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Jmap Standard NYS ALGEBRA 1

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Last updated about 1 year ago
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Question 1
1.

The formula for the surface area of a right rectangular prism is A = 2lw + 2hw + 2lh, where l, w, and h represent the length, width, and height, respectively. Which term of this formula is not dependent on the height?

Question 2
2.

To watch a varsity basketball game, spectators must buy a ticket at the door. The cost of an adult ticket is $3.00 and the cost of a student ticket is $1.50. If the number of adult tickets sold is represented by a and student tickets sold by s, which expression represents the amount of money collected at the door from the ticket sales?

Question 3
3.

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?

Question 4
4.

Bryan's hockey team is purchasing jerseys. The company charges $250 for a one-time setup fee and $23 for each printed jersey. Which expression represents the total cost of x number of jerseys for the team?

Question 5
5.

Konnor wants to burn 250 Calories while exercising for 45 minutes at the gym. On the treadmill, he can burn 6 Cal/min. On the stationary bike, he can burn 5 Cal/min. If t represents the number of minutes on the treadmill and b represents the number of minutes on the stationary bike, which expression represents the number of Calories that Konnor can burn on the stationary bike?

Question 6
6.

What is the constant term of the polynomial 4d + 6 + 3d^2?

Question 7
7.

When 3x^2 + 7x - 6 + 2x^3 is written in standard form, the leading coefficient is

Question 8
8.

An expression of the fifth degree is written with a leading coefficient of seven and a constant of six. Which expression is correctly written for these conditions?

Question 9
9.

When (x)(x - 5)(2x + 3) is expressed as a polynomial in standard form, which statement about the resulting polynomial is true?

Question 10
10.

Which polynomial has a leading coefficient of 4 and a degree of 3?

Question 11
11.

Students were asked to write an expression which had a leading coefficient of 3 and a constant term of -4. Which response is correct?

Question 12
12.

An example of a sixth-degree polynomial with a leading coefficient of seven and a constant term of four is:

Question 13
13.

Mrs. Allard asked her students to identify which of the polynomials below are in standard form and explain why. Which student's response is correct?

Question 14
14.

Students were asked to write 6x^5 + 8x - 3x^3 + 7x^7 in standard form. Shown below are four student responses. Which student is correct?

Question 15
15.

Which student’s response is correct?

Question 16
16.

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

Question 17
17.

The property Kate used when solving p^2 + 5 = 8p - 7 is:

Question 18
18.

Which property justifies Emily's first step?

Question 19
19.

Which property justifies Jennifer's first step?

Question 20
20.

Which property justifies Evan's step?

Question 21
21.

Which two properties did Britney use to get to step 1?

Question 22
22.

In the process of solving the equation 10x^2 - 12x - 16x = 6, George wrote 2(5x^2 - 14x) = 2(3), followed by 5x^2 - 14x = 3. Which properties justify George's process?

Question 23
23.

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.

Question 24
24.

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 [____________________]

Question 25
25.

Which value of x satisfies the equation (7/3)x + (9/28) = 20?

Question 26
26.

What is the value of x in the equation (x - 2)/3 + 1/6 = 5/6?

Question 27
27.

An equation is given below: 4(x - 7) = 0.3(x + 2) + 2.11. The solution to the equation is:

Question 28
28.

Which value of x satisfies the equation (5/6) * (3/8) - x = 16?

Question 29
29.

The value of x which makes (2x/3 - 1/4) = (1/5)x - 4/3 true is:

Question 30
30.

The solution to -2(1 - 4x) = 3x + 8 is:

Question 31
31.

What is the solution to the equation (3/5)x + 4/3 = 1.04?

Question 32
32.

The value of x that satisfies the equation 4/3 = x + 10/15 is:

Question 33
33.

Which value of x makes (x - 3/4 + 2/3) = 17/12 true?

Question 34
34.

The solution to 3(x - 8) + 4x = 8x + 4 is:

Question 35
35.

Which of the equations below have the same solution?

Question 36
36.

What is the solution to 2 + 3(2a + 1) = 3(a + 2)?

Question 37
37.

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

Question 38
38.

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

Question 39
39.

