Several cities in the US are starting bike share programs. Riders can pick up and drop off a bicycle at any rental station. These bicycles are typically used for short trips within the city center, either one-way or roundtrip. The idea is to help people get around town on a bike instead of a car. Those making longer trips (such as commuting to work) are likely to use their own bikes. Some of the challenges are how to determine where to locate the rental stations, how many bikes to have at each station, how/where to add new locations as the program grows, how many bikes to move to another location and when (time of day, day of week).

The purpose of this task is to introduce radian measure for angles in a situation where it arises naturally.

A number of communities (campuses, towns, cities, etc.) around the world have proposed and enacted plastic water bottle bans in some form.

In 2013 the small town of Concord, Massachusetts (population approximately 19,000) became the first town or city in the United States to ban the sale of single-serving Polyethylene terephthalate (PET) bottles less than or equal to 1 liter (34 ounces) containing water which is non-sparkling and non-flavored (in other words, plain water)[1]. The sale of water in bottles of any size made of other types of plastic or other materials, as well as PET bottles of flavored or sparkling water, soda, tea, juices, and other non-plain water beverages, regardless of size, is allowed[2]. See attached FAQ document.

The purpose of this task is to give an application arising from a real-world situation in which a quadratic equation arises, and where it is natural to use a graphical method to find an approximate solution and the quadratic formula to find an exact solution

The purpose of this task is to assess a student's ability to explain the meaning of independence in a simple context.

This task can be used as an instructional task to develop students understanding of independence and students ability to calculate the probability of intersection events using the multiplication rule for independent events.

The emphasis in this task is not on complex solution procedures. Rather, the progression of equations, from two that involve different values of the sales tax, to one that involves the sales tax as a parameter, is designed to foster the habit of looking for regularity in solution procedures, so that students don't approach every equation as a new problem but learn to notice familiar types.

The goal of this task is to study some values of sinx and cosx looking for and then explaining patterns.

The goal of this task is to set up and solve an equation involving a simple rational expression.

The purpose of this task is to use finite geometric series to investigate an amazing mathematical object that might inspire students' curiosity. The Cantor Set is an example of a fractal.

Some people rent a car when they are going on a long trip. They are convinced they save money. Even if they do not save money, they feel that the knowledge that "if the car breaks down on the trip, the problem is the rental company's" makes the rental worth it. Analyze this situation and determine under what conditions renting a car is a more appropriate option. Determine mileage limits on one's own car and a break-even value of "ease of mind" for the driver and her family.

The task requires the student to use logarithms to solve an exponential equation in the realistic context of carbon dating, important in archaeology and geology, among other places.

In the task ''Carbon 14 Dating'' the amount of Carbon 14 in a preserved plant is studied as time passes after the plant has died. In practice, however, scientists wish to determine when the plant died and, as this task shows, this is not possible with a simple measurement of the amount of Carbon 14 remaining in the preserved plant.

This problem introduces the method used by scientists to date certain organic material. It is based not on the amount of the Carbon 14 isotope remaining in the sample but rather on the ratio of Carbon 14 to Carbon 12. This ratio decreases, hypothetically, at a constant exponential rate as soon as the organic material has ceased to absorb Carbon 14, that is, as soon as it dies.

The purpose of this task is to use geometric and algebraic reasoning to model a real-life scenario.

In our school and social lives we exist in a mobile electronic world. Each day we "plug in" and charge our electronic devices and equipment. These electronics may range from small items (cell phones) to large items (electric vehicles). While in our own home, our family is most likely responsible for purchasing the charging equipment, and then paying an electric company/provider for the electricity we use.

The proliferation of electronic buses (e-buses) in cities across the globe represents a significant stride toward sustainable urban transport. With the mounting concerns over air pollution and climate change, many cities have been prompted to reconsider their reliance on traditional diesel buses. According to a recent report by Bloomberg New Energy Finance[1], e-buses are set to dominate the public transit sector, becoming the majority of all buses on the road globally by 2032. China has been particularly noteworthy in this transition, as it is home to most of the world’s e-buses, driven in large part by government policies that prioritize electric vehicles and stringent emission standards. Cities throughout the world (e.g., Bogota, Colombia, New York, USA, and Berlin, Germany) are also making concerted efforts to incorporate e-buses into their fleets, albeit at a more gradual pace.

This task is assessing a simple but important piece of conceptual understanding, namely the correspondence between intersection points of the two graphs and solutions of the system.

This task shows that the three perpendicular bisectors of the sides of a triangle all meet in a point, using the characterization of the perpendicular bisector of a line segment as the set of points equidistant from the two ends of the segment.

The goal of this task is to study where a circumscribed triangle can meet a given circle.