A.CED.4 [576489]StudentClassDate

Read the following and answer the questions below:

Wendy's Novel

Wendy's NovelWendy wrote her first novel. Patrick, a publisher, helped her edit and publish the book through online retailers.

Patrick developed equations designed to model the revenue that he would receive from the sales of the novel and the costs that he would incur. The publisher’s share of the revenue, R dollars, is modeled by the equation

where n is the number of novels sold. The cost for Patrick to print the novel and release it to the market, C dollars, is modeled by the equation

Patrick gave Wendy two payment options for her novel. If she chose Option 1, she would receive a $1,000 payment immediately, and then she would earn $0.65 for each book sold. If she chose Option 2, she would receive no initial payment, but she would earn $1.05 for each book sold.

When Wendy’s book was released, the sales of the novel started off moderate, increased at a steady rate for the first week, and then decreased at a steady rate. The daily sales of Wendy’s novel, s, are modeled by the equation where x is the number of days since the book was released. For the first 21 days after the novel was released, Patrick’s model was accurate to within 3% of the book’s actual sales.

1. Read "Wendy's Novel" and answer the question.In the passage Wendy's Novel, the cost for Patrick to print the novel is modeled by the equation below:

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where C is the total cost for n number of novels sold. Which equation could Patrick use to determine how many novels have been printed, based on his cost?

A.

B.

C.

D.

2.What is the equation when it is solved for x?

A.

B.

C.

D.

3. Grace uses the equation y = 25x + 20 to calculate the dollar amount, y,

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she earns from renting out a lawnmower x times. She wants to solve for x in order to find the number of times she needs to rent a lawnmower to earn a given amount. Which equation should she use?

A.

B.

C.

D.

4. The perimeter of a rectangle can be found using the formula P = 2L + 2W, where L is the length and W is the width. Which formula represents the length of a rectangle in the terms of the perimeter and width?

A.

B.

C.

D.

5. The kinetic energy, E, of an object having mass m and moving with

velocity v is given by the formula Which expression can be used

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to find the velocity?

A.

B.

C.

D.

6.The equation  gives the distance, d, traveled by an object with an initial velocity, v, and acceleration, a, after time t. What is the formula written in terms of the acceleration?

7. Newton's Second Law, describes the relationship between an object's mass, a force acting on it, and the resulting acceleration, where:               F is force, in Newtons              m is mass, in kilograms              a is acceleration, in meters per second squaredA young boy and his tricycle have a combined mass of 30 kilograms. If the boy's sister gives him a push with a force of 60 Newtons, what is his acceleration?

A. meter per second squared

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B. 2 meters per second squared

C. 30 meters per second squared

D. 90 meters per second squared

8.Which equation, when solved for x, is equivalent to ?

A. x = mp – 2

B. x = mp – 2p

C. x = mp + 10p

D. x = mp + 10

9.The formula that describes an object’s motion is given by  where S is the distance traveled, u is the initial velocity, a is the acceleration, and t is the time. Which equation represents a in terms of the other variables?

A.

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B.

C.

D.

10. What is the value of x in the equation rx + 7 = pq – 10?

A.

B.

C.

D.

11. Which choice is equivalent to the equation  ?

A.

B.

C.

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D.

12. Solve the equation for the variable y?

A.

B.

C.

D.

13. According to Graham’s law, the rate of diffusion of two gases is inversely

proportional to density and is given by where and are rates of diffusion of two gases and  are their respective densities. Which equation represents in terms of the other variables?

A.

B.

C.

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D.

14. For a cone with volume V and height h, which expression provides the radius of the base r ?

A.

B.

C.

D.

15.The radius of a black hole can be calculated using the equation where G represents the gravity constant, M represents mass of the black hole, and c represents the speed of light. Which equation can be used to find the value of  gravity?

A.

B.

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C.

D.

16. Which equation is equivalent to x = m(p – q)?

A.

B.

C.

D.