A parking garage charges a base rate of $3.50 up to 2 hours, and an hourly rate for each additional hour. The sign below gives the prices for up to 5 hours of parking: 2 hours - $3.50, 3 hours - $9.00, 4 hours - $14.50, 5 hours - $20.00. Which linear equation can be used to find x, the additional hourly parking rate?

Question 40
40.

John has four more nickels than dimes in his pocket, for a total of $1.25. Which equation could be used to determine the number of dimes, x, in his pocket?

Question 41
41.

Kendal bought x boxes of cookies to bring to a party. Each box contains 12 cookies. She decides to keep two boxes for herself. She brings 60 cookies to the party. Which equation can be used to find the number of boxes, x, Kendal bought?

Question 42
42.

Nicci's sister is 7 years less than twice Nicci's age, a. The sum of Nicci's age and her sister's age is 41. Which equation represents this relationship?

Question 43
43.

Joe has dimes and nickels in his piggy bank totaling $1.45. The number of nickels he has is 5 more than twice the number of dimes, d. Which equation could be used to find the number of dimes he has?

Question 44
44.

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.

Question 45
45.

The amount of energy, Q, in joules, needed to raise the temperature of m grams of a substance is given by the formula Q = mC(T_f - T_i), where C is the specific heat capacity of the substance. If its initial temperature is T_i, an equation to find its final temperature, T_f, is:

Question 46
46.

The formula for blood flow rate is given by F = (p1 - p2)/r, where F is the flow rate, p1 is the initial pressure, p2 is the final pressure, and r is the resistance created by blood vessel size. Which formula cannot be derived from the given formula?

Question 47
47.

Students were asked to write a formula for the length of a rectangle by using the formula for its perimeter, p = 2l + 2w. Three of their responses are shown below. Which responses are correct?

Question 48
48.

The formula for the volume of a cone is V = (1/3)Ï€r^2h. The radius, r, of the cone may be expressed as:

Question 49
49.

The equation for the volume of a cylinder is V = πr^2h. The positive value of r, in terms of h and V, is:

Question 50
50.

The distance a free falling object has traveled can be modeled by the equation d = 1/2at^2, where a is acceleration due to gravity and t is the amount of time the object has fallen. What is t in terms of a and d?

Question 51
51.

The formula for electrical power, P, is P = I^2R, where I is current and R is resistance. The formula for I in terms of P and R is:

Question 52
52.

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.

Question 53
53.

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.

Question 54
54.

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.

Question 55
55.

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

Question 56
56.

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.

Question 57
57.

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

Question 58
58.

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.

Question 59
59.

Bamboo plants can grow 91 centimeters per day. What is the approximate growth of the plant in inches per hour?

Question 60
60.

Sarah travels on her bicycle at a speed of 22.7 miles per hour. What is Sarah's approximate speed in kilometers per minute?

Question 61
61.

The Utica Boilermaker is a 15-kilometer road race. Sara is signed up to run this race and has done the following training runs: I. 10 miles II. 44,880 feet III. 15,560 yards. Which run(s) are at least 15 kilometers?

Question 62
62.

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.

Question 63
63.

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.

Question 64
64.

Patricia is trying to compare the average rainfall of New York to that of Arizona. A comparison between these two states for the months of July through September would be best measured in:

Question 65
65.

The owner of a landscaping business wants to know how much time, on average, his workers spend mowing one lawn. Which is the most appropriate rate with which to calculate an answer to his question?

Question 66
66.

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.

Question 67
67.

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.

Question 68
68.

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

Question 69
69.

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.

Question 70
70.

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

Question 71
71.

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

Question 72
72.

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.

Question 73
73.

During which time interval did the cost increase at the greatest average rate?

Question 74
74.

The table below shows the year and the number of households in a building that had high-speed broadband internet access. Number of Households: 11, 16, 23, 33, 42, 47 Year: 2002, 2003, 2004, 2005, 2006, 2007 For which interval of time was the average rate of change the smallest?

Question 75
75.

