Given an equation involving x as a power on e, the student must solve for x. Hints are included in the question to aid the student as needed.

Given an equation with log terms added together, the student must solve for x. Hints are included in the question to aid the student as needed.

Given an equation with log terms added together, the student must solve for x. Hints are included in the question to aid the student as needed.

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Solving an equation of the form $ax \equiv b\;\textrm{mod}\;n$ where $a$ and $n$ are coprime.

The students should solve a Blakley secret sharing scheme and find the secret.

This question asks students to solve a discrete logarithm problem with Pollard's rho algorithm as exposed in the book "introduction to cryptography with open source software" by McAndrew.

This question tests the student's ability to solve Integer Programming problems applying Population-based Metaheuristics.

This question tests the student's ability to solve Integer Programming problems applying Single State Metaheuristics.

This question tests the student's ability to model and solve Integer Programming problems by Branch and bound method

This question tests the student's ability to model and solve Integer Programming problems by Branch and bound method

This question tests the student's ability to solve Linear Programming problems by hand using the Simplex Method.

This question tests the student's ability to solve Linear Programming problems by hand using the Simplex Method.

This question tests the student's ability to model and solve Integer Programming problems

This question tests the student's ability to model and solve Integer Programming problems

This question tests the student's ability to model and solve Integer Programming problems

This question tests the student's ability to model and solve Integer Programming problems

This question tests the student's ability to model and solve Integer Programming problems

This question tests the student's ability to solve Linear Programming problems by applying Geometric method.

This question tests the student's ability to solve Linear Programming problems by applying Geometric method.

This question tests the student's ability to solve Linear Programming problems by applying Geometric method.

This question tests the student's ability to solve simple linear equations by elimination. Part a) involves only having to manipulate one equation in order to solve, and part b) involves having to manipulate both equations in order to solve. 

Solve a logarithmic equation

A quadratic equation (equivalent to $(x+a)^2-b$) is given and sketched. Three equations are given that can be solved using the graph. There is a chance there will only be one solution.

Finding X-Y intercepts for quadratic and cubic equations.

A few quadratic equations are given, to be solved by completing the square. The number of solutions is randomised.

Calculate a repeated integral of the form $\displaystyle I=\int_0^1\;\int_0^{x^{m-1}}mf(x^m+a)dy \;dx$

The $y$ integral is trivial, and the $x$ integral is of the form $g'(x)f'(g(x))$, so it straightforwardly integrates to $f(g(x))$.

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This just an equilibrium of a particle problem, but posed in context of a joint as a warm-up for the method of joints.

Advice is brief.