17. What is

A. 3

B. 4

C. 8

D. 35

18. Consider the following equation:

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Which choice correctly expresses the quantity t1in terms of the other quantities?

A.

B., where Q ≠ 0

C.

D., where r ≠ 0

19.When solved for b, which equation is equivalent to  ?

A.

B.

C.

D.

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20.The volume for a cone is given by the equation Which equation represents this formula in terms of r?

A.

B.

C.

D.

21. The volume of a rectangular prism can be found using the formula V = Bh, where B is the area of the base and h is the height. Which formula can be used to find the height, h, of the prism?

A.

B.

C.

D.

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22.Which equation is equivalent to  ?

A.

B.

C.

D.

23.To determine the amount of money in a savings account, we can use the formula:

where:

the amount after t time periodsthe initial amount, sometimes referred to as the principalthe rate of growth or decaythe number of time periods

Sandy receives a $5,000 bonus for being Employee of the Year. She decides to invest this bonus in a savings account. There are two savings accounts to choose from.

Savings account 1 has an annual interest rate of 5.1%, and provides a

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free calendar.Savings account 2 has an annual interest rate of 7.2%.

Part A.  If Sandy makes no additional deposits or withdrawals, how much money would each savings account contain after 3 years?

Part B.  Rearrange the formula given at the start of the task to solve for t.

Part C.  To the nearest tenth of a year, how many years would it take for each savings account to contain at least $7,000?

Part D.  Rearrange the formula given at the start of the task to solve for r.

Part E.  Sandy decides that at the end of 10 years she wants her savings account to contain at least $9,000. To the nearest tenth of a percent, what interest rate would meet this stipulation?

Part F.  Do either of Sandy’s choices provide her with at least $9,000 at the end of 10 years? If so, which choice would provide her with at least $9,000? Explain your reasoning.

24.The formula for the area of a trapezoid is , where h is the height of the trapezoid, and b1 and b2 are the base lengths of the trapezoid. Which formula can be used to find the length of b1?

A.

B.

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C.

D.

25.Which equation is equivalent to ?

A.

B.

C.

D.

26. The formula to convert degrees Fahrenheit to degrees Celsius is

. Which formula can be used to convert degrees Celsius to degrees Fahrenheit?

A.

B.

C.

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D.

27.The volume of a spherical tank is given by If the volume of the tank is known, which expression can be used to find its radius?

A.

B.

C.

D.

28.Which equation is equivalent to  , when solved for m?

A.

B.

C.

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D.

29.The kinetic energy, E, of a falling ball is given as where m is the mass and v is the velocity of the ball. Which of these equations can be used to find the velocity of the ball?

A.

B.

C.

D.

30. The formula for finding the surface area of a right circular cylinder is  where S represents the surface area, r represents the radius, and h represents the height of the cylinder. Which equation can be used to find the height of a right circular cylinder in terms of its surface area and radius?

A.

B.

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C.

D.

31. Nicki used the equation v = at + v0, where v is velocity at time t, a is acceleration, and v0 is velocity at time 0. Given the equation, which could be used to find the acceleration of an object?

A.

B.

C.

D.

32.Which equation is equivalent to  when solving for T?

A.

B.

C.

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D.

33. Which equation is equivalent to , when solved for x?

A.

B.

C.

D.

34. Jeanette read that the highest daytime temperature recorded in her city in the month of July this year was 36.5 degrees Celsius (C). She wants to convert this temperature to degrees Fahrenheit (F) using the formula shown below.

Part 1. Solve the formula for degrees Fahrenheit.Part 2. Convert the Celsius temperature of 36.5 degrees to degrees Fahrenheit.

35. The formula W = fd can be used to calculate the amount of work it takes to move a force, f, a specific distance, d. Which formula can be used to calculate distance, d?

A.

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B.

C.

D.

36. The formula to find the equivalent resistance, R, of two resistors with

resistances and  is given by Which equation gives in terms of R and

A.

B.

C.

D.

37. Assume that the equation holds true for all values of x and y between and Which expression is equal to y over that domain?

A.

