Mad Scientist Disease


I recently had a very encouraging session. A girl whose progress had stalled out around 650 on the GMAT wanted to come in and do one session before her test. She already had the test date scheduled and wanted to at least get a sense of direction so that we could plan out her next attempt. As we worked together however, I found that her skills were excellent. She knew all of the concepts and formulas and had a strong enough math background to do very well on the test. The problem was that she had mad scientist disease.

Now mad scientist disease is a phrase I coined for someone who upon seeing a math problem erupts in a flurry of activity. Notes are scribbled, equations laid out and many important things are figured out. The problem is that many of those things are irrelevant! What the mad scientist does is largely a waste of time. She mixes together lots of chemicals and hopes that one of the compounds she finds is useful and that nothing blows up in her face!

In the one session we had before this student’s test we talked about how to approach problems. We focused on patiently organizing thinking and planning on what needed to be solved before solving anything. I got the student to slow down and relax.

Now I can’t claim that this is a typical result, but after that one session this student’s score went up to 730! An 80-point gain in a week! And all it took was a simple cure for mad scientist disease. Slow down and plan what you’re going to do before you do it.



I recently came across a problem that required knowledge of parabola formulas. That surprised me. Although parabola problems show up relatively frequently, they usually require little more than logic. However, I thought that provided a nice opportunity to refresh on all things parabola.

A parabola is defined mathematically by this formula: y= ax^2 + bx + c. We see parabolas in nature most often when we look at projectiles, like a cannonball shot out of a cannon or a jump shot out of the hand of Steph Curry. Parabolas are generally u-shaped and are symmetrical about the vertex, which is either the highest or lowest point of the parabola, depending on the orientation.

Whether our parabola is cupped upward or downward is determined by the sign of the “a” term in the formula we saw above. When a is positive, the parabola will have a vertex at the bottom and open upward. When a is negative, the parabola will have a vertex at the top and open downward.

However, there is more than one way to define a parabola mathematically. We can also solve a parabola if we have the vertex and another point on the parabola. We do that by using the similar formula y = a(x-h)^2 + k. The coordinates of the vertex are (h,k).

So using that information, find the equation of a parabola with vertex (-2,1) containing the point (1, 19). The first thing we need to do is solve for a by inserting our points into the formula. We get:

19 = a(1-(-2)^2 + 1

19= a(3^2) + 1

19= 9a + 1

Now, we put our a into the formula with our vertex (h,k), but instead of using the x and y from a specific

point we’re going to solve for the generic x and y.

y= 2(x-(-2)^2 + 1

y= 2(x+2)^2 +1

Now expand:

y=2(x+2)(x+2) +1

y=2x^2 + 8x + 9

Now we’ve solved for the equation of this parabola and we could mathematically figure out all of the

points on this curve.

I hope that’s been a good refresher on parabolas!

 The New PSAT: Math Quick Thoughts


I recently had an opportunity to take a sample test for the new PSAT, and I have to say I was surprised. For all the bluster about a new SAT I didn’t expect a whole lot of difference. I will say, it’s different. Here are some of my high-level thoughts about the math section. I’ll be digging into more details of the test and more specifics in coming weeks.

1. The new non-calculator section is going to be a major time crunch: I’m traditionally a fast worker, I’m extremely comfortable doing mental math and I still only finished with about a minute and a half left.

2. Finishing on time is going to require either exceptional math skills or exceptional strategy: And to be honest, a combination is probably the best path to a great score. One problem I saw involved some fairly complicated geometry. However, a quick estimate told me that only one of the answers could have been correct and saved me quite a bit of time. Mindlessly plugging ahead is a sure way to get in time trouble on this test.

3. The combination of time pressure and some tough problem should make perfection tougher to achieve: If you’re not an 800-level math student, that shouldn’t cause you to panic because the scoring will still curve out approximately the same. My guess is that the need for a little more speed may do a better job separately the truly exceptional from the very very good. The current test often makes silly mistakes the dividing line between perfect and near perfect.

I’m still digesting what these changes mean, but I’ll keep updating you over the coming weeks!

 Closing the Gap


Chris and Evan are outstanding runners. One day in practice they do a 1500 meter training run. Being competitors, Chris and Evan can’t do any training run without it turning into a competition, so they decide to race. Chris and Evan were dead even until Chris tripped at the 1100 meter mark. His misfortune allowed Evan to take a 15 meter lead. Jolted by adrenaline Chris immediately ups his pace to 6.7 meters/second. Evan continues at his consistent pace of 6.4 meters/second. Who wins the race?

This problem mimics some themes we often see in math problems in content, although not exactly in form. The common thread is that you have two rates. Dealing with two rates simultaneously, however, can be tricky, so it’s easier to deal only with the difference between the rates. In this case (at least at first), let’s not worry about 6.4 and 6.7. All we need to know is that Chris gains 0.3 meter every second. With a difference of 15 meters, it’s quick to figure out that it will take 15/0.3 = 50 seconds to close the gap.

Only one question remains: When Chris does catch up, will it be before or after the finish line? Since we know the two runners will be tied 50 seconds after the trip, all we need to do is multiply one of the runners’ rates by 50 seconds to figure out where on the course he will be when that occurs. Let’s chooses Chris. 6.4 m/s * 50 seconds = 320 meters. Adding that to the 1115 meters he has already traveled (since he’s already gained the 15 meter lead by the time both men are running again) and we find that Chris will be 1435 meters into the race when Evan pulls even with him.

Despite his trip, Evan will pull even with Chris and pass him down the back stretch to win the 1500 meter race.