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.

In this question the students have to solve a linear recurrence of order 2. The sequence is asked in recurrence form and the goal is to find its closed form.

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 $f(g(x))$.

Solve equations involving logs and exponential functions, by using inverse operations.

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Homework set.  Trusses solved using the method of sections

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.

Solve a Differential equation with 3 simple linear factors

Solve equation involving exponential function

Solve equation involving exponential function.

Solve equation involving exponential function.

Solve equation involving logarithmic function.

Solve equation involving logarithmic function.

Set up and solve an equation = 1, to ensure a function is a CRV

Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix. 

Solve a trigonometric equation

Solve a trigonometric equation involving a conversion to tangent by division by cosine.

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. 

Some quadratics are to be solved by factorising