Alright, here are some questions:
1. Mathematics:
    a) Suppose x and y satisfy the differential equation dy=0.01y(100-y)dx. Solve for y as a function of x if y is 20 when x is 0, then use the answer to find y when x = 3 and x when y = 80.
    b) Prove that AB and BA have the same eigenvalues if A and B are square matrices.
2. Finance:
    a) Explain the reasoning behind the popular 'rule of 72'.
    b) Explain the concept of an indifference curve.
3. Data Analysis:
    a) If a normally distributed variable has a mean of 90 and a standard deviation of 10, what is the probability a randomly chosen value is between 100 and 110?
    b) Two dice with the same number of sides are thrown several times. The products of their spins are 10, 28, 27, 50, 18, 8, 4, 1, 80, and 14. How many sides do they most likely have?
4. Programming:
    a) Write a MATLAB program to simulate a group of particles acting under the influence of each other's gravity.
    b) Write an R program to solve for the roots of any polynomial.
5. Communication:
    a) Explain the motivations for diversifying one's portfolio.
    b) Explain why actively managed funds are unlikely to perform better than passively managed ones.
I hope these questions are a helpful start for identifying your deficiencies. I can generate more if you like.
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