Jmap Standard NYS ALGEBRA 1

Last updated over 1 year ago

286 questions

Jmap Standard NYS ALGEBRA 1

Last updated over 1 year ago

286 questions

Andy has $310 in his account. Each week, w, he withdraws $30 for his expenses. Which expression could be used if he wanted to find out how much money he had left after 8 weeks?

Do you agree with Pat's answer? Explain your reasoning.

A student is in the process of solving an equation. The original equation and the first step are shown below: Original: 3a + 6 = 2 - 5a + 7, Step one: 3a + 6 = 2 + 7 - 5a. Which property did the student use for the first step? Explain why this property is correct.

John was given the equation 4(2a + 3) = -3(a - 1) + 31 - 11a to solve. Some of the steps and their reasons have already been completed. State a property of numbers for each missing reason. Given: 4(2a + 3) = -3(a - 1) + 31 - 11a, 8a + 12 = -3a + 3 + 31 - 11a [], 8a + 12 = 34 - 14a [Combining like terms], 22a + 12 = 34 []

Solve the equation algebraically for the exact value of x: 6 - 2/3(x + 5) = 4x

Solve algebraically for x: -2/3(x + 12) + 2/3x = -5/4x + 2

A gardener is planting two types of trees: Type A is three feet tall and grows at a rate of 15 inches per year. Type B is four feet tall and grows at a rate of 10 inches per year. Algebraically determine exactly how many years it will take for these trees to be the same height.

The formula for the area of a trapezoid is A = 1/2h(b1 + b2). Express b1 in terms of A, h, and b2. The area of a trapezoid is 60 square feet, its height is 6 ft, and one base is 12 ft. Find the number of feet in the other base.

The volume of a large can of tuna fish can be calculated using the formula V = πr^2h. Write an equation to find the radius, r, in terms of V and h. 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 sum of the degree measures of the interior angles of a polygon is S = 180(n - 2). Solve for n, the number of sides of the polygon, in terms of S.

Solve the equation below for x in terms of a: 4(ax + 3) - 3ax = 25 + 3a

The formula for the volume of a cone is V = 1/3πr^2h. Solve the equation for h in terms of V, r, and π.

Using the formula for the volume of a cone, express r in terms of V, h, and π.

The formula Fg = GM1M2/r^2 calculates the gravitational force between two objects where G is the gravitational constant, M1 is the mass of one object, M2 is the mass of the other object, and r is the distance between them. Solve for the positive value of r in terms of Fg, G, M1, and M2.

A typical marathon is 26.2 miles. Allan averages 12 kilometers per hour when running in marathons. Determine how long it would take Allan to complete a marathon, to the nearest tenth of an hour. Justify your answer.

A news report suggested that an adult should drink a minimum of 4 pints of water per day. Based on this report, determine the minimum amount of water an adult should drink, in fluid ounces, per week.

A two-inch-long grasshopper can jump a horizontal distance of 40 inches. An athlete, who is five feet nine, wants to cover a distance of one mile by jumping. If this person could jump at the same ratio of body-length to jump-length as the grasshopper, determine, to the nearest jump, how many jumps it would take this athlete to jump one mile.

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 the speed of the plane, at cruising altitude, in miles per minute.

Write an equation to represent the number of miles the plane has flown, y, during x minutes at cruising altitude, only. Assuming that the plane maintains its speed at cruising altitude, determine the total number of miles the plane has flown 2 hours into the flight.

Determine the total hours it will take them to reach their destination.

Calculate to the nearest tenth of an hour how much time the family will save if her dad drives the remainder of the trip.

Write equations to model the distances Aidan and Ella traveled. Graph these equations. How many seconds does it take Aidan to catch up to Ella? Justify your answer.

Determine the average rate of change between hour 2 and hour 7, including units.

Calculate the average rate of change from 3 to 9 seconds, in feet per second.

Which interval, 1 a.m. to 12 noon or 6 a.m. to 3 p.m., has the greater rate of snowfall, in inches per hour? Justify your answer.

The graph below shows the variation in the average temperature of Earth's surface from 1950-2000, according to one source. During which years did the temperature variation change the most per unit time? Explain how you determined your answer.