The table below shows the average diameter of a pupil in a person’s eye as he or she grows older. Age (years): 20, 30, 40, 50, 60, 70, 80 Average Pupil Diameter (mm): 4.7, 4.3, 3.9, 3.5, 3.1, 2.7, 2.3 What is the average rate of change, in millimeters per year, of a person’s pupil diameter from age 20 to age 80?

Question 76
76.

Joey enlarged a 3-inch by 5-inch photograph on a copy machine. He enlarged it four times. The table below shows the area of the photograph after each enlargement. Enlargement: 0, 1, 2, 3, 4 Area (square inches): 15, 18.8, 23.4, 29.3, 36.6 What is the average rate of change of the area from the original photograph to the fourth enlargement, to the nearest tenth?

Question 77
77.

Which statement does not correctly interpret voting rates by age based on the given graph?

Question 78
78.

During which time interval did the temperature in the kiln show the greatest average rate of change?

Question 79
79.

Which statement about average resting heart rates is *not* supported by the graph?

Question 80
80.

Over which interval does the helicopter have the *slowest* average rate of change?

Question 81
81.

What is the average speed, in meters per second, of the rock between 5 and 10 seconds after it was dropped?

Question 82
82.

The average rate of change for Tony's investment was $19 per:

Question 83
83.

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

Question 84
84.

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

Question 85
85.

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.

Question 86
86.

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.

Question 87
87.

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.

Question 88
88.

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.

Question 89
89.

In 2013, the United States Postal Service charged $0.46 to mail a letter weighing up to 1 oz. and $0.20 per ounce for each additional ounce. Which function would determine the cost, in dollars, c(z), of mailing a letter weighing z ounces where z is an integer greater than 1?

Question 90
90.

Last weekend, Emma sold lemonade at a yard sale. The function P(c) = 0.50c - 9.96 represented the profit, P(c), Emma earned selling c cups of lemonade. Sales were strong, so she raised the price for this weekend by 25 cents per cup. Which function represents her profit for this weekend?

Question 91
91.

A high school club is researching a tour package offered by the Island Kayak Company. The company charges $35 per person and $245 for the tour guide. Which function represents the total cost, C(x), of this kayak tour package for x club members?

Question 92
92.

At Benny's Cafe, a mixed-greens salad costs $5.75. Additional toppings can be added for $0.75 each. Which function could be used to determine the cost, c(s), in dollars, of a salad with s additional toppings?

Question 93
93.

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.

Question 94
94.

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.

Question 95
95.

Jim is a furniture salesman. His weekly pay is $300 plus 3.5% of his total sales for the week. Jim sells x dollars' worth of furniture during the week. Write a function, p(x), which can be used to determine his pay for the week. Use this function to determine Jim's pay to the nearest cent for a week when his sales total is $8250.

Question 96
96.

The cost of airing a commercial on television is modeled by the function C(n) = 110n + 900, where n is the number of times the commercial is aired. Based on this model, which statement is true?

Question 97
97.

A satellite television company charges a one-time installation fee and a monthly service charge. The total cost is modeled by the function y = 40 + 90x. Which statement represents the meaning of each part of the function?

Question 98
98.

Each day, a local dog shelter spends an average of $2.40 on food per dog. The manager estimates the shelter's daily expenses, assuming there is at least one dog in the shelter, using the function E(x) = 30 + 2.40x. Which statements regarding the function E(x) are correct?

Question 99
99.

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.

Question 100
100.

A student plotted the data from a sleep study and used the equation y = -0.09x + 9.24 to model the data. What does the rate of change represent in terms of these data?

Question 101
101.

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?

Question 102
102.

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:

Question 103
103.

Which function has the same y-intercept as the given graph?

Question 104
104.

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.

Question 105
105.

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.

Question 106
106.

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.

Question 107
107.

How many of the equations listed below represent the line passing through the points (2,3) and (4,-7)?

Question 108
108.

The graph of a linear equation contains the points (3,11) and (-2,1). Which point also lies on the graph?

Question 109
109.

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.

Question 110
110.

The inequality 7 - 2/3x < x - 8 is equivalent to:

Question 111
111.

When 3x + 2 <= 5(x - 4) is solved for x, the solution is:

Question 112
112.

Which value of x is a solution to the equation 13 - 36x^2 = -12?

Question 113
113.

