few_shots: Example:
Problem/activity:
Find the general solution for:
$${\mathrm{cos}\left({\pi\over2}+x\right)=\mathrm{tan}{\pi\over4}}$$


Mathematical concept/skill options: 
A. Prove and apply trigonometric identities.
B. Model periodic phenomena with trigonometric functions.
C. Interpret functions that arise in applications in terms of the context.
D. Build a function that models a relationship between two quantities.
E. Define, evaluate, and compare functions.
F. Use functions to model relationships between quantities.
G. Understand the concept of a function and use function notation.
H. Analyze functions using different representations.
I. Extend the domain of trigonometric functions using the unit circle.
J. Interpret expressions for functions in terms of the situation they model.
K. Build new functions from existing functions.
L. Construct and compare linear and exponential models and solve problems.


Your response:
Thought: This problem applies trigonometric identities, including the angle addition formula for cosine.
Answer: A

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: fl_problem_001894

HS
options: Summarize and describe distributions.

Use the rules of probability to compute probabilities of compound events in a uniform probability model.

Interpret linear models.

Understand and evaluate random processes underlying statistical experiments.

Summarize, represent, and interpret data on a single count or measurement variable.

Summarize, represent, and interpret data on two categorical and quantitative variables.

Investigate patterns of association in bivariate data.

Make inferences and justify conclusions from sample surveys, experiments, and observational studies.

Develop understanding of statistical variability.

Investigate chance processes and develop, use, and evaluate probability models.

Understand independence and conditional probability and use them to interpret data.

Draw informal comparative inferences about two populations.

Use probability to evaluate outcomes of decisions.

Calculate expected values and use them to solve problems.

Use random sampling to draw inferences about a population.
problem_activity: Task
Jerry forgot to plug in his laptop before he went to bed. He wants to take the laptop to his friend's house with a full battery. The pictures below show screenshots of the battery charge indicator after he plugs in the computer.
[IMG]
When can Jerry expect that his laptop battery is fully charged?
At 9:27 AM Jerry makes a quick calculation:
The battery seems to be charging at a rate of 1 percentage point per minute. So the battery should be fully charged at 10:11 AM.
Explain Jerry's calculation.  Is his estimate most likely an under- or over-estimate? How does it compare to your prediction?
Compare the average rate of change of the battery charging function on the first given time interval and on the last given time interval. What does this tell you about how the battery is charging?
How long would it take for the battery to charge if it started out completely empty?


correct_option_index: 5