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.

A population of rabbits in a lab, p(x), can be modeled by the function p(x) = 20(1.014)^x, where x represents the number of days since the population was first counted. Explain what 20 and 1.014 represent in the context of the problem. Determine, to the nearest tenth, the average rate of change from day 50 to day 100.

Alex is selling tickets to a school play. An adult ticket costs $6.50 and a student ticket costs $4.00. Alex sells x adult tickets and 12 student tickets. Write a function, f(x), to represent how much money Alex collected from selling tickets.

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

The cost of belonging to a gym can be modeled by C(m) = 50m + 79.50, where C(m) is the total cost for m months of membership. State the meaning of the slope and y-intercept of this function with respect to the costs associated with the gym membership.

During a recent snowstorm in Red Hook, NY, Jaime noted that there were 4 inches of snow on the ground at 3:00 p.m., and there were 6 inches of snow on the ground at 7:00 p.m. If she were to graph these data, what does the slope of the line connecting these two points represent in the context of this problem?

The table below shows the height in feet, h(t), of a hot-air balloon and the number of minutes, t, the balloon is in the air:

On the set of axes provided, draw the graph of the equation y = -3/4x + 3. Is the point (3,2) a solution to the equation? Explain your answer based on the graph drawn.

Samantha buys a package of sugar cookies. The nutrition label states that each serving size of 3 cookies contains 160 Calories. Samantha creates the graph below showing the relationship between the number of cookies eaten and the number of Calories consumed. Explain why it is appropriate for Samantha to draw a line through the points on the graph.

On the set of axes below, graph the line whose equation is 2y = -3x - 2. This linear equation contains the point (2, k). State the value of k.

Sue and Kathy were doing their algebra homework. They were asked to write the equation of the line that passes through the points (-3,4) and (6,1). Sue wrote y - 4 = -1/3(x + 3) and Kathy wrote y = -1/3x + 3. Justify why both students are correct.

Solve the quadratic equation 4x^2 - 5 = 75 for the exact values of x.

Solve 5x^2 = 180 algebraically.

Solve 6x^2 - 42 = 0 for the exact values of x.

How many feet did the object fall between one and two seconds after it was dropped? Determine, algebraically, how many seconds it will take for the object to reach the ground.

In the equation x^2 + 10x + 24 = (x + a)(x + b), b is an integer. Find algebraically all possible values of b.

Solve x^2 - 8x - 9 = 0 algebraically. Explain the first step you used to solve the given equation.

Solve 6x^2 + 5x - 6 = 0 algebraically for the exact values of x.

Solve 8m^2 + 20m = 12 for m by factoring.

Solve the equation 4x^2 - 12x = 7 algebraically for x.

Solve the equation for y: (y - 3)^2 = 4y - 12.

Amy solved the equation 2x^2 + 5x - 42 = 0. She stated that the solutions to the equation were 7/2 and -6. Do you agree with Amy's solutions? Explain why or why not.

Write an equation that defines m(x) as a trinomial where m(x) = (3x - 1)(3 - x) + 4x^2 + 19. Solve for x when m(x) = 0.

Janice is asked to solve 0 = 64x^2 + 16x - 3. Use Janice's procedure to solve the equation for x. Explain the method Janice used to solve the quadratic equation.

Solve the equation x^2 - 6x = 15 by completing the square.

Solve the following equation by completing the square: x^2 + 4x = 2.

Use the method of completing the square to determine the exact values of x for the equation x^2 - 8x + 6 = 0.

Determine the exact values of x for x^2 - 8x - 5 = 0 by completing the square.

A student was given the equation x^2 + 6x - 13 = 0 to solve by completing the square. State the value of c that creates a perfect square trinomial. Explain how the value of c is determined.

Solve for x to the nearest tenth: x^2 + x - 5 = 0.

Use the quadratic formula to solve x^2 - 4x + 1 = 0 for x. Round the solutions to the nearest hundredth.

Solve 4w^2 + 12w - 44 = 0 algebraically for w, to the nearest hundredth.

Solve 3x^2 - 5x - 7 = 0 algebraically for all values of x, rounding to the nearest tenth.

