Rooted Learning Icon
RootedLearning

Create Standards-Aligned Questions Instantly

Powered by AI. Backed by pedagogy. Ready in seconds.

Sample Question of the Day

Multiple select📘 G.SRT.D.10🧠 DOK 1

Question:

Which of the following statements correctly describe the application of the Law of Sines or the Law of Cosines in solving triangles? Select all that apply.

Answer Choices:

  • A) The Law of Sines can be used to find the length of a side in a right triangle when two angles and one side are known.
  • B) The Law of Cosines can be used to find the length of a side in a non-right triangle when two sides and the included angle are known.
  • C) The Law of Sines is only applicable to right triangles.
  • D) The Law of Cosines applies only to isosceles triangles.
  • E) The Law of Sines can be used to find an unknown angle in a non-right triangle when two sides and one angle are known.
✅ Answer:
The Law of Sines can be used to find the length of a side in a right triangle when two angles and one side are known.;The Law of Cosines can be used to find the length of a side in a non-right triangle when two sides and the included angle are known.;The Law of Sines can be used to find an unknown angle in a non-right triangle when two sides and one angle are known.

💡 Explanation:

  • The Law of Sines is applicable for any triangle, not just right triangles, and can be used when we know two angles and one side or two sides and one angle.

  • The Law of Cosines, on the other hand, is useful for finding unknown sides or angles in any triangle, not just isosceles triangles, particularly when two sides and the included angle are known.

Standard: G.SRT.D.10 | DOK: 1

Recent Questions

Short answer📘 G.SRT.C.6🧠 DOK 3

Question:

Given a right triangle with angles A, B, and C, where angle C is the right angle, explain the relationship between the sine of angle A and the cosine of angle B. Use this relationship to solve the following problem: If the sine of angle A is 0.6, what is the cosine of angle B?

✅ Answer:
The sine of angle A is equal to the cosine of angle B because angles A and B are complementary (A + B = 90°). Therefore, if the sine of angle A is 0.6, the cosine of angle B is also 0.6.

💡 Explanation:

  • In a right triangle, the two non-right angles are complementary, meaning they add up to 90 degrees.

  • The sine of one angle is equal to the cosine of its complementary angle.

  • Therefore, if the sine of angle A is 0.6, the cosine of angle B is also 0.6 because the two angles are complementary.

Standard: G.SRT.C.6 | DOK: 3

Short answer📘 HS-ESS2-2🧠 DOK 1

Question:

Explain how the melting of polar ice can lead to changes in other Earth systems.

✅ Answer:
The melting of polar ice reduces the Earth's albedo (reflectivity), which causes more solar energy to be absorbed by the Earth's surface. This increase in absorbed heat accelerates global warming, leading to further melting of ice, rising sea levels, and changes in ocean currents. These changes can impact weather patterns and climate systems, demonstrating a feedback loop.

💡 Explanation:

  • When polar ice melts, there is less white surface to reflect sunlight, leading to a cycle of increased heat absorption and further ice melting.
  • This feedback loop affects ocean temperatures and currents, potentially altering weather and climate patterns globally.

Standard: HS-ESS2-2 | DOK: 1

Short answer📘 HS-LS2-5🧠 DOK 3
Photosynthesis and cellular respiration are two fundamental biological processes that play a crucial role in the carbon cycle, which involves the movement of carbon among the biosphere, atmosphere, hydrosphere, and geosphere. In photosynthesis, plants absorb carbon dioxide from the atmosphere and, using energy from sunlight, convert it into glucose and oxygen. This process not only provides energy for plants but also introduces oxygen into the atmosphere, which is essential for the survival of aerobic organisms. On the other hand, cellular respiration is the process by which organisms, including plants and animals, convert glucose and oxygen back into carbon dioxide and water, releasing energy stored in glucose. This process returns carbon dioxide to the atmosphere, completing the cycle. Both processes are interconnected and ensure the continuous movement and transformation of carbon in various forms throughout different Earth systems.

Question:

Develop a model to explain how photosynthesis and cellular respiration contribute to the cycling of carbon among the biosphere, atmosphere, hydrosphere, and geosphere. Include in your model the transformations of carbon compounds and the movement of energy through these processes.

