A variety of trigonometric equations which can be solved using inverse operations.

Find the eigenfunctions of an irregular Sturm–Liouville problem and hence solve an inhomogeneous boundary value problem by writing the solution as an eigenfunction expansion.

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

Solve linear equations with unknowns on one. Including brackets and fractions. Solutions may require rounding.

Homework set.  Rigid body equilibrium solved using the three-force body principle.

Solve linear equations with one unknown. Including brackets and fractions.

Solve linear equations with unkowns on both sides. Including brackets and fractions.

Solve an ODE by first writing it in canonical form.

Solve a random oblique triangle for sides and angles.

Rigid body equilibrium problem.  Easiest to solve by replacing forces on the perimiter of the pulley with equivalent forces at the axle.

Pulley supported by a cable, so the tension in the rope is constant.    Advice is a youtube video showing how to solve the problem.

Homework set.  Trusses solved using the method of sections

Use the parallelogram rule to solve a force triangle.

Solve linear equations with one unknown. Including brackets and fractions.

This question uses a Geogebra applet to solve a linear program with two variables using the graphical method. It contains three steps:

1. Construct the feasible area (polygon) by adding the constraints one by one. The students can see what happens when the constraints are added.
2. Add the objective function, and the level set of the objective value is shown, as well as its (normalised) gradient.
3. Compute the optimal solution by moving the level set of the objective around.

Solving a quadratic equation via factorisation (or otherwise) with the $x^2$-term having a coefficient of 1.

Solve linear equations with unkowns on both sides. Including brackets and fractions.

Solve linear equations with unkowns on both sides. Including brackets and fractions.

Solve linear equations with unkowns on both sides. Including brackets and fractions.

Classic problem of a vehicle parked on an incline.  Best solved by rotating the coordinate system.

Image Credit: https://svgsilh.com/image/34325.html  CC-0

Solving a quadratic equation via factorisation, with the $x^2$-term having a coefficient of 1.

Solve Truss by the method of joints.  The solution is simplified by recognizing symmetry.

Solving simple linear equations in $\mathbb{Q}$ and $\mathbb{Z}_n$ for $n= 13, \;17$ or $19$.

Use the simplex method to solve a linear program.

In this question the students have to solve a linear recurrence of order 1. The sequence is asked in recurrence form and the goal is to find its closed form.

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.

Copy the problem parameters into the handout provided and solve the Building Fabric heat loss problem by hand. Enter your answers into this quiz to get your score. Upload a copy of your written answer to the submission on Brightspace. Good Luck!

Questions to test if the student knows the inverse of an even power (and how to solve equations that contain a single power that is even). 

Questions to test if the student knows the inverse of an odd power (and how to solve equations that contain a single power that is odd).