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The derivative of $\displaystyle x ^ {m}(ax^2+b)^{n}$ is of the form $\displaystyle x^{m-1}(ax^2+b)^{n-1}g(x)$. Find $g(x)$.

Multiple response question (3 correct out of 6) re properties of convergent and divergent sequences. Selection of questions from a pool.

Multiple response question (4 correct out of 8) covering properties of convergent and divergent sequences and boundedness of sets. Selection of questions from a pool.

Differentiate

\[ \sqrt{a x^m+b})\]

Differentiate $\displaystyle (ax^m+bx^2+c)^{n}$.

Differentiate $\displaystyle \ln((ax+b)^{m})$

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Find $\displaystyle I=\int \frac{2 a x + b} {a x ^ 2 + b x + c}\;dx$ by substitution or otherwise.

Preparing solutions to given concentrations/dilutions.

Given a generator matrix for a linear code, write a parity check matrix, compute the syndrome of a word, and decide if it's a codeword.

Calculation of modulus, argument, multiplication by complex conjugate, given two complex numbers.

Find the solution of a constant coefficient second order ordinary differential equation of the form $ay''+by=0$. Complex roots.

Linear program described in words. Student must write out constraints as equations in standard form, then identify the optimal solution in a finished simplex tableau.

Express $\displaystyle a \pm  \frac{c}{x + d}$ as an algebraic single fraction.

Given  $P(A)$, $P(A\cup B)$, $P(B^c)$ find $P(A \cap B)$, $P(A^c \cap B^c)$, $P(A^c \cup B^c)$ etc..

Compute the information rate and minimum distance of some binary codes.

Curl and divergence of a vector field.  Determine whether the vector field is irrotational or solenoidal.

Given random set of data (between 13 and 23 numbers all less than 100), find their stem-and-leaf plot.
This version of the question asks for 10 fields to be filled rather than the full 25, although the question statement asks for 25. I am sure that the first version asked for all 25.

Correct an error in a received message which was encoded using Hamming's square code

Compute the word length, minimum distance and dimension of some given Hamming codes.

Write down the lexicographic parity check matrix for a Hamming code, and correct two received codewords.

Write down a lexicographic parity check matrix for a Hamming code and correct two received codewords.

Decode a message of two codewords encoded using Hamming's [7,4] code, with at most one error per codeword.

Find upper and lower bounds on the number of codewords in three maximal codes given their codeword lengths and minimum distances.

Uses Hamming, Singleton and Gilbert-Varshamov bounds.

List all vectors in a spanning set.

(repeated 3 times)

When are vectors $\boldsymbol{v,\;w}$ orthogonal?

Part b) is not answered in Advice, the given solution is for a different question.