✅ Answer:
A comprehensive model should illustrate that photosynthesis absorbs carbon dioxide from the atmosphere, converting it into glucose and oxygen in the biosphere. Plants, as primary producers, use photosynthesis to store energy in glucose, which is then available to other organisms through the food chain. Cellular respiration, occurring in both plants and animals, breaks down glucose and oxygen to release energy, returning carbon dioxide to the atmosphere and completing the cycle. The model should also highlight how these processes facilitate energy flow and carbon distribution among the biosphere, atmosphere, hydrosphere, and geosphere.

💡 Explanation:

  • The model developed should detail the processes of photosynthesis and cellular respiration, emphasizing their role in transforming carbon compounds and facilitating energy movement.
  • Photosynthesis removes carbon dioxide from the atmosphere and stores it in glucose, while cellular respiration releases carbon dioxide back into the atmosphere, maintaining a balance in the carbon cycle across different Earth systems.

Standard: HS-LS2-5 | DOK: 3

Multiple choice📘 MS-ESS3-1🧠 DOK 1

Question:

Which of the following best explains why certain minerals are found in specific locations on Earth?

Answer Choices:

  • A) A) Minerals are evenly distributed across the Earth's surface.
  • B) B) Minerals are only found in regions with high human activity.
  • C) C) The distribution of minerals is a result of geoscience processes such as volcanic activity and plate tectonics.
  • D) D) Minerals are randomly scattered without any specific pattern.
✅ Answer:
C) The distribution of minerals is a result of geoscience processes such as volcanic activity and plate tectonics.

💡 Explanation:

  • The uneven distribution of Earth's minerals is due to past and current geoscience processes, including volcanic activity, plate tectonics, and the formation of mountains.
  • These processes concentrate minerals in specific areas, leading to the uneven distribution observed today.

Standard: MS-ESS3-1 | DOK: 1

Dropdown📘 MS-ESS1-4🧠 DOK 3

Question:

Scientists use the geologic time scale to organize Earth's history. Based on evidence from rock strata, which of the following statements best explains how the geologic time scale is used to understand Earth's 4.6-billion-year-old history?

Answer Choices:

  • A) The geologic time scale is a tool that organizes Earth's history into different time periods based on significant events in fossil records and rock layers.
  • B) The geologic time scale is a timeline that predicts future geological events based on the current rock formations.
  • C) The geologic time scale organizes Earth's history by listing all the species that have ever lived in chronological order.
  • D) The geologic time scale estimates the future climate changes based on past volcanic activity.
✅ Answer:
The geologic time scale is a tool that organizes Earth's history into different time periods based on significant events in fossil records and rock layers.

💡 Explanation:

  • The geologic time scale is a system that divides Earth's history into different periods based on the types of fossils found in rock strata and significant geological events.
  • This scale helps scientists understand the sequence and timeline of events that have occurred over Earth’s 4.6 billion years of history.

Standard: MS-ESS1-4 | DOK: 3

Dropdown📘 A.CED.A.3🧠 DOK 4

Question:

A community is planning to build a rectangular community garden. The length of the garden should be at most 3 times its width. Additionally, the perimeter of the garden needs to be no more than 120 meters. Let the width of the garden be denoted as 'w' meters and the length as 'l' meters. Which of the following systems of inequalities correctly represents the constraints for this situation, and what does each inequality represent?

Answer Choices:

  • A) 1. l ≤ 3w, 2w + 2l ≤ 120
  • B) 2. l ≥ 3w, 2w + 2l ≥ 120
  • C) 3. w ≤ 3l, 2w + 2l ≤ 120
✅ Answer:
1. l ≤ 3w, 2w + 2l ≤ 120

💡 Explanation:

  • The constraint 'the length of the garden should be at most 3 times its width' translates to the inequality l ≤ 3w.

  • The constraint 'the perimeter of the garden needs to be no more than 120 meters' translates to the inequality 2w + 2l ≤ 120.

  • Therefore, the correct system of inequalities is l ≤ 3w and 2w + 2l ≤ 120.

Standard: A.CED.A.3 | DOK: 4

← Previous
Page 11 of 13
Next →