The solution of the equation (x + 3)^2 = 7 is:

Question 114
114.

The solutions to (x + 4)^2 - 2 = 7 are:

Question 115
115.

What are the solutions to the equation 3(x - 4)^2 = 27?

Question 116
116.

What is the solution of the equation 2(x + 2)^2 - 4 = 28?

Question 117
117.

A correct next step in the solution of the problem is:

Question 118
118.

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

Question 119
119.

Solve 5x^2 = 180 algebraically.

Question 120
120.

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

Question 121
121.

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.

Question 122
122.

What is the solution set of the equation (x - 2)(x - a) = 0?

Question 123
123.

Which equation has the same solutions as 2x^2 + x - 3 = 0?

Question 124
124.

What are the solutions to the equation 3x^2 + 10x = 8?

Question 125
125.

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

Question 126
126.

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

Question 127
127.

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

Question 128
128.

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

Question 129
129.

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

Question 130
130.

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

Question 131
131.

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.

Question 132
132.

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.

Question 133
133.

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.

Question 134
134.

The quadratic equation x^2 - 6x = 12 is rewritten in the form (x + p)^2 = q, where q is a constant. What is the value of p?

Question 135
135.

Which equation has the same solution as x^2 - 6x - 12 = 0?

Question 136
136.

Which equation has the same solutions as x^2 + 6x - 7 = 0?

Question 137
137.

When solving the equation x^2 - 8x - 7 = 0 by completing the square, which equation is a step in the process?

Question 138
138.

The method of completing the square was used to solve the equation 2x^2 - 12x + 6 = 0. Which equation is a correct step when using this method?

Question 139
139.

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

Question 140
140.

When solving x^2 - 10x - 13 = 0 by completing the square, which equation is a step in the process?

Question 141
141.

When using the method of completing the square, which equation is equivalent to x^2 - 12x - 10 = 0?

Question 142
142.

What are the roots of the equation x^2 + 4x - 16 = 0?

Question 143
143.

What are the solutions to the equation x^2 - 8x = 24?

Question 144
144.

What are the solutions to the equation x^2 - 8x = 10?

Question 145
145.

When directed to solve a quadratic equation by completing the square, Sam arrived at the equation (x - 5/2)^2 = 13/4. Which equation could have been the original equation given to Sam?

Question 146
146.

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

Question 147
147.

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

Question 148
148.

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

Question 149
149.

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

Question 150
150.

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.

Question 151
151.

If the quadratic formula is used to find the roots of the equation x^2 - 6x - 19 = 0, the correct roots are:

Question 152
152.

The roots of x^2 - 5x - 4 = 0 are:

Question 153
153.

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

Question 154
154.

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

Question 155
155.

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

Question 156
156.

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

Question 157
157.

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.

Question 158
158.

How many real-number solutions does the equation 4x^2 + 2x + 5 = 0 have?

Question 159
159.

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

Question 160
160.

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

Question 161
161.

Sam and Jeremy have ages that are consecutive odd integers. The product of their ages is 783. Which equation could be used to find Jeremy’s age, j, if he is the younger man?

Question 162
162.

Abigail's and Gina's ages are consecutive integers. Abigail is younger than Gina and Gina's age is represented by x. If the difference of the square of Gina's age and eight times Abigail's age is 17, which equation could be used to find Gina's age?

Question 163
163.

The length of the shortest side of a right triangle is 8 inches. The lengths of the other two sides are represented by consecutive odd integers. Which equation could be used to find the lengths of the other sides of the triangle?

Question 164
164.

Joe has a rectangular patio that measures 10 feet by 12 feet. He wants to increase the area by 50% and plans to increase each dimension by equal lengths, x. Which equation could be used to determine x?

Question 165
165.

The length of a rectangular patio is 7 feet more than its width, w. The area of the patio, A(w), can be represented by the function:

Question 166
166.

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.

Question 167
167.

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.

Question 168
168.

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.

Question 169
169.

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.

Question 170
170.

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.

Question 171
171.

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.

Question 172
172.

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.

Question 173
173.

In the function f(x) = (x - 2)^2 + 4, the minimum value occurs when x is:

Question 174
174.

