Solving an inequality of the form ax+b < c where a is negative.

Solving an inequality of the form ax+b < c

Solving an inequality of the form ax+b < c

Solving an inequality of the form x/a < b

Solving an inequality of the form ax < b

Solving an inequality of the form x+a < b

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

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. 

Use the parallelogram rule to solve a force triangle.

Solve a random oblique triangle for sides and angles.

Homework set.  Trusses solved using the method of sections

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

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

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.

Solve a logarithmic equation

Solve for an angle which will result in equilibrium for a triangle subjected to three couples.   A trial and error solution is recommended.

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.

Two forces act on a bell crank. This problem has two unknown magnitudes and an unknown direction which makes it tricky to solve by the equilibrium equation method.  

The solution is much simpler if three force body principle is used.

A hand truck on wheels.  Easiest to solve by rotating coordinate system.

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

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

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

Solve for the internal force in three members of a truss.

Solve for the internal force in three members of a truss.

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

A cmprehensive set of questions covering the different ways to solve quadratics by factorising

Given the following three vectors $\textbf{v}_1,\;\textbf{v}_2,\;\textbf{v}_3$ Find out whether they are a linearly independent set are not. Also if linearly dependent find the relationship $\textbf{v}_{r}=p\textbf{v}_{s}+q\textbf{v}_{t}$ for suitable $r,\;s,\;t$ and integers $p,\;q$.