###### To enable every aspiring TJ student to present their best self

###### See previous Problem Solving Essay prompts here

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##### Preparing for the essays has always been a vague, sometimes debated concept. One easy way to prepare for the Problem solving (also called math based, science based and ethics) essays is to try the previous years'. Each one should be done in an hour end to end. The most important thing to do in these is to explain and show your thoughts. Though the right answer is a great, being able to show your thoughts is so much more important. Remember to write them without the use of a calculator and an application that does not have spell check (ie. notepad)

#### Prompt 1:

2016:

It is 5:30 AM, and as a helicopter pilot you’ve just been told there’s an injured man on a boat you need to get to a hospital. The boat is going towards where you are at 10 mph, but is currently 400 miles away. You need to get him as soon as possible, but you only have 6600 lbs of fuel in your helicopter, which burns 1200 lbs per hour, and always travels at 150 mph. Also, you need to account for 30 min of fuel spent hovering over the boat to get the man into the helicopter, and 1 extra hour of fuel due to helicopter standards. When do you leave and why?

#### Prompt 2:

2017:

You are a researcher in the Falkland Islands You’ve been asked to estimate the penguin population. The current population is 1000 penguins. 500 pairs produce one chick per pair per year. At the end of each year there is a loss of 20% of the total population. Figure out how many penguins there will be at the end of seven years. Develop a formula that solves the problem.

#### Prompt 3:

2018:

When designing a stairway, an architect can use the riser-tread formula 2h +d = 25, where h is the riser height, in inches, and d is the tread depth, in inches. For any given stairway, the riser heights are the same and the tread depths are the same for all steps in that stairway.

The number of steps in a stairway is the number of its risers. For example, there are 5 steps in the stairway in the figure above. The total rise of a stairway is the sum of the riser heights as shown in the figure.

An architect wants to use the riser-tread formula to design a stairway with a total rise of 9 feet, a riser height between 7 and 8 inches, and an odd number of steps. With the architect’s constraints, which of the following must be the tread depth, in inches, of the stairway?

To see the figure, click here

#### Prompt 4:

2019:

The Chesapeake Bay holds about 18 trillion gallons of water. The Chesapeake Bay covers about 4,480 square miles or about 3,000,000 acres. Each acre can hold 750,000 oysters and each oyster is capable of filtering 50 gallons of water per day. Can there be enough oysters to filter the Chesapeake Bay in one day?

***Please not that these are most likely not exactly how the prompts were worded. We searched the internet to compile these and cross referenced to find the most consistent version. These are great practice but not guaranteed the prompts verbatim***