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Sample Question of the Day
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.
💡 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
Question:
A researcher is studying the relationship between the number of hours students study and their resulting test scores. She creates a linear model to predict test scores based on study hours, given by the equation: , where is the test score and is the number of hours studied. What do the slope and y-intercept of the model represent in this context?
Answer Choices:
- A) A) The slope represents the test score a student starts with, and the y-intercept represents how much the score increases per hour of study.
- B) B) The slope represents the increase in test score per additional hour of study, and the y-intercept represents the base test score when no hours are studied.
- C) C) The slope represents the total test score after studying, and the y-intercept represents the score decrease without study.
- D) D) The slope represents the decrease in test score per hour of study, and the y-intercept represents the maximum possible test score.
💡 Explanation:
In the equation , the slope 2.5 represents the increase in the test score for each additional hour of study.
The y-intercept 65 represents the test score when no hours are studied, meaning it is the baseline score.
Standard: S.ID.C.7 | DOK: 4
Question:
Which of the following represents an equation that can be used to determine the number of solutions for the quadratic function f(x) = 2x^2 - 4x + 1?
Answer Choices:
- A) A) 2x^2 - 4x + 1 = 0
- B) B) f(x) = 0
- C) C) 2x^2 + 4x - 1 = 0
- D) D) 2x^2 - 4x - 1 = 0
💡 Explanation:
The equation f(x) = 2x^2 - 4x + 1 represents a quadratic function.
To find the number of solutions, we set the function equal to zero, resulting in the equation 2x^2 - 4x + 1 = 0.
Standard: A.CED.A.1 | DOK: 1
As the sun dipped below the horizon, painting the sky with hues of orange and pink, Maya stood on the edge of the cliff, her heart pounding with a mix of fear and exhilaration. She felt the weight of the decision pressing down on her shoulders, knowing that this choice could alter the course of her life forever. The world below seemed both inviting and intimidating, a vast unknown waiting to be explored. In that moment, Maya realized that her journey was not just about finding a new path, but also about discovering who she truly was.
Question:
How does the author convey Maya's internal conflict and perspective in the passage?
💡 Explanation:
- The passage uses descriptive language to paint a picture of Maya's surroundings and her emotions, illustrating her internal struggle between fear and excitement.
- The metaphor of the cliff and the unknown world below symbolizes her uncertainty and the potential for personal growth, revealing her introspective perspective.
Standard: RL.PP.6.5 | DOK: 3
Many animals live in the forest. Some animals, like deer and rabbits, eat plants. Others, like wolves and bears, hunt for meat. Birds build nests in trees to keep their eggs safe.
Question:
What do wolves and bears do in the forest?
💡 Explanation:
- The passage states that wolves and bears hunt for meat, which indicates their role as predators in the forest ecosystem.
Standard: L.KL.6.2.a | DOK: 1
Question:
Find the greatest common factor (GCF) and the least common multiple (LCM) of the numbers 18 and 24. Then, use the distributive property to express the sum of 18 and 24 as a product of their GCF and another sum.
💡 Explanation:
To find the GCF, list the factors of each number: 18 (1, 2, 3, 6, 9, 18) and 24 (1, 2, 3, 4, 6, 8, 12, 24).
The greatest common factor is 6.
For the LCM, list the multiples: 18 (18, 36, 54, 72, ...) and 24 (24, 48, 72, ...).
The least common multiple is 72.
Using the distributive property, 18 + 24 equals 42, and it can be rewritten as 6(3 + 4) because 6 is the greatest common factor.
Standard: 6.NS.B.4 | DOK: 2
The scientist observed the reaction with intense concentration. She noted that the substances combined to form a new compound, illustrating the process of synthesis. This chemical synthesis is crucial for creating materials that are not found in nature. Understanding synthesis allows scientists to innovate and develop new technologies.
Question:
What does the word "synthesis" most likely mean based on the passage?
Answer Choices:
- A) A process of breaking down substances
- B) A process of combining substances
- C) A process of observing reactions
- D) A process of natural occurrence
💡 Explanation:
- The word "synthesis" is derived from the Greek root 'syn' meaning 'together' and 'thesis' meaning 'placing'.
- In the passage, synthesis is described as the process where substances are combined to form a new compound, which aligns with the root meanings.
Standard: L.VL.8.3.c | DOK: 2