few_shots: 
Example 1:
Concept/skill: 
Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

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


Answer: 
Yes. An initial step when solving for x in this problem requires the use of the addition formula for cosine on the left side of the equation.

Example 2:
Concept/skill: 
Solve quadratic equations in one variable.

Problem/activity:
Task
Solve the quadratic equation
$$ x^2 = (2x - 9)^2 $$
using as many different methods as possible.


Answer: 
Yes. This task shows one quadratic equation with one variable, x.

Example 3:
Concept/skill: 
Construct a tangent line from a point outside a given circle to the circle.

Problem/activity:
Task
Suppose $A$ is an angle with vertex $P$, as pictured below:
[IMG]
Draw a circle with center $P$ and with  radius $r \gt 0$.  Explain why the circle
meets each ray of angle $A$ in a single point.  Label these points $Q$ and $R$ respectively.
Draw circles with centers $Q$ and $R$ respectively and radius $r$.  These circles meet at $P$ and a second point to be labelled $B$.
Show that ray $\overrightarrow{PB}$  bisects angle $P$.


Answer: 
No. This task does not involve drawing lines that are tangent to circles. The only line that may be drawn is the ray between points P and B.

Now, determine whether the following problem or activity can enable students to understand the concepts or skills in the provided description.

shot_info: fl_problem_001894_pos_0

HS_0

im_task_000870_pos_0

HS_1

im_task_001160_neg_0

HS_2
standard_description: Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate mortgage payments.
problem_activity: Task
In 1966, a Miami boy smuggled three Giant African Land Snails into the country. His grandmother eventually released them into the garden, and in seven years there were approximately 18,000 of them. The snails are very destructive and had to be eradicated. According to the USDA, it took 10 years and cost \$1 million to eradicate them.
Assuming the snail population grows exponentially, write an expression for the population, $P$, in terms of the number, $t$, of years since their release.
How long does it take for the population to double?
Assuming the cost of eradicating the snails is proportional to the population, how much would it have cost to eradicate them if
they had started the eradication program a year earlier?
they had let the population grow unchecked for another year?


aligns: no