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Een stelsel van drie eerstegraadsvergelijkingen met drie onbekenden oplossen. 

Trouver le nombre de nucléons/protons/neutrons à partir de la donnée des deux autres

Q1. True/false questions about basic facts.

Q2 and Q3. Velocity-time graphs are given with areas underneath them shaded. The area of the shaded regions are given. From this, changes in position, distances are to be calculated.

A graph is drawn. A student is to identify the derivative of this graph from four other graphs. There are four such questions.

Faire le lien entre la formule chimique d'un ion, sa charge électrique et le nombre d'électrons gagnés/perdus par l'atome dont il est issu.

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Use two points on a line graph to calculate the gradient and $y$-intercept and hence the equation of the straight line running through both points.

The answer box for the third part plots the function, which allows the student to check their answer against the graph before submitting.

This particular example has a 0 gradient.

Asks to determine whether or not 6 statements are propositions or not i.e. we can determine a truth value or not.

Matrices vermenigvuldigen

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Given a 3 x 3 matrix, and two eigenvectors find their corresponding eigenvalues. Also fnd the characteristic polynomial and using this find the third eigenvalue and a normalised eigenvector $(x=1)$.

This question shows a JSXGraph diagram above a mathematical expression input, containing a plot of the expression the student enters.

Exam for Maths 4, Review week 2025.

This question concerns the evaluation of the eigenvalues and corresponding eigenvectors of a 2x2 matrix.

Calcul de la concentration d'une solution fille à partir du protocole de préparation.

construction de l'image réelle ou virtuelle d'un objet plan par une lentille mince convergente

prise de mesures algébriques

Utiliser la relation de conjugaison d'une lentille mince convergente

Tester om studenten kan gjøre feilpropagering med \(\sqrt{\sum\left(\frac{\partial f}{\partial x_i}\delta x_i\right)^2}\)

Forbedring: overensstemmelse mellom siffer i størrelse og usikkerhet i input.

Used to asses ability to do basic kinetic energy calculations using US Customary units.  Student must convert given data into appropriate units then find specific energy, total energy and power in specified units.  Question randomizes mass, final speed and time to accelerate to final speed.  

Used to asses ability to do basic kinetic energy calculations using SI units.  Student must convert given data into appropriate units then find specific energy, total energy and power in specified units.  Question randomizes mass, final speed and time to accelerate to final speed.  

The purpose of this activity is to guide the student to understand how the simplex method works, and to then show how it can be applied through the method of tableaux. The focus is on understanding the mechanisms.

A random linear program with two variables is generated. This allows the student to visualise what happens as he applies the steps of the simplex method. 

It comprises four parts:

First part: visual intuition.

First we get the student to visually inspect the feasible polygon and move the point along its edges. The coefficients of the objective along each edge are shown, so they can see which edge provides an ascent direction, and which edge provides a descent direction. The student can then move the solution along edges until they reach an optimal point. 

Second part: algebraic intuition.

In this part, we introduce the student to the steps of the simplex method, by applying algebraic techniques they are familiar with, namely variable substitution. 

First, the student is asked to rewrite the constraints and the objective as equality constraints (for each constraint, a slack variable is added and an extra variable is added for the objective). This gives them an underdetermined linear system. 

Then, the student is guided through a sequence of substitution steps, where they choose which variable to substitute into the equations, and which equation to use to construct the substitution. Once the substitution is done, the student is then shown that this yields a solution at a different vertex of the polygon, and they can repeat the operation until the solution they have found is optimal.

By the end of this part, the student should have a good understanding of how the simplex algorithm works, as repeated application of operations like substitution/elimination, and why the pivot is chosen as it is.

Third part: method of tableaux.

The last part repeats the operations in the first part, but using the method of tableaux. The student is first asked to generate their tableau, from the linear equations they obtained at the start of Part 2. They will see that this is nothing but an augmented matrix. 

Then, the student is guided through a series of elimination steps. This is the simplex method as it is conventionally applied. The operation is repeated until a solution is attained. 

Fourth part: conclusion.

Once the student has completed all parts, they are led to a summary of what they did, to recapitulate the process they went through.

Limieten grafisch bepalen

Limieten grafisch bepalen

Limieten grafisch bepalen

Limieten grafisch bepalen

Limieten grafisch bepalen

Cofactors Determinant and inverse of a 3x3 matrix.

Applied calculation broken down in core calculation steps.