3 Repeated integrals of the form $\int_a^b\;\int_c^{f(x)}g(x,y)\;dy \;dx$ where $g(x,y)$ is a polynomial in $x,\;y$ and $f(x)$ is a degree 0, 1 or 2 polynomial in $x$.

Calculate a repeated integral of the form $\displaystyle I=\int_0^1\;\int_0^{x^{m-1}}mf(x^m+a)dy \;dx$

The $y$ integral is trivial, and the $x$ integral is of the form $g'(x)f'(g(x))$, so it straightforwardly integrates to $f(g(x))$.

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Rolling a pair of dice. Find probability that at least one die shows a given number.

English sentences which are propositions are given and the appropriate logical expression chosen for the negation of the sentence.

English sentences which are propositions are given and for each the appropriate proposition  involving quantifiers is to be chosen. 

Write down the lexicographic parity check matrix and generator matrix for a Hamming code, which is the dual of a Simplex code, then determine if a given word is a codeword of the corresponding Simplex code.

Compute tables of Hamming distances in given codes, then determine which codes are equivalent.

Given a generating matrix for a binary linear code, construct a parity check matrix, list all the codewords, list all the words in a given coset, give coset leaders, calculate syndromes for each coset, correct a codeword with one error.

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A right-angled triangle is displayed either pointing left or right with one of the other angles and one of the sides given. Use SOH CAH TOA to find the side indicated with an x.

Find the reactions of a rigid body (a triangular plate) at a pin and roller.  The load is at an angle.

Esercizio che chiede di calcolare la distanza e il punto medio tra due punti di coordinate intere assegnate. La distanza è sempre un numero naturale.

Risolvi per $x$ e $y$:  \[ \begin{eqnarray} a_1x+b_1y&=&c_1\\   a_2x+b_2y&=&c_2 \end{eqnarray} \]

Cálculo de forma normal reducida por filas.

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Wybór rodzaju zmiennej (ilościowa lub jakościowa). 

Zadaniem studenta jest wyznaczenie miar pozycyjnych dla losowego zbioru 32 wartości.

A demo of the main new features in Numbas v5: explore mode, alternative answers and "Choose from a menu" question navigation.

All the answers in this question are equations. In order to mark each equation, Numbas needs to pick some values that satisfy the equation and some that don't, and check that the student's answer agrees with the expected answer.

Any equation with the same solution set as the expected answer will be marked correct.

Simple exercise in collecting terms in different powers of \(x\)

Factorise three quadratic equations of the form $x^2+bx+c$.

The first has two negative roots, the second has one negative and one positive, and the third is the difference of two squares.

Simple exercise in collecting terms in different powers of \(x\)

The answer to this question is a differential equation involving $y''$, $y'$ and $y$.

A variable value generator for $y$ ensures that the right values are tested to check that the student's answer is equivalent to the expected equation.

Sirve para usar con el muro de fracciones

A student selects a card from a deck of 52 and rolls a dice once.

rebelmaths

Find the tensions is a system of cables supporting two loads.

Match up equations with the corresponding lines on a graph.