Fred's teacher gave the class the quadratic function f(x) = 4x^2 + 16x + 9. a) State two different methods Fred could use to solve the equation f(x) = 0. b) Using one of the methods stated in part a, solve f(x) = 0 for x, to the nearest tenth.

How many real solutions does the equation x^2 - 2x + 5 = 0 have? Justify your answer.

Is the solution to the quadratic equation 0 = 2x^2 + 3x - 10 rational or irrational? Justify your answer.

A school is building a rectangular soccer field that has an area of 6000 square yards. The soccer field must be 40 yards longer than its width. Determine algebraically the dimensions of the soccer field, in yards.

A landscaper is creating a rectangular flower bed such that the width is half of the length. The area of the flower bed is 34 square feet. Write and solve an equation to determine the width of the flower bed, to the nearest tenth of a foot.

A contractor has 48 meters of fencing to use as the perimeter of a rectangular garden. The length of one side of the garden is represented by x, and the area of the garden is 108 square meters. Determine, algebraically, the dimensions of the garden in meters.

The length of a rectangular sign is 6 inches more than half its width. The area of this sign is 432 square inches. Write an equation in one variable that could be used to find the number of inches in the dimensions of this sign. Solve this equation algebraically to determine the dimensions of this sign, in inches.

A rectangular garden measuring 12 meters by 16 meters is to have a walkway installed around it with a width of x meters. Together, the walkway and the garden have an area of 396 square meters. Write an equation that can be used to find x, the width of the walkway. Describe how your equation models the situation. Determine and state the width of the walkway, in meters.

New Clarendon Park is undergoing renovations to its gardens. One garden that was originally a square is being adjusted so that one side is doubled in length, while the other side is decreased by three meters. The new rectangular garden will have an area that is 25% more than the original square garden. Write an equation that could be used to determine the length of a side of the original square garden. Explain how your equation models the situation. Determine the area, in square meters, of the new rectangular garden.

A rectangular picture measures 6 inches by 8 inches. Simon wants to build a wooden frame for the picture so that the framed picture takes up a maximum area of 100 square inches on his wall. The pieces of wood used to build the frame all have the same width. Write an equation or inequality that could be used to determine the maximum width of the pieces of wood for the frame Simon could create. Explain how your equation or inequality models the situation. Solve the equation or inequality to determine the maximum width of the pieces of wood used for the frame to the nearest tenth of an inch.

The expression $-4.9t^2 + 50t + 2$ represents the height, in meters, of a toy rocket $t$ seconds after launch. What is the initial height of the rocket, in meters?

A football player attempts to kick a football over a goal post. The path of the football can be modeled by the function h(x) = -1/225x^2 + 2/3x, where x is the horizontal distance from the kick, and h(x) is the height of the football above the ground, both measured in feet. On a set of axes, graph the function y = h(x) over the interval 0 ≤ x ≤ 150.

Determine the vertex of the function y = h(x).

Interpret the meaning of this vertex in the context of the problem.

The goal post is 10 feet high and 45 yards away from the kick. Will the ball be high enough to pass over the goal post? Justify your answer.

Rhonda deposited $3000 in an account at Merrick National Bank, earning 4.2% interest, compounded annually, with no additional deposits or withdrawals. Write an equation to find B, her account balance after t years.

Write an exponential equation for the graph shown below. Explain how you determined the equation.

Mike wants to find another point on the graph of an exponential function. Is he correct in stating (5, 28.6) is a point on the function? Explain your reasoning.

The breakdown of a sample of a chemical compound is represented by $ p(t) = 300(0.5)^t $. Explain what 0.5 and 300 represent.

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 of change each year? Explain how you arrived at your answer.

The value, v(t), of a car depreciates according to the function v(t) = P(0.85)^t, where P is the purchase price of the car and t is the time, in years, since the car was purchased. State the percent that the value of the car decreases by each year. Justify your answer.

Graph the function f(x) = 2x - 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.

If C = G - 3F, find the trinomial that represents C when F = 2x^2 + 6x - 5 and G = 3x^2 + 4.

Factor completely: 3y^2 - 12y - 288.

Factor completely: 4x^3 - 49x

Factor the expression x^4 - 36x^2 completely.