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Short answer📘 MS-PS2-3🧠 DOK 1

Question:

What factors can affect the strength of electric and magnetic forces?

✅ Answer:
The factors that can affect the strength of electric and magnetic forces include the magnitude of the charges or currents, the distance between the objects, and the medium through which the forces are acting.

💡 Explanation:

  • Electric and magnetic forces can be affected by several factors.
  • The magnitude of the charges or currents involved will influence the strength of the forces; larger charges or currents generally result in stronger forces.
  • The distance between the objects also plays a crucial role; the greater the distance, the weaker the force.
  • Additionally, the medium through which the forces are acting can affect their strength, as some materials can enhance or diminish the forces.

Standard: MS-PS2-3 | DOK: 1

Recent Questions

Multiple choice📘 N.VM.C.12🧠 DOK 1

Question:

If vector **v** = [23] \begin{bmatrix} 2 \\ 3 \end{bmatrix} and matrix **A** = [1001] \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} , what is the resulting vector when **A** multiplies **v**?

Answer Choices:

  • A)

    [23] \begin{bmatrix} 2 \\ 3 \end{bmatrix}

  • B)

    [56] \begin{bmatrix} 5 \\ 6 \end{bmatrix}

  • C)

    [32] \begin{bmatrix} 3 \\ 2 \end{bmatrix}

  • D)

    [00] \begin{bmatrix} 0 \\ 0 \end{bmatrix}

✅ Answer:

[23] \begin{bmatrix} 2 \\ 3 \end{bmatrix}

💡 Explanation:

  • Multiplying vector [23] \begin{bmatrix} 2 \\ 3 \end{bmatrix} by the identity matrix [1001] \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} results in the same vector [23] \begin{bmatrix} 2 \\ 3 \end{bmatrix} , since the identity matrix does not alter the vector.

Standard: N.VM.C.12 | DOK: 1

Multiple select📘 F.TF.A.2🧠 DOK 4

Question:

Consider the unit circle in the coordinate plane. Select all statements that correctly describe how the unit circle enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.

Answer Choices:

  • A) The unit circle allows the definition of sine and cosine for any real number as the y-coordinate and x-coordinate of the corresponding point on the circle, respectively.
  • B) The unit circle can only be used to define trigonometric functions for angles between 0 and 2π radians.
  • C) The periodic nature of the trigonometric functions is a direct result of the circular nature of the unit circle, allowing repetition of values as angles increase.
  • D) By using the unit circle, the trigonometric functions can be extended to negative angles, as these correspond to clockwise traversal around the circle.
  • E) The unit circle restricts the sine and cosine functions to values between -1 and 1, which limits their application to real numbers.
✅ Answer:
The unit circle allows the definition of sine and cosine for any real number as the y-coordinate and x-coordinate of the corresponding point on the circle, respectively.; The periodic nature of the trigonometric functions is a direct result of the circular nature of the unit circle, allowing repetition of values as angles increase.; By using the unit circle, the trigonometric functions can be extended to negative angles, as these correspond to clockwise traversal around the circle.

💡 Explanation:

  • The unit circle is a fundamental tool in trigonometry as it provides a way to define the sine and cosine functions for all real numbers.

  • The x-coordinate of a point on the unit circle corresponds to the cosine of the angle, and the y-coordinate corresponds to the sine of the angle.

  • This definition holds true for angles beyond the initial 0 to 2π range due to the periodic nature of the sine and cosine functions, which is a result of the circular nature of the unit circle.

  • Additionally, the unit circle allows for negative angles by considering clockwise movement, thereby extending the domain of the trigonometric functions to all real numbers.

Standard: F.TF.A.2 | DOK: 4

Multiple select📘 S.MD.B.5🧠 DOK 3

Question:

A small business owner is deciding whether to invest in a new project. The project could result in a profit of $10,000, a break-even scenario with no profit or loss, or a loss of $5,000. The probabilities of these outcomes are 0.3 for the profit, 0.4 for the break-even, and 0.3 for the loss. Which of the following statements are true regarding the expected value of the project and the decision-making process based on this expected value?

Answer Choices:

  • A) The expected value of the project is $1,500.
  • B) The expected value of the project is $0.
  • C) The expected value of the project is negative, indicating it is a loss-making decision.
  • D) Investing in the project is a risk-neutral decision based on the expected value.
  • E) The project should be rejected since the expected value is negative.
✅ Answer:
  • The expected value of the project is $1,500.
  • Investing in the project is a risk-neutral decision based on the expected value.

💡 Explanation:

  • To calculate the expected value, multiply each outcome by its probability and sum the results: (0.3 * $10,000) + (0.4 * $0) + (0.3 * -$5,000) = $3,000 + $0 - $1,500 = $1,500.

  • The positive expected value suggests that, on average, the project yields a profit, making it a risk-neutral decision for the business owner.

Standard: S.MD.B.5 | DOK: 3

Multiple choice📘 RI.IT.8.3🧠 DOK 1
In a small town surrounded by mountains, a young girl named Lily loved exploring the outdoors. She often hiked up the trails, collecting unique rocks and observing wildlife. Her curiosity led her to learn more about the local ecosystem and how each plant and animal played a role in it. Inspired by her discoveries, Lily started a nature club at her school to share her knowledge with her classmates.

Question:

How did Lily's curiosity about the outdoors influence her actions?

Answer Choices:

  • A) She decided to become a scientist.
  • B) She started a nature club at her school.
  • C) She moved to a bigger city.
  • D) She stopped exploring the outdoors.
✅ Answer:
She started a nature club at her school.

💡 Explanation:

  • Lily's curiosity about the local ecosystem inspired her to start a nature club to share her knowledge with her classmates.

Standard: RI.IT.8.3 | DOK: 1

Multiple choice📘 L.SS.8.1.g🧠 DOK 1
Sarah eagerly opened her new book, "The Adventures of Tom Sawyer." As she turned the pages, she noticed the author's unique style of writing. Some words were spelled differently than she was used to seeing. Despite this, she found the story captivating and couldn't put it down.

Question:

What is the main reason some words in Sarah's new book are spelled differently than she is used to?

Answer Choices:

  • A) The author made spelling errors.
  • B) The book uses old-fashioned spelling conventions.
  • C) The printer made a mistake in the book.
  • D) Sarah is not familiar with English spelling.
✅ Answer:
The book uses old-fashioned spelling conventions.

💡 Explanation:

  • The passage mentions the author's unique style of writing, which includes using different spelling conventions that might appear old-fashioned compared to modern spelling.

Standard: L.SS.8.1.g | DOK: 1

Dropdown📘 F.LE.A.6🧠 DOK 1

Question:

Consider two functions: a linear function f(x) = 3x + 2 and an exponential function g(x) = 2^x. As x increases, which function eventually grows faster?

Answer Choices:

  • A) f(x) = 3x + 2
  • B) g(x) = 2^x
✅ Answer:
g(x) = 2^x

💡 Explanation:

  • Exponential functions grow faster than linear functions as x increases.

  • While the linear function increases by a constant amount, the exponential function grows by a factor, which eventually surpasses the linear growth.

Standard: F.LE.A.6 | DOK: 1

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