If Lylah completes the square for f(x) = x^2 - 12x + 7 in order to find the minimum, she must write f(x) in the general form f(x) = (x - a)^2 + b. What is the value of a for f(x)?

Question 175
175.

Which equation is equivalent to y = x^2 + 24x - 18?

Question 176
176.

Which equation and ordered pair represent the correct vertex form and vertex for j(x) = x^2 - 12x + 7?

Question 177
177.

Which equation is equivalent to y - 34 = x(x - 12)?

Question 178
178.

The function f(x) = 3x^2 + 12x + 11 can be written in vertex form as

Question 179
179.

An equation that represents the function could be

Question 180
180.

Based on the provided data, which statement is not a valid conclusion about the rocket's flight?

Question 181
181.

For which interval is the ball's height always decreasing on the given graph?

Question 182
182.

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?

Question 183
183.

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. What does the number 5 in the function represent?

Question 184
184.

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.

Question 185
185.

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

Question 186
186.

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

Question 187
187.

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.

Question 188
188.

A laboratory technician used the function t(m) = 2(3)^{2m + 1} to model her research. Consider the following expressions: - I. 6(3)^{2m} - II. 6(6)^{2m} - III. 6(9)^m The function t(m) is equivalent to which of the following?

Question 189
189.

The growth of a certain organism can be modeled by C(t) = 10(1.029)^{24t}, where C(t) is the total number of cells after t hours. Which function is approximately equivalent to C(t)?

Question 190
190.

A computer application generates a sequence of musical notes using the function f(n) = 6(16)^n, where n is the number of the note in the sequence and f(n) is the note frequency in hertz. Which function will generate the same note sequence as f(n)?

Question 191
191.

The number of bacteria grown in a lab can be modeled by P(t) = 300 * 2^{4t}, where t is the number of hours. Which expression is equivalent to P(t)?

Question 192
192.

Mario's $15,000 car depreciates in value at a rate of 19% per year. The value, V, after t years can be modeled by the function V = 15,000(0.81)^t. Which function is equivalent to the original function?

Question 193
193.

Nora inherited a savings account that was started by her grandmother 25 years ago. This scenario is modeled by the function A(t) = 5000(1.013)^t + 25, where A(t) represents the value of the account, in dollars, t years after the inheritance. Which function below is equivalent to A(t)?

Question 194
194.

The population of a city can be modeled by P(t) = 3810(1.0005)^{7t}, where P(t) is the population after t years. Which function is approximately equivalent to P(t)?

Question 195
195.

Krystal was given $3000 when she turned 2 years old. Her parents invested it at a 2% interest rate compounded annually, with no deposits or withdrawals made. Which expression can be used to determine how much money Krystal had in the account when she turned 18?

Question 196
196.

The country of Benin in West Africa has a population of 9.05 million people, growing at a rate of 3.1% each year. Which function can be used to find the population 7 years from now?

Question 197
197.

Anne invested $1000 in an account with a 1.3% annual interest rate, with no deposits or withdrawals for 2 years. If interest was compounded annually, which equation represents the balance in the account after 2 years?

Question 198
198.

A high school sponsored a badminton tournament. After each round, half of the players were eliminated. If there were 64 players at the start, which equation models the number of players left after 3 rounds?

Question 199
199.

Emily was given $600 for her high school graduation and invested it in an account that earns 2.4% interest per year, with no deposits or withdrawals made. Which expression can be used to determine the amount of money in the account after 4 years?

Question 200
200.

Sunny purchases a new car for $29,873. The car depreciates 20% annually. Which expression can be used to determine the value of the car after t years?

Question 201
201.

A student invests $500 for 3 years in a savings account earning 4% interest per year, with no further deposits or withdrawals. Which statement does not yield the correct balance at the end of 3 years?

Question 202
202.

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.

Question 203
203.

The table shows the temperature T(m) of a cup of hot chocolate chilling over several minutes m:

Question 204
204.

Jill invests $400 in a savings bond. The table shows the value V(x) of the bond, in hundreds of dollars, after x years:

Question 205
205.

Marc bought a new laptop for $1250 and tracked its value over the next three years. Which function can be used to determine the value of the laptop for *x* years after the purchase?