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B.

C.

D.

38.Which equation is equivalent to ?

A.

B.

C.

D.

39. What equation shows solved for B?

A.

B.

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C.

D.

40. The formula for simple interest is I = Prt, where I is interest, P is principal, r is interest rate, and t is time in years. Which equation can be used to calculate principal, P?

A.

B.

C.

D.

41. Consider the following equation:

 

Which choice correctly expresses the quantity a in terms of D, m, and v?

A., where D ≠ mv

B., where 2D ≠ mv

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C., where v ≠ 0

D., where v ≠ 0

42. The final velocity, v, of a marble rolling on a table in a straight line can be calculated using the formula, v = u + at, where u represents the initial velocity, a represents acceleration, and t is the time elapsed. Which formula can be used to calculate the acceleration, a, of the marble?

A.

B.

C.

D.

43.The formula can be used to find the volume of a cone that has base area B and height h. Which formula expresses the height of the cone in terms of volume and base area?

A.

B.

C.

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D.

44. What equation is equivalent to 24 = ax + 4y – 10, when solving for y?

A.

B. 

C.

D.

45. The time period, T, of a simple harmonic motion is calculated by the

formula  where m is the mass attached to the spring and k is the spring constant. Solve the equation for k in terms of m and T.

Use words, numbers, and/or pictures to show your work.

46.The equation  shows the relationship between the temperature in degrees Celsius (C) and the same temperature measured in degrees Fahrenheit (F). Which equation correctly solves the formula for C in terms of F?

A.

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B.

C.

D.

47. The formula represents the total amount of money, A, that is in a savings account including the simple interest earned. Which expression represents the time, t, the money has been in the account?

A.

B.

C.

D.

48. The period of a pendulum T, in seconds, is the time it takes for a pendulum of length L to make a complete swing back and forth and is

given by the formula where g is the acceleration of gravity. What will be the length  of a pendulum that has a period of  seconds?

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A.

B.

C.

D.

49. The electrical resistance of a wire changes with a change in temperature and is given by the relation where a = temperature coefficient of resistance. Which of these equations can be used to find the value of a?

A.

B.

C.

D.

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50. The circumference of a circle is given by the formula  , where d is the diameter of the circle. Which formula represents the radius of the circle, r, in terms of the circumference?

A.

B.

C.

D.

51. The escape velocity, v, with which a body should be projected so that it overcomes the gravitational pull of the Earth is given as where g is the acceleration due to gravity on the Earth and R is the radius of the Earth.

Part A. Find the formula that can be used to calculate the acceleration due to gravity on the Earth, given the escape velocity and the radius of the Earth.

Part B. Find the formula that can be used to calculate the radius of the Earth, given the acceleration due to gravity and the escape velocity.

Use words, numbers, and/or pictures to show your work.

52. Which equation shows w = 2sr solved for s?

A. s = w – 2r

B. s = 2r – w

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C.

D.

53. Which equation is equivalent to tw + 3xy = z?

A.

B., where t ≠ 0

C., where t ≠ 0

D., where t ≠ 0

54. The eccentricity of an ellipse is the measure of how circular the ellipse is.

The ecccentricity e can be represented by the equation where a is the length of the major axis of the ellipse and b is the length of the minor axis. Which equation represents the formula in terms of b?

A.

B.

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C.

D.

55. The front of a tent is an equilateral triangle with the ratio of its base, b, to

its height, h, given by Which equation can be used to find the tent's height?

A.

B.

C.

D.

56. The total surface area of a cylinder is given by the formula where r represents the radius and h represents the height of the cylinder. What equation can be used to find the value of h?

57.Which formula represents the equation , when solved for y?

A.

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B.

C.

D.

58. The lid of a cylindrical oil barrel broke. The barrel has a volume of V cubic inches and a height of h inches. Which equation can be used to find the diameter, d, of the lid required to cover the barrel?

A.

B.

C.

D.

59. Which expression represents the value of x in the equation ?

A.

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B.

C.

D.

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