of the equations to model this situation, where x represents the number of years since 2010.

1

Central High School had five members on their swim team in 2010. Over the next several years, the team increased by an average of 10 members per year. The same school had 35 members in their chorus in 2010. The chorus saw an increase of 5 members per year.

Write the other equation to model this situation, where x represents the number of years since 2010.

1

Central High School had five members on their swim team in 2010. Over the next several years, the team increased by an average of 10 members per year. The same school had 35 members in their chorus in 2010. The chorus saw an increase of 5 members per year.

What is the point of intersection for this system of equations?

1

Central High School had five members on their swim team in 2010. Over the next several years, the team increased by an average of 10 members per year. The same school had 35 members in their chorus in 2010. The chorus saw an increase of 5 members per year.

Explain in detail what each coordinate the point of intersection of these equations means in the context of this problem.

1

On the same set of coordinate axes, graph the following system of equations and label the solution set.

y = 2x + 4
x + y = 7

1

The function r(x) is defined by the expression x2 + 3x - 18 .

Use factoring to determine the zeros of r(x) .

1

The function r(x) is defined by the expression x2 + 3x - 18 .

Explain what the zeros represent on the graph of r(x) .

1

If f(x) = x2 and g(x) = x , determine the value(s) of x that satisfy the equation f(x) = g(x) .

1

A school is building a rectangular soccer field that has an area of 6,000 square yards. The soccer field must be 40 yards longer than its width.

Determine algebraically the dimensions of the soccer field, in yards.

1

Find three consecutive positive even integers such that the product of the second and third integers is twenty more than ten times the first integer.

[Only an algebraic solution will be accepted.]

1

On the axes below, graph f(x) = |3x| .

If g(x) = f(x) - 2 , how is the graph of f(x) translated to form the graph of g(x) ?

1

On the axes below, graph f(x) = |3x| .

If h(x) = f (x - 4) , how is the graph of f(x) translated to form the graph of h(x) ?

1

Describe the effect that each transformation below has on the function f(x) = | x | , where a > 0.

g(x) = | x - a |

1

Describe the effect that each transformation below has on the function f(x) = | x | , where a > 0.

h(x) = | x | - a

1

Express in simplest form:

1

Rachel states that the expression (n - 5) 2 is equivalent to n 2 - 10n + 25. Scott disagrees and states that the expression (n - 5) 2 is equivalent to n2 + 25.

Who is correct? Justify your answer.

1

What is the common factor between the expressions x2 - 49 and x2 + 9x + 14 ?

1

Factor completely using the GCF techniques:

4x 2 + 8xy - 5xy - 10y 2

1

The cost of 3 markers and 2 pencils is $1.80. The cost of 4 markers and 6 pencils is $2.90.

What is the cost of a marker?

1

The cost of 3 markers and 2 pencils is $1.80. The cost of 4 markers and 6 pencils is $2.90.

What is the cost of a pencil?

1

During its first week of business, a market sold a total of 108 apples and oranges. The second week, five times the number of apples and three times the number of oranges were sold. A total of 452 apples and oranges were sold during the second week.

Determine how many apples were sold the first week.

[Only an algebraic solution can receive full credit.]

1

During its first week of business, a market sold a total of 108 apples and oranges. The second week, five times the number of apples and three times the number of oranges were sold. A total of 452 apples and oranges were sold during the second week.

Determine how many oranges were sold the first week.

[Only an algebraic solution can receive full credit.]

1

The table shows the points received by the top ten paintball teams at a tournament.

Use your calculator to find a best-fit line rounded to the nearest hundredth.

1

The table shows the points received by the top ten paintball teams at a tournament.

Estimate how many points the 20th-ranked team received rounded to the nearest point.

1

The table below shows the attendance at a museum in select years from 2007 to 2013.

State the linear regression equation represented by the data table when x = 0 is used to represent the year 2007 and y is used to represent the attendance. Round all values to the nearest hundredth.

1

The table below shows the attendance at a museum in select years from 2007 to 2013.

State the correlation coefficient to the nearest hundredth.

1

The prices of seven race cars sold last week are listed in the table.What is the mean value of these race cars, in dollars?

The prices of seven race cars sold last week are listed in the table.What is the median value of these race cars, in dollars?

The prices of seven race cars sold last week are listed in the table.State which of these measures of central tendency best represents the value of the seven race cars.Explain your answer.

The heights, in feet, of former New York Knicks basketball players are listed.Using the heights given, complete the frequency table.

The heights, in feet, of former New York Knicks basketball players are listed.Using the heights given, complete the frequency table.

Solve the following system of inequalities on the grid and label the solution S.3x + 4y > 20x < 3y - 18Is the point (3, 7) in the solution set?Explain your answer.

Let f be the function represented by the graph shown.Let g be the function such thatDetermine which function has the larger maximum value.Justify your answer.

The vertex of the parabola represented by f(x) = x 2 - 4x + 3 has coordinates (2, -1).Find the coordinates of the vertex of the parabola defined by g(x) = f (x - 2) .