Question 206
206.

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

Question 207
207.

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.

Question 208
208.

The equation y = 5000(0.98)^x represents the value y of a savings account that was left inactive for a period of *x* years. What is the y-intercept of this equation, and what does it represent?

Question 209
209.

The function V(t) = 1350(1.017)^t represents the value V(t), in dollars, of a comic book *t* years after its purchase. What is the yearly rate of appreciation of the comic book?

Question 210
210.

In the equation \( A = 1300(1.02)^7 \), what does 1.02 represent?

Question 211
211.

Milton has his money invested in a stock portfolio. The value, \( v(x) = 30,000(0.78)^x \), where \( x \) is the number of years since he made his investment. Which statement describes the rate of change of the value of his portfolio?

Question 212
212.

A population of bacteria can be modeled by the function \( f(t) = 1000(0.98)^t \), where \( t \) represents the time since the population started decaying, and \( f(t) \) represents the population at time \( t \). What is the rate of decay for this population?

Question 213
213.

The equation \( V(t) = 12,000(0.75)^t \) represents the value of a motorcycle \( t \) years after it was purchased. Which statement is true?

Question 214
214.

The 2014 winner of the Boston Marathon runs as many as 120 miles per week. During the last few weeks of his training, his mileage can be modeled by \( M(w) = 120(0.90)^w - 1 \). Which statement is true about the model \( M(w) \)?

Question 215
215.

In the equation \( A = P(1 \pm r)^t \), \( A \) is the total amount, \( P \) is the principal, \( r \) is the interest rate, and \( t \) is the time in years. Which statement correctly relates to the interest rate for each given equation?

Question 216
216.

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.

Question 217
217.

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.

Question 218
218.

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.

Question 219
219.

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.

Question 220
220.

If point (K, -5) lies on the line whose equation is 3x + y = 7, then the value of K is:

Question 221
221.

The point (3, w) is on the graph of y = 2x + 7. What is the value of w?

Question 222
222.

Which ordered pair does not fall on the line formed by the other three?

Question 223
223.

Which point is not on the graph represented by y = x^2 + 3x - 6?

Question 224
224.

Which ordered pair below is not a solution to f(x) = x^2 - 3x + 4?

Question 225
225.

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

Question 226
226.

Which expression is equivalent to (x + 4)^2 (x + 4)^3?

Question 227
227.

The expression 1/3 x(6x^2 - 3x + 9) is equivalent to:

Question 228
228.

When written in standard form, the product of (3 + x) and (2x - 5) is:

Question 229
229.

The expression (m - 3)^2 is equivalent to:

Question 230
230.

Which trinomial is equivalent to 3(x - 2)^2 - 2(x - 1)?

Question 231
231.

When (2x - 3)^2 is subtracted from 5x^2, the result is:

Question 232
232.

Which expression is not equivalent to -4x^3 + x^2 - 6x + 8?

Question 233
233.

What is the product of 2x + 3 and 4x^2 - 5x + 6?

Question 234
234.

Fred is given a rectangular piece of paper. If the length of Fred's piece of paper is represented by 2x - 6 and the width is represented by 3x - 5, then the paper has a total area represented by:

Question 235
235.

When written in factored form, 4w^2 - 11w - 3 is equivalent to:

Question 236
236.

Which product is equivalent to 4x^2 - 3x - 27?

Question 237
237.

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?

Question 238
238.

The expression 4x^2 - 4x - 120 is equivalent to:

Question 239
239.

Which expression is equivalent to x^4 - 12x^2 + 36?

Question 240
240.

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

Question 241
241.

Which expression is equivalent to 36x^2 - 100?

Question 242
242.

Which expression is equivalent to 16x^2 - 36?

Question 243
243.

The expression 49x^2 - 36 is equivalent to:

Question 244
244.

The expression 4x^2 - 25 is equivalent to:

Question 245
245.

The expression 16x^2 - 81 is equivalent to:

Question 246
246.

The expression 36x^2 - 9 is equivalent to:

Question 247
247.

Which expression is equivalent to 18x^2 - 50?

Question 248
248.

Which expression is equivalent to y^4 - 100?

