Manipulation of algebraic fractions

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 positive gradient.

Generates two sets of matrices that can be added and asks the student to add them. Will ensure that the dimensions in part a) are different to the dimensions in part b) to offer some variety.

Generates two sets of matrices that can be added and asks the student to add them. Will ensure that the dimensions in part a) are different to the dimensions in part b) to offer some variety.

Several problems involving the multiplication of fractions, with increasingly difficult examples, including a mixed fraction and a squared fraction. The final part is a word problem. 

Calculating the integral of a function of the form $ax^2 \cos(bx)$ using integration by parts.

Calculating the integral of a function of the form $\frac{c}{(x+a)(x+b)}$ using partial fractions.

Rewrite the expression $\frac{mx^2+nx+k}{(x+a)(x^2+bx+c)}$ as partial fractions in the form $\frac{A}{x+a}+\frac{Bx+C}{x^2+bx+c}$.

Factorise an expression of 2 or 3 terms where the gcd is a letter times a number. Part of HELM Book 1.3.4

Find all forces on a two-part, symmetrical frame supporting a load. 

A demo of the mathematical expression part and its options.

Part (a) - dividing a total quantity given a ratio

Part (b) - given the value of one part of the ratio to find the total quantity.

Public

Example showing how to mark a "choose one from a list" part where the student has to pick the range a given number lies in.

In the first part, the student is asked to enter dimensions of a box in a spreadsheet.

The values are extracted as a list of numbers by changing the interpreted_answer note in the first part's marking algorithm, and the calculated volume is used as the answer to the second part, through adaptive marking.

Elementary examples of multiplication and addition of complex numbers. Four parts.

Asks students to find the partil fraction decomposition for a rational function Denominator is a quadratic with distinct factors.

Example of an explore mode question. Student is given a 3x3 matrix and is asked to find the characteristic polynomial and eigenvalues, and then eigenvectors for each eigenvalue. The part asking for eigenvectors can be repeated as often as the student wants, to be used for different eigenvalues.

Assessed: calculating characteristic polynomial and eigenvectors.

Feature: any correct eigenvalue will be recognised by the marking algorithm, even multiples of the obvious one(s) (which can be read off from the reduced row echelon form)

Randomisation: Not randomised, just using particular matrices. I am still working on how to randomise this for 3x3; a randomised 2x2 version exists. I have several different versions for 3x3 (not all published yet), so I could make a random choice between these in a test.

The implementation uses linear algebra functions such as "find reduced echelon form" or "find kernel of a reduced echelon form", from the extension "linalg2".

This is a copy of a question from the Numbas demos project, with references to the editor removed.

The student is shown a plot of a mystery function. They can enter values of $x$ check, within the bounds of the plot.

They're asked to give the formula for the function, and then asked for its value at a very large value of $x$.

A plot of the student's function updates automatically as they type. Adaptive marking is used for the final part to award credit if the student gives the right value for their incorrect function.

Split $\displaystyle \frac{ax+b}{(cx + d)(px+q)}$ into partial fractions.

Find $\displaystyle\int \frac{ax+b}{(x+c)(x+d)}\;dx,\;a\neq 0,\;c \neq d $.

Split $\displaystyle \frac{ax+b}{(cx + d)(px+q)}$ into partial fractions.

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Straightforward solving linear equations question.

Adapted from 'Simultaneous equations by substitution 2 with parts' by Joshua Boddy.

A demo of the matrix entry part and its options.

A few questions which show off the new matrix entry part.

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.

Multiplication and addition of complex numbers. Four parts.

Oefeningen:

BASIS: Maak een extra "part" aan, waar om het product van de twee breuken gevraagd wordt.

BASIS: Zoek uit waar typische_fout voor dient (bij de variabelen) en hoe die typische fout dan effectief gesignaleerd wordt.

GEMIDDELD: Zorg dat geen/enkel (jouw keuze) noemers voorkomen die geen gemeenschappelijke deler hebben. (Hint: gcd(a,b) kan een hulp zijn, met een for-loop.)