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Are you smarter than a Russian 12th grader? by Kseniya Garaschuk (University of British Columbia)

As you might suspect, the mechanism of entering a university depends on the country where said university is located. In Belarus (where I am originally from), just like in many other countries of the former Soviet Union, the higher education is free — if you’re good enough, that is. Your “goodness” is determined by the entrance exams and the competition is fierce. By grade 9 of the 12-year secondary education, you already know which faculty you will be applying to and you start preparing for the entrance exams: you take evening classes, do endless exercises similar to problems appearing on previous years’ exams, and might even switch high schools to one that has a specialized class for the subject of your choice. Hard sciences are always popular. In my year, the number of students writing the exams for the Faculty of Mechanics and Mathematics of Belarusian State University was 17 times the number of places available. Let me make it clear: you had to beat out 16 other students on the entrance exams in order to get in. You can only apply to one faculty within one top-tier public university. If you don’t get in, you can try less prestigious universities and/or private universities where you pay for your education (they strategically hold their entrance exams later in the summer). Or you can try again next year, unless you are male, in which case your mandatory military service will delay your second attempt by 2 years. You get the idea — the stakes are high. So what do these entrance exams look like? Here are the problems from 2009 written entrance exam to the Faculty of Mechanics and Mathematics of Moscow State University, the top university in the country. You can find the archive here: http://new.math.msu.su/admission 1. Find all values of x for which the functions

y= 11 + 24x

17x2 ,

y = arccos (x2

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11 + 24x

y = arccos (x2

2x + 1),

17x2 , 2x + 1),

3. How many fish did Andrey catch, if we know that he caught 55% of all salmon and cod caught by the boys? 4. A circle of radius 2 with its centre on the base of an isosceles triangle is tangent to two of the triangle’s sides. One of the tangency points is connected to the opposite vertex of the triangle by a line segment. This line segment is divided by the altitude dropped to the base of the triangle in a 4 : 3 ratio, starting from the vertex. Find the area of the triangle.

Kseniya Garaschuk Be a good department citizen, particularly after you get tenure: go to department meetings, actually contribute to the committees, participate in outreach, go to department tea. While the research distinguishes department members as scientists, it is the service that distinguishes them as community members.

5. Find all values of x 2 [19, 29] which satisfy the inequality

a6 + 8a5 − 2  1, ax where a is a root of y

17

+ 2y 11 + 4y 5 = 1 .

If you score high enough on the written exam, you proceed to the oral stage, where you draw 2–3 random problems, are given a short time to solve them, and then get to discuss your solutions with the hiring committee. Yes, very intimidating. Just to give you some idea of what the problems might be like, here are two from 2009: 1. Solve the equation

⇣ cos 4x + sin 2x

a⇡ ⌘ = sin 3x, 64

where a is the smallest two-digit natural number which, when written to the right of 20092009, produces a ten-digit number divisible by 36.

2. Find all values of c such that the set of solutions 2 y = arccos (x(x, 2xof+the1), y = log3 (x2 ) y) system

y = log3 (x2 )

y = log3 (x2 )

are defined and at least one of them is equal to zero. 2. Andrey and Boris are tallying up the results of their fishing trip where they caught salmon and cod. Boris, whose total catch consists of no more than 100 fish, has 25% fewer salmon than Andrey, but Andrey has 25% fewer cod than Boris.

forms a line segment. I can’t help but wonder, should I give this exam to my students here in Canada next time I teach a first-year course? Will it be a sobering experience for them as they realize what it takes to get a higher education in another country? 3