I assume the answer you were looking for is "push"?
Yep. Otherwise you'll spend more time in the downdrafts than the updrafts, and you won't climb. Push in the downs, pull in the ups to get as much help as you can.
Here's the quiz, with answers, as I originally wrote it:
1) Winds are calm. Which side of a mountain/ridge will have updrafts, and which will have downdrafts? Bonus question: How far from the mountain will these updrafts be felt?
Answer: The side the sun is shining on will have updrafts. This one should be fairly obvious. Bonus answer: Thermal lift usually extends 100-300 feet out from the face of the mountain and directly above the ridge.
2) You camp overnight at a backcountry airstrip in a canyon (say, Johnson Creek above), and you want to fly out to breakfast in the morning. Which way should you expect the wind to be blowing in the morning when you take off? How about in the evening when you fly back in to have a cookout at your campsite?
Answer: The wind will tend to blow from downstream (as in, wind is blowing upstream), or from lower elevation towards higher elevation. in the morning. As the sun rises, the canyon walls will begin heating from the top down, and the shallower upstream portions of the canyon will be fully lit long before the deep downstream portions. The cool air that collected overnight in the downstream portion will begin to flow upstream to replace the rising warmer air in the upstream portion. In the evening, the upstream part, being at a higher altitude, will begin cooling sooner and the winds will tend to flow downstream.
3) You're flying an Archer (180hp) from a strip at a DA of 8,000 feet. What is your approximate available horsepower?
Answer: A normally-aspirated aircraft engine loses around 3.5% hp per 1000 foot increase in DA. So, our 180hp engine at 8,000 feet has lost about 28% of its power, leaving 72% available. 0.72 * 180 = 129.6. So, your Archer has turned into a bit less than a Cherokee 140.
3a) Maximum gross weight on your Archer is 2550 pounds. How much weight must you remove from the cabin to achieve book performance at 8,000 feet DA?
Answer: Sea level power loading is 2550/180=14.666666... pounds per horsepower. At the 129.6 hp available at 8,000, to get book performance we'll need to reduce to 14.6666 lb/hp * 129.6 hp = 1,836 pounds. (For reference, in our Archers, just me and an hour of fuel is 1,905 pounds.)
3b) Your Archer can climb 1,000 fpm at sea level at max gross. What will be your rate of climb at 10,000 feet DA?
Answer: Rate of climb = (Excess HP * 33,000)/gross weight. So, at sea level, that means you have 77.3 excess hp available, and that it takes 102.7hp just to keep the plane level.
Now, at 10,000 feet DA you've lost roughly 35% of your available horsepower (63hp), so you're down to 117hp at full power. Thus, you have 14.3 excess hp available for climb. Plug that into the formula again, and your rate of climb will be a dismal 185 feet per minute. Now, you'd better pay close attention to where those downdrafts are likely to be, because many of them will be a lot more than 185 feet per minute!
4) You encounter a downdraft and you begin descending at full power and Vy. What should you do?
Answer: Push the nose over and increase airspeed. You will not outclimb the downdraft, so you want to get through it as fast as you can. Likewise, in rising air you want to pull the nose up even farther to slow down and maximize the time spent in the rising air. Holding altitude (or attempting a steady rate of climb) is one of the worst things you can do when flying through up and down drafts.
5) You're flying an airplane through a 1000-foot-wide canyon at 110 knots. You realize you can't make it out of the canyon. You roll into a 45-degree-bank turn. Will you be able to complete the turn successfully? What speed *should* you fly through the canyon?
Answer: The formula for turn radius is v^2/(11.26*tan(bank)). At 110 knots and 45 degrees of bank, turn radius will be 1,074.6 feet, so the full diameter of the turn will be 2,149.2 feet, nearly 1/2 mile. Add on at least 50 feet for the span of the outer wing as well (on a 172, for example, that would have you with your wingtip 7 feet off the canyon wall on both ends of the turn).
At 100 knots, turn radius will be 888 feet.
At 90 knots, turn radius will be 719 feet.
At 80 knots, 568 feet.
At 70 knots, 435 feet. This is enough for your average single to make the turn, provided they started close enough to one wall. So, you probably shouldn't be flying faster than 70 knots in this particular canyon! (Ahem, Corey Lidle)