The vertex of the parabola represented by f(x) = x 2 - 4x + 3 has coordinates (2, -1).If g(x) = f (x - 2) , explain how you arrived at your answer.

Let f(x) = -2x 2 and g(x) = 2x - 4 .On the set of axes, draw the graphs of y = f(x) and y = g(x) .Using this graph, determine and state all values of x for which f(x) = g(x) .

The volume of a large can of tuna fish can be calculated using the formulaWrite an equation to find the radius, r, in terms of V and h.

The volume of a large can of tuna fish can be calculated using the formulaDetermine the diameter, to the nearest inch, of a large can of tuna fish that has a volume of 66 cubic inches and a height of 3.3 inches.

The formula for the area of a trapezoid isExpress b1 in terms of A, h, and b2 .

The formula for the area of a trapezoid isThe area of a trapezoid is 60 square feet, its height is 6 feet and one base is 12 feet.Find the number of feet in the other base.

Solve the inequality below to determine and state the smallest possible value for x in the solution set.

Solve for x algebraically:

The number of carbon atoms in a fossil is given by the function y = 5100(0.95) x , where x represents the number of years since being discovered.What is the percent change each year?

The number of carbon atoms in a fossil is given by the function y = 5100(0.95) x , where x represents the number of years since being discovered.Explain how you arrived at your answer.

Rhonda deposited $3,000 in an account in the Merrick National Bank, earning 4.2% interest, compounded annually. She made no deposits or withdrawals.Write an equation that can be used to find B, her account balance after t years.

Jackson is starting an exercise program. The first day he will spend 30 minutes on a treadmill. He will increase his time on the treadmill by 2 minutes each day.Write an equation for T(d) , the time, in minutes, on the treadmill on day d.

Jackson is starting an exercise program. The first day he will spend 30 minutes on a treadmill. He will increase his time on the treadmill by 2 minutes each day.Find T (6), the minutes he will spend on the treadmill on day 6.

Determine and state whether the sequence 1, 3, 9, 27, ... displays exponential behavior.Explain how you arrived at your decision.

On the same set of coordinate axes, graph the following system of equations and label the solution set.y = 2x + 4x + y = 7

The function r(x) is defined by the expression x2 + 3x - 18 .Use factoring to determine the zeros of r(x) .

The function r(x) is defined by the expression x2 + 3x - 18 .Explain what the zeros represent on the graph of r(x) .

If f(x) = x2 and g(x) = x , determine the value(s) of x that satisfy the equation f(x) = g(x) .

A school is building a rectangular soccer field that has an area of 6,000 square yards. The soccer field must be 40 yards longer than its width.Determine algebraically the dimensions of the soccer field, in yards.

Find three consecutive positive even integers such that the product of the second and third integers is twenty more than ten times the first integer.[Only an algebraic solution will be accepted.]

On the axes below, graph f(x) = |3x| .If g(x) = f(x) - 2 , how is the graph of f(x) translated to form the graph of g(x) ?

On the axes below, graph f(x) = |3x| .If h(x) = f (x - 4) , how is the graph of f(x) translated to form the graph of h(x) ?

Describe the effect that each transformation below has on the function f(x) = | x | , where a > 0.g(x) = | x - a |

Describe the effect that each transformation below has on the function f(x) = | x | , where a > 0.h(x) = | x | - a

Express in simplest form:

Rachel states that the expression (n - 5) 2 is equivalent to n 2 - 10n + 25. Scott disagrees and states that the expression (n - 5) 2 is equivalent to n2 + 25.Who is correct? Justify your answer.

What is the common factor between the expressions x2 - 49 and x2 + 9x + 14 ?

Factor completely using the GCF techniques:4x 2 + 8xy - 5xy - 10y 2

The cost of 3 markers and 2 pencils is $1.80. The cost of 4 markers and 6 pencils is $2.90.What is the cost of a marker?

The cost of 3 markers and 2 pencils is $1.80. The cost of 4 markers and 6 pencils is $2.90.What is the cost of a pencil?

The table shows the points received by the top ten paintball teams at a tournament.Use your calculator to find a best-fit line rounded to the nearest hundredth.

The table shows the points received by the top ten paintball teams at a tournament.Estimate how many points the 20th-ranked team received rounded to the nearest point.

The table below shows the attendance at a museum in select years from 2007 to 2013.State the linear regression equation represented by the data table when x = 0 is used to represent the year 2007 and y is used to represent the attendance. Round all values to the nearest hundredth.

The table below shows the attendance at a museum in select years from 2007 to 2013.State the correlation coefficient to the nearest hundredth.

The table below shows the attendance at a museum in select years from 2007 to 2013.Determine whether the data suggests a strong or weak association.

The prices of seven race cars sold last week are listed in the table.

What is the mean value of these race cars, in dollars?

The prices of seven race cars sold last week are listed in the table.

What is the median value of these race cars, in dollars?

The prices of seven race cars sold last week are listed in the table.

State which of these measures of central tendency best represents the value of the seven race cars.

Explain your answer.

The heights, in feet, of former New York Knicks basketball players are listed.

