Here are lists of problems for 1st and 2nd year students from New York University in Abu Dhabi during their preparation to IMC2018.
0 
Start test 
May 15th 
10 problems with short answers 

1 
Example+Estimate 
May 15th 
A problem of this kind consists of two parts to be treated separately. First, one should give an example with the optimal value. Second, one should prove that a better example does not exist (this can be usually done by giving – proving – an upper or a lower estimate for all possible examples) 

2 
Quadratic polynomials 
May 15th 
A quadratic polynomial makes a good step towards a general polynomial. Train your intuition. Try to decide if the answer is yes or no before you find a complete solution of the problem. If you think there should be an example, try to find it. Otherwise try to find an explanation why any example is not possible. 

3 
Sequences and Sums 
May 16th 
How to find sums using equations 

4T 
Prime Factorization: Right or Wrong 
May 16th 
11 problems with short answers 

4C 
Prime Factorization: Construct using primes 
May 16th 
An example can be built of elements. Here we build integers as a product of prime numbers. 

5 
Polynomials and Equations 
May 17th 
Polynomials occur quite often in mathematics. One can look at them from different point of view – as expressions, as functions, as curves. Learn you to switch from one point of view to another at the right moment. 

6 
Coding 
May 17th 
A coding makes onetoone corresponding between objects or situations from a the problem to some combinatorial set. For example, such a correspondence to sequences of 0 and 1 is called a binary coding. 

7 
Polynomials with Integer Coefficients 
May 18th 
The main idea: if m, n are distinct integers, and P is a polynomial with integer coefficients, then P(m)–P(n) is divisible by m–n. 

8 
Right or Wrong: Examples in Calculus 
May 20th 
10 problems with short answers 

9 
Inequalities and derivatives 
May 20th 
You know how to find intervals where a function is increasing or decreasing. Then you can compare function values and prove inequalities! 

10 
Vectors. Dot Product 
May 20th 
Vectors in the plane and in space and dot product: geometric and algebraic view without coordinates. 

11 
Inequalities and Second Derivatives 
May 21st 
Jensen's inequality give us many inequalities with few variables 

12 
Remainders and Modular Arithmetic 
May 21st 
If the polynomial equation has an integer solution, it has a solution modulo any positive integer. And vice versa: if the equation has no solution module some positive integer it has no integer solution. 

13 
Gobetweens in Inequalities 
May 22nd 
One can prove A>B by prooving A>P and P>B. The art is to choose an appropriate gobetween P. 

14 
Vector Spaces. Dimension 
May 22nd 
The notion of dimension helps us to use the pigeonhole principle for vector spaces: though a space usually consists of an infinite number of vectors, the number of vectors in a basis is finite. 

15 
Functional Equations 
May 23d 
Functional equations: substitution method. 

16 
Dimension and Matrices 
May 23d 
Subspace and its dimension. Linear span. Matrix subspaces. 

17 
Theorems in Modular Arithmetic 
May 24th 
Remainder cancellation, Fermat's little theorem, Wilson's theorem, Chinese remainder theorem 

18 
Sturm's method for inequalities 
May 24th 
Let A and B be expressions on same variables, equal both to C when all variables has the same mean value. To prove Ai values equal to mean value. 

19 
Rank and Determinant 
May 25th 
Rank of matrix as dimension of a linear span of its columns or rows. Rank of a matrix product. 

20 
Finite Fields Z_{p} 
May 25th 
Projection of integer polynomials and vectors to remainder polynomial and vectors helps to prove divisibility and nonsingularity. 

21 
Matrix Algebra 
May 27th 
Algebraic properties of matrices, examples of matrices. 

22 
Integral and Differential Inequalities 
May 27th 
The main idea: integral of a positive function is positive. 

23 
Integral and Differential Inequalities 
May 28th 
Eigenvalues of matrix and its characteristic polynomial. 

24 
Integral and Differential Inequalities 
May 28th 
An algorithm can check an infinite sequence of hypotheses one by one until find the right one. 

25 
Continuous Functions 
May 29th 
Arithmetic of continuous functions, intermediate value theorem and extreme value theorem. 

26 
Selected problems 
May 29th 
A dozen credit problems with interesting solutions. 