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.

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

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.

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

Student needs to solve a quadratic equation to calculate time taken for a diver to hit the water after diving from a diving board. Height of the board and initial upward velocity of the diver are randomly generated values. student needs to know that surface of the water is height 0, and only positive root of quadratic has physical meaning. Question is set to always give one positieve and one negative root.

Real numbers $a,\;b,\;c$ and $d$ are such that $a+b+c+d=1$ and for the given vectors $\textbf{v}_1,\;\textbf{v}_2,\;\textbf{v}_3,\;\textbf{v}_4$ $a\textbf{v}_1+b\textbf{v}_2+c\textbf{v}_3+d\textbf{v}_4=\textbf{0}$. Find $a,\;b,\;c,\;d$.

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 system of simultaneous congruences using the Chinese Remainder Theorem.

An explore mode question which allows you to write a solution straight away, or break it down into steps.

After solving a system of three congruences, you can ask for a new problem with more congruences.

Solve a problem using a linear equation.

This question tests the students ability to factorise simple quadratic equations (where the coefficient of the x^2 term is 1) and use the factorised equation to solve the equation when it is equal to 0.

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

Use the parallelogram rule to solve a force triangle.

Solving linear equations

Basic solving of linear equations

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.

Solve a random oblique triangle for sides and angles.

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Resolver una ecuación de 1er grado sin fracciones

Resolver una ecuación de 1er grado sin fracciones

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.

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

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

Resolver una ecuación de 1er grado con fracciones

An economic dispatch problem with three generators. The steps help the students to solve this using lagrangian multipliers. This question is designed to allow students studying economic dispatch to practice solving the problem.

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.

Solve linear equations with unknowns on one. Including brackets and fractions.

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

Students need to solve a quadratic equation and recognise that only the positive root has physical significance. Roots are randomised with one always negative and one positive. Equation can be factorised fairly easily or the quadratic formula can be used to find the solution. Advice gives solution by factorisation.

Simultaneous equation problem as circuit analysis to find unknown currents. Students need to solve the equations and type in the solutions for each variable. Advice is given in terms of solution by elimination.