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Long division of a quartic by a quadratic

Quotient and remainder, polynomial division.

Uses JSXGraph to generate a plot for a cubic, with given critical points, along with three other incorrect graphs with modified properties. JSXGraph code is commented.

Questions involving various techniques for rearranging and solving quadratic expressions and equations

Determine the largest possible domain of a rational function.

Determine if a function is odd, even or neither. 

Determine the correct interval notation for various sets.

$A$ a $3 \times 3$ matrix. Using row operations on the augmented matrix $\left(A | I_3\right)$ reduce to $\left(I_3 | A^{-1}\right)$.

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Small demo using the JME implementation of JSXGraph inline in a multiple choice question. This version uses a JME variable to store the expressions and then calls a function wherever a plot is required.

coba saja

En Teoría de la Información, se provee una matriz de probabilidades conjuntas P(ai,bj) de un canal 2x2.

Se trata de hallar la matriz del canal.

Small demo using the JME implementation of JSXGraph inline in a multiple choice question.

This is my first trial of Numbas.

This is the test description. Placeholder text can be changed per test.

English sentences are given and for each the appropriate proposition involving quantifiers is to be chosen. Also choose whether the propositions are true or false.

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This question is the one described in method 1 of the example "Apply a standard integral" in the Numbas documentation.

The student is shown a randomly chosen function to integrate. The function is one of $e^{kx}$, $x^k$, $\cos(kx)$, $\sin(kx)$, with $k$ a randomly chosen integer.

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Customised for the Numbas demo exam

Factorise $x^2+cx+d$ into 2 distinct linear factors and then find $\displaystyle \int \frac{ax+b}{x^2+cx+d}\;dx,\;a \neq 0$ using partial fractions or otherwise.

Video in Show steps.

Demonstration of adaptive marking: the student must first add up the number of apples to buy, then work out how much that would cost. Adaptive marking carries an incorrect number of apples into the cost calculation.

Given the gradient of a slope and the coefficient of friction for a mass resting on it, use the equations of motion to calculate how it moves.

Includes a GeoGebra rendering of the model.