Questions to test if the student knows the inverse of fractional power or root (and how to solve equations that contain them). 

Solve a simple linear equation algebraically. The unknown appears on both sides of the equation.

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

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

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 $a,\;b,\;c,\;d$.

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.

Basic solving of linear equations

Solving 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.

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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.

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.

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.

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

Students are asked to solve two simulatineous linear equations in an application of mixing two liquids to arrive at a given final volume and concentration. Students are expected to write up working for their solution and upload it seperately. Final volume, final concentration and concentrations of each solution are randomised.

The proportion of the sodium carbonate, $p$, which has dissolved by time $t$ seconds is given by the formula $ p=\frac{bt-at^2}{c}$. The aim is to calculate the proportion of sodium carbonate in a solution at a given time and vice versa.

The student must solve a pair of simultaneous equations in $x$ and $y$.

The variables are generated backwards: first $x$ and $y$ are picked, then values for the coefficients of the equations are chosen satisfying those values.

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

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.

Given an equation with variable x in the power on two different bases, students must solve for x. Hints are included in the question to aid the student as needed.

Given an equation where x is the base of a log term, the student must solve for x. Hints are included in the question to aid the student as needed.