Newcastle University Mathematics and Statistics

Given a linear programming problem in standard form, write down the dual problem.

Given a linear programming problem in standard form, write down the dual problem.

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

Questions used in a university course titled "Group theory".

The questions deal with permutations written in cycle or two-line notation.

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

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.

4 questions on using partial fractions to solve indefinite integrals.

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.

Questions used in a university course titled "Coding theory".

Ready to use as all 20 questions are stated as ready to use.

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.

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.

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

List all vectors in a spanning set.

(repeated 3 times)

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