Question 249
249.

When factored completely, the expression p^4 - 81 is equivalent to:

Question 250
250.

The expression x^4 - 16 is equivalent to:

Question 251
251.

The expression w^4 - 36 is equivalent to:

Question 252
252.

Which expression is equivalent to 16x^4 - 64?

Question 253
253.

If the area of a rectangle is expressed as x^4 - 9y^2, then the product of the length and the width of the rectangle could be expressed as:

Question 254
254.

Factor completely: 4x^3 - 49x

Question 255
255.

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

Question 256
256.

Factor x^4 - 16 completely.

Question 257
257.

Factor the expression x^4 + 6x^2 - 7 completely.

Question 258
258.

The graphs below represent functions defined by polynomials. For which function are the zeros of the polynomials 2 and -3?

Question 259
259.

The graphs below represent four polynomial functions. Which of these functions has zeros of 2 and -3?

Question 260
260.

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

Question 261
261.

Which function has zeros of -4 and 2?

Question 262
262.

Keith determines the zeros of the function $ f(x) $ to be -6 and 5. What could be Keith's function?

Question 263
263.

Which polynomial function has zeros at -3, 0, and 4?

Question 264
264.

A cubic function is graphed on the set of axes below. Which function could represent this graph?

Question 265
265.

A polynomial function is graphed below. Which function could represent this graph?

Question 266
266.

Compared to the graph of f(x) = x^2, the graph of g(x) = (x - 2)^2 + 3 is the result of translating f(x):

Question 267
267.

How does the graph of f(x) = 3(x - 2)^2 + 1 compare to the graph of g(x) = x^2?

Question 268
268.

If the parent function of f(x) is p(x) = x^2, then the graph of the function f(x) = (x - k)^2 + 5, where k > 0, would be a shift of:

Question 269
269.

Caitlin graphs the function f(x) = ax^2, where a is a positive integer. If Caitlin multiplies a by -2, when compared to f(x), the new graph will become:

Question 270
270.

What would be the order of these quadratic functions when they are arranged from the narrowest graph to the widest graph?

Question 271
271.

If the original function f(x) = 2x^2 - 1 is shifted to the left 3 units to make the function g(x), which expression would represent g(x)?

Question 272
272.

Given: f(x) = (x - 2)^2 + 4, g(x) = (x - 5)^2 + 4, When compared to the graph of f(x), the graph of g(x) is:

Question 273
273.

Josh graphed the function f(x) = -3(x - 1)^2 + 2. He then graphed the function g(x) = -3(x - 1)^2 - 5 on the same coordinate plane. The vertex of g(x) is:

Question 274
274.

If x = 2, y = sqrt(2), and w = sqrt(8), which expression results in a rational number?

Question 275
275.

Given the following expressions, which expression(s) result in an irrational number?

Question 276
276.

Given: L = 2, M = 3^(3/2), N =16, P = 9, which expression results in a rational number?

Question 277
277.

Is the product of two irrational numbers always irrational? Justify your answer.

Question 278
278.

Ms. Fox asked her class, 'Is the sum of 4.2 and sqrt(2) rational or irrational?' Patrick answered that the sum would be irrational. State whether Patrick is correct or incorrect. Justify your reasoning.

Question 279
279.

Determine if the product of sqrt(3) and sqrt(8) is rational or irrational. Explain your answer.

Question 280
280.

Is the sum of sqrt(3) and sqrt(4) rational or irrational? Explain your answer.

Question 281
281.

Jakob is working on his math homework. He decides that the sum of the expression (1/3) + (6/5)sqrt(7) must be rational because it is a fraction. Is Jakob correct? Explain your reasoning.

Question 282
282.

State whether 7 - sqrt(2) is rational or irrational. Explain your answer.

Question 283
283.

Is the product of 16 and sqrt(4) rational or irrational? Explain your reasoning.

Question 284
284.

State whether the product of 3 and 9 is rational or irrational. Explain your answer.

Question 285
285.

Is the product of 1024 and -3.4 rational or irrational? Explain your reasoning.

Question 286
286.

Is the product of 8 and sqrt(98) rational or irrational? Justify your answer.