Using the heights given, complete the frequency table.

The heights, in feet, of former New York Knicks basketball players are listed.

Using the heights given, complete the frequency table.

Solve the following system of inequalities on the grid and label the solution S.

3x + 4y > 20
x < 3y - 18

Is the point (3, 7) in the solution set?

Explain your answer.

Let f be the function represented by the graph shown.

Let g be the function such that

Determine which function has the larger maximum value.

Justify your answer.

The vertex of the parabola represented by f(x) = x 2 - 4x + 3 has coordinates (2, -1).

Find the coordinates of the vertex of the parabola defined by g(x) = f (x - 2) .

The vertex of the parabola represented by f(x) = x 2 - 4x + 3 has coordinates (2, -1).

If g(x) = f (x - 2) , explain how you arrived at your answer.

Let f(x) = -2x 2 and g(x) = 2x - 4 .

On the set of axes, draw the graphs of y = f(x) and y = g(x) .

Using this graph, determine and state all values of x for which f(x) = g(x) .

The volume of a large can of tuna fish can be calculated using the formula

Write an equation to find the radius, r, in terms of V and h.

The volume of a large can of tuna fish can be calculated using the formula

Determine the diameter, to the nearest inch, of a large can of tuna fish that has a volume of 66 cubic inches and a height of 3.3 inches.

The formula for the area of a trapezoid is

Express b1 in terms of A, h, and b2 .

The formula for the area of a trapezoid is

The area of a trapezoid is 60 square feet, its height is 6 feet and one base is 12 feet.

Find the number of feet in the other base.

The number of carbon atoms in a fossil is given by the function y = 5100(0.95) x , where x represents the number of years since being discovered.

What is the percent change each year?

The number of carbon atoms in a fossil is given by the function y = 5100(0.95) x , where x represents the number of years since being discovered.

Explain how you arrived at your answer.

Rhonda deposited $3,000 in an account in the Merrick National Bank, earning 4.2% interest, compounded annually. She made no deposits or withdrawals.

Write an equation that can be used to find B, her account balance after t years.

Jackson is starting an exercise program. The first day he will spend 30 minutes on a treadmill. He will increase his time on the treadmill by 2 minutes each day.

Write an equation for T(d) , the time, in minutes, on the treadmill on day d.

Jackson is starting an exercise program. The first day he will spend 30 minutes on a treadmill. He will increase his time on the treadmill by 2 minutes each day.

Find T (6), the minutes he will spend on the treadmill on day 6.

Determine and state whether the sequence 1, 3, 9, 27, ... displays exponential behavior.

Explain how you arrived at your decision.

On the same set of coordinate axes, graph the following system of equations and label the solution set.

y = 2x + 4
x + y = 7

The function r(x) is defined by the expression x2 + 3x - 18 .

Use factoring to determine the zeros of r(x) .

The function r(x) is defined by the expression x2 + 3x - 18 .

Explain what the zeros represent on the graph of r(x) .

A school is building a rectangular soccer field that has an area of 6,000 square yards. The soccer field must be 40 yards longer than its width.

Determine algebraically the dimensions of the soccer field, in yards.

Find three consecutive positive even integers such that the product of the second and third integers is twenty more than ten times the first integer.

[Only an algebraic solution will be accepted.]

On the axes below, graph f(x) = |3x| .

If g(x) = f(x) - 2 , how is the graph of f(x) translated to form the graph of g(x) ?

On the axes below, graph f(x) = |3x| .

If h(x) = f (x - 4) , how is the graph of f(x) translated to form the graph of h(x) ?

Describe the effect that each transformation below has on the function f(x) = | x | , where a > 0.

g(x) = | x - a |

Describe the effect that each transformation below has on the function f(x) = | x | , where a > 0.

h(x) = | x | - a

Rachel states that the expression (n - 5) 2 is equivalent to n 2 - 10n + 25. Scott disagrees and states that the expression (n - 5) 2 is equivalent to n2 + 25.

Who is correct? Justify your answer.

Factor completely using the GCF techniques:

4x 2 + 8xy - 5xy - 10y 2

The cost of 3 markers and 2 pencils is $1.80. The cost of 4 markers and 6 pencils is $2.90.

What is the cost of a marker?

The cost of 3 markers and 2 pencils is $1.80. The cost of 4 markers and 6 pencils is $2.90.

What is the cost of a pencil?

The table shows the points received by the top ten paintball teams at a tournament.

Use your calculator to find a best-fit line rounded to the nearest hundredth.

The table shows the points received by the top ten paintball teams at a tournament.

Estimate how many points the 20th-ranked team received rounded to the nearest point.

The table below shows the attendance at a museum in select years from 2007 to 2013.

State the linear regression equation represented by the data table when x = 0 is used to represent the year 2007 and y is used to represent the attendance. Round all values to the nearest hundredth.

The table below shows the attendance at a museum in select years from 2007 to 2013.

State the correlation coefficient to the nearest hundredth.

The table below shows the attendance at a museum in select years from 2007 to 2013.

Determine whether the data suggests a strong or weak association.