Given a graph of a line of the form $y=ax+b$ where $a$ and $b$ are integers, find the equation of the line. 

Given a graph of a line of the form $y=mx+b$ where $m$ and $b$ are integers, find the equation of the line. 

Rearrange formula

This question uses a "formatted text template" variable to define a long passage of text which is shown to the student after they submit a part. A custom marking algorithm adds the text as a comment after the standard marking algorithm has finished.

This question uses the linear algebra extension to generate a system of linear equations which can be solved.

We want to produce an equation of the form $\mathrm{A}\mathbf{x} = \mathbf{y}$, where $\mathrm{A}$ and $\mathbf{y}$ are given, and $\mathbf{x}$ is to be found by the student.

First, we generate a linearly independent set of vectors to form $\mathrm{A}$, then freely pick the value of $\mathbf{x}$, and calculate the corresponding $\mathbf{y}$.

To generate $\mathrm{A}$, we generate more vectors we need, then pick a linearly independent subset of those using the subset_with_dimension function.

Apply the quadratic formula to find the roots of a given equation. The quadratic formula is given in the steps if the student requires it.

Convert Index form into an Ordinary number

Objetivo: Resolver ecuaciones de segundo grado de la forma $x^2+bx+c=0$ que se pueden factorizar.

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Alle Beispiele des Tutorials in der formativen Fassung (man kann neue Fragen generieren und sich direkt Lösungen anzeigen lassen)

Template question. The student is asked to perform a two factor ANOVA to test the null hypotheses that the measurement does not depend on each of the factors, and that there is no interaction between the factors.

Rechnen mit der Näherungsformel und exakt.

Template question. The student is asked to perform a two factor ANOVA to test the null hypotheses that the measurement does not depend on each of the factors, and that there is no interaction between the factors.

Find the common ratio of a given geometric sequence, write down the formula for the nth term and use it to calculate a given term in the sequence.

The student is asked to factorise a quadratic $x^2 + ax + b$. A custom marking script uses pattern matching to ensure that the student's answer is of the form $(x+a)(x+b)$, $(x+a)^2$, or $x(x+a)$.

To find the script, look in the Scripts tab of part a.

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Crear una tabla de verdad para una expresión lógica de la forma :

                $( a \ {op1} \ b) \ {op2} \ (c \ {op} \ d) \ {op4} \ e $

donde cada una de $a, \; b, \; c, \; d, \; e, \; f $ puede ser una de las variables booleanas $ p, \; q, \; \neg q, \; \neg p $ y cada uno de los operados $\{op}$  puede ser uno de los operadores $\lor, \; \land, \; \to$.

Create a truth table for a logical expression of the form $(a \operatorname{op1} b) \operatorname{op2}(c \operatorname{op3} d)$ where $a, \;b,\;c,\;d$ can be the Boolean variables $p,\;q,\;\neg p,\;\neg q$ and each of $\operatorname{op1},\;\operatorname{op2},\;\operatorname{op3}$ one of $\lor,\;\land,\;\to$.

For example: $(p \lor \neg q) \land(q \to \neg p)$.

The student's answer is a fraction of two polynomials. First check that the student's answer is a fraction, then check that the numerator is of the form $x+a$.

To find the script, look in the Scripts tab of part a.

Rechnen mit der Näherungsformel und exakt.

Horizontal and vertical shifts and scales of a random cubic spline

A graph of $f$ is drawn. Graph of a transformed version of $f$ is to be sketched, by dragging various points around.

A graph of $f$ is drawn. Graph of a transformed version of $f$ is to be sketched, by dragging various points around.

A graph of $f$ is drawn. Graph of a transformed version of $f$ is to be sketched, by dragging various points around.

A graph of $f$ is drawn. Graph of a transformed version of $f$ is to be sketched, by dragging various points around.

A graph of $f$ is drawn. Graph of a transformed version of $f$ is to be sketched, by dragging various points around.

A graph of $f$ is drawn. Graph of a transformed version of $f$ is to be sketched, by dragging various points around.

A graph of $f$ is drawn. Graph of a transformed version of $f$ is to be sketched, by dragging various points around.