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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📘 F.TF.A.4🧠 DOK 1

Question:

Explain how the unit circle helps to understand why the sine function is an odd function.

✅ Answer:

The unit circle helps to understand why the sine function is an odd function because for any angle $\theta$ , the sine of $-\theta$ is equal to the negative of the sine of $\theta$ . This reflects the symmetry of sine across the origin on the unit circle, where $\sin(-\theta) = -\sin(\theta)$ .

💡 Explanation:

The sine function is considered odd because it satisfies the condition $\sin(-x) = -\sin(x)$ for all $x$ .
On the unit circle, the coordinates of a point corresponding to the angle $\theta$ are $(\cos(\theta), \sin(\theta))$ .
When you take the angle $-\theta$ , the coordinates become $(\cos(-\theta), \sin(-\theta))$ , which are $(\cos(\theta), -\sin(\theta))$ , showing that $\sin(-\theta) = -\sin(\theta)$ .
Thus, the unit circle visually demonstrates the odd symmetry of the sine function.

Standard: F.TF.A.4 | DOK: 1

Short Answer📘 MS-PS1-5🧠 DOK 1

Question:

Explain how the concept of conservation of mass applies to a chemical reaction.

✅ Answer:

In a chemical reaction, the total number of atoms of each element remains the same, which means that the mass is conserved. This means that the mass of the reactants equals the mass of the products.

💡 Explanation:

According to the Law of Conservation of Mass, atoms are neither created nor destroyed during a chemical reaction.
They are simply rearranged to form new substances.
Therefore, the total mass of the reactants must equal the total mass of the products in a closed system.

Standard: MS-PS1-5 | DOK: 1

Multiple choice📘 F.LE.A.5🧠 DOK 2

Question:

The population of a small town was 5,000 people in 2010 and grew to 6,500 people by 2015. Assuming the population growth follows an exponential model, what is the annual growth rate, expressed as a percentage, of the town's population?

Answer Choices:

A) A) 5%
B) B) 6%
C) C) 7%
D) D) 8%

✅ Answer:

A) 5%

💡 Explanation:

To find the annual growth rate of an exponential function, we use the formula for exponential growth: $P(t) = P_0(1 + r)^t$ .
Here, $P_0$ is the initial population, $P(t)$ is the population at time $t$ , $r$ is the growth rate, and $t$ is the time in years.
Substituting the values, we have $6500 = 5000(1 + r)^5$ .
Solving for $r$ , we get $1.3 = (1 + r)^5$ .
Taking the fifth root of both sides gives $1 + r = 1.053$ , so $r = 0.053$ or 5.3%.
Rounding to the nearest percentage gives a growth rate of 5%.

Standard: F.LE.A.5 | DOK: 2

Dropdown📘 S.ID.A.4🧠 DOK 1

Question:

A researcher is analyzing the test scores of a large group of high school students. The scores are normally distributed with a mean of 75 and a standard deviation of 10. What percentage of students scored below 65?

Answer Choices:

A) 16%
B) 32%
C) 50%
D) 68%

✅ Answer:

16%

💡 Explanation:

In a normal distribution, scores below one standard deviation from the mean (mean - 1 standard deviation) account for approximately 16% of the data.
Since the mean is 75 and the standard deviation is 10, scores below 65 (which is one standard deviation below the mean) represent 16% of the population.

Standard: S.ID.A.4 | DOK: 1

Multiple select📘 6.1.8.CivicsHR.3.c🧠 DOK 4

Question:

Which of the following arguments explain how the expansion of slavery in the United States during the 19th century violated human rights and contradicted American ideals? Select all that apply.

Answer Choices:

A) Slavery denied the fundamental human right to freedom, which is considered an inalienable right in American ideals.
B) The expansion of slavery contradicted the American ideal of 'all men are created equal,' as stated in the Declaration of Independence.
C) Slavery promoted economic growth for all Americans, aligning with the ideal of prosperity for everyone.
D) The institution of slavery limited democratic participation and representation for enslaved individuals, contradicting the principles of a democratic society.
E) Slavery was a way to integrate and civilize African Americans, aligning with the American ideal of cultural assimilation.

✅ Answer:

Slavery denied the fundamental human right to freedom, which is considered an inalienable right in American ideals.; The expansion of slavery contradicted the American ideal of 'all men are created equal,' as stated in the Declaration of Independence.; The institution of slavery limited democratic participation and representation for enslaved individuals, contradicting the principles of a democratic society.

💡 Explanation:

Slavery violated human rights by denying individuals their freedom, which is an inalienable right according to American principles.
It also directly contradicted the American ideal that 'all men are created equal,' as stated in the Declaration of Independence.
Furthermore, slavery restricted democratic participation, as enslaved people were denied the right to vote or have representation, which runs counter to the democratic ideals upon which the United States was founded.

Standard: 6.1.8.CivicsHR.3.c | DOK: 4

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

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