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

Find all words with given Hamming distance from a given codeword.

Given a set of vectors, find a basis which generates their span as a subspace of $\mathbb{Z}_n$.

Given a matrix in the field $\mathbb{Z}_n$. By reducing it to row-echelon form (or otherwise), find a basis for the row space of the matrix, as a list of vectors.

Given a set of codewords generating a code, write down a generator matrix, encode three data vectors, and decode one codeword.

Given a set of codewords generating a code, give a generating matrix, encode three data vectors, and decode one codeword.

Given a set of codewords generating a code, give a generating matrix, encