Finding the confidence interval at either 90%, 95% or 99% for the population variance of a sample. $\chi^2$ tables are used. A single scenario is given.

Fairly simple questions using differentiation "power rule" and "sum or difference rules" to differentiate single term functions and polynomials.

Some co-efficients and indices can be negative and/or fractional.

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.

Students are asked to move an x-axis slider representing standard deviation on a normal distribution to make the area between (mean - slider value) and (mean + slider value) equal to a certain percentage. The 3 possible percentages correspond to the mean plus or minus 1, 2 or 3 standard deviations.

Friction

Students are asked to move an x-axis slider on a normal distribution to make the area to the left of the slider equal to a certain percentage. The 6 possible percentages correspond to the mean plus or minus 1, 2 or 3 standard deviations.

Finding the modulus and argument (in radians) of four complex numbers; the arguments between $-\pi$ and $\pi$ and careful with quadrants!

Find modulus and argument of two complex numbers. Then use De Moivre's Theorem to find positive powers of the complex numbers.

Find modulus and argument of the complex number $z_1$ and find the $n$th roots of $z_1$ where $n=5,\;6$ or $7$.

Find the derivative of a function of the form $y=ax^b$ using a table of derivatives.

Factorise $\displaystyle{ax ^ 2 + bx + c}$ into linear factors. 

Given a generating matrix for a linear code, give a parity check matrix

Volume of a tetrahedron using integrals

Calculating the area enclosed between a linear function and a quadratic function by integration. The limits (points of intersection) are not given in the question and must be calculated.

Inputing Integrals tutorial

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.