It is well known that about 20 questions on the FAA 107 commercial UAS pilot exam are concerned with navigation. These questions test knowledge or the ability of the test-taker to use a navigational chart or "sectional map."

KTLH sectional map

Being able to read a sectional map is important for pilots to maintain situational awareness. The exam, then, tests for ability to read sectional maps, METARS, NOTANS, and airport supplementals. For example, some questions test knowledge of location (finding a location based on longitude and latitude) while others ask about direction, airspace, elevations, and obstacles such as towers, or types of airport operations that pilots need to know in order to be on alert. Some airports offer parachuting lessons, hang gliding, balloons, or ultra-light aircraft. Pilots use sectionals, Notices to Airmen (NOTAMS) and weather reports to determine their flight plans and ensure safety. 

While navigation questions vary topically, they always refer to the supplemental workbook that accompanies the part 107 exam. If you are preparing to take the 107 exam, download the supplemental and if nothing else, study the key which describes the various icons that appear on the maps.

One of the more difficult navigation questions on the exam asks for the location of an aircraft relative to an airport, which is flying in or entering into a traffic pattern, or perhaps is on a landing approach. These questions always refer to a page in the supplement that reference to an airport, a plane and her relative location to an airstrip. Here's an example --

(Refer to FAA-CT-8080-2H, Figure 26, Area 2.)
While monitoring the Cooperstown CTAF you hear an aircraft announce that they are midfield left downwind to RWY 13. Where would the aircraft be relative to the runway?

A) The aircraft is East.
B) The aircraft is South.
C) The aircraft is West.

Figure 26, Area 2

Let's break it down....

1) The question uses a runway as a point of reference on a sectional map.
2) The question refers to the location of an aircraft relative to the direction of the wind. 

Unless you have some idea of how airports are laid out, this one is nearly impossible to "guestimate."  Let's dig into what you need to know in order to reason through this type of question.

The basics of take-off and landing
The FAA publication Airplane Flying Handbook contains the information necessary to reason through this type of question. One of the important concepts here is the difference between ground speed and air speed, which are rarely the same due to the effects of wind and weather. For example, think of yourself standing outside on a windy day where the wind is blowing at 20 miles per hour.  Your ground speed is zero because you are standing still, but your air speed is 20 miles per hour. 

Now let's think about a plane that is on a runway, preparing to take-off. In order to generate enough lift to become airborne your plane has to have an airspeed of 60 miles per hour (for example). If your plane is pointing down-wind (a tail wind of 20), your ground speed will have to be 80 miles per hour (60 + 20 = 80) in order to achieve an airspeed of 60 miles per hour (take-off speed). If your aircraft is pointed into the wind (head wind) then you already have an airspeed of 20 miles per hour standing still - bonus! In this case your ground speed will only need to be 40 miles per hour in order to achieve an airspeed of 60 (40+20=60). On take-off this means you use less runway, and it's cheaper (less fuel). When landing into the wind your ground speed is slower which again means less runway, and lower speeds help to reduce the force of impact on touch-down. You might say that when you hit something at a lower speed it hurts less.

Runway numbers
Ever wonder where runway numbers come from? Every airport is different, but why?

Think of it like this: airport designers construct runways so that they run in-line with the direction prevailing winds in order to use the "lift" advantage that wind provides. While prevailing winds vary slightly in normal conditions, laying out a runway in this manner gives Pilots access to the airspeed "boost" on take-off and the gentle touchdown that a moderate head-wind can provide. If a prevailing wind is from the Southeast in Cooperstown then the runway will lay in that direction and numbered accordingly (minus a zero).

So runways get their numbers based on their direction. For example, a runway that points due east/west, then the runways will be numbered 9 and 27 (90 degrees and 270 degrees). Here's a compass to illustrate how the number system works.

 

If your airstrip is runway 13, then the prevailing wind blows from that direction, the Southeast. In other words, the cockpit compass wiil read 130 degrees on take-off and landing.

Airport traffic patterns
This one is easy. Most airport traffic circles in a left-hand pattern. In other words if you are circling an airport in a left-hand pattern, you should see the runway when you look out of the window on the left side of the plane.

Solving the question
"an aircraft announces that they are midfield left downwind to RWY 13."

Given all of this information, let's work out the important clues --

1.) midfield left downwind to RWY 13 = the wind corresponds to the runway number so its blowing from 130 degrees( Southeast).
2.) the plane is traveling downwind (traveling in the opposite direction of 130 degrees or the aircraft heading is about 310 degrees or Northwest).
3.) "to the left" means the airport is indeed using a left-hand pattern so the runway will be seen when looking out of the left-hand window.

Where is the plane? Well, you are moving downwind (Northwest) with the runway to the left of the plane.

The aircraft position, then, would be East of the airport.

Here's another question that is similar (hint: this arircraft is also East of the runway). Can reason it out?

An aircraft announces, “left downwind for runway one six”. This means that the aircraft is on a heading of:

A) 80 degrees
B) 160 degrees
C) 340 degrees

 

Reference
Airplane Flying Handbook, chapters 3 & 7.
FAA PLT146 Questions