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

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

Homework set. Find the forces in truss members using the method of joints.

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.

This question tests learner's knowledge of the inverse matrix method for a 3x3 matrix.

Solve for $x$ and $y$:  \[ \begin{eqnarray} a_1x+b_1y&=&c_1\\   a_2x+b_2y&=&c_2 \end{eqnarray} \]

The included video describes a more direct method of solving when, for example, one of the equations gives a variable directly in terms of the other variable.

In four parts, the student builds up the definition of a class representing a rectangle. First they write the constructor, then add methods to compute area and perimeter.

In the final part, they must use the methods to write a function which determines if a rectangle's area is larger than its perimeter.

This question gives the student the formula for the charge on a capacitor as a function of time then asks them to find the value of k, the exponential constant given other values and hence write out the formula for the given case. A custom function (in Extensions & scripts) extracts the student's formula and plots it on a JSXGraph object in the question. The student is then asked to evaluate the function at a given point using the plot or other methods. The value of the capacitor (Q_0), time (t) and charge at time t are randomised as is the value at which the formula is to be evaluated.

Simultaneous equations question. values for the coefficients are generated to be small numbers, random values are generated for the weights and the resultant energies are calculated for the question. Student needs to solve equations to find coefficients. Advice gives solution using method of elimination.

The subtraction algortihm using the borrow and pay back method with integers.

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.

Find the reactions of a rigid body (a triangular plate) at a pin and roller, using the three-force body principle.

The student is asked to calculate a division by the method of long division, which they should enter in a grid.

The process is simulated and the order in which cells are filled in is recorded, so the marking feedback tries to identify the first cell that the student got wrong, or should try to fill in next.

They're asked to give the quotient as a plain number in a second part, to check that they can interpret the finished grid properly.

Given three vectors, arrange them in a tip to tail arrangement using geogebra, then estimate the magnitude and direction of their resultant.

Homwork Set.  Covers graphical, and trigonometric methods of vector addition.

Different methods of loading a geogebra applet.

Find forces required to hold a particle in equilibrium when subjected to a downward load.  Directions of the reactions are given.  

Questions on integration using various methods such as parts, substitution, trig identities and partial fractions.

Practice question solving linear homogeneous second order differentials using the auxiliary equation 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 model and solve Integer Programming problems by Branch and bound method

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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.

LP: 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 Linear Programming problems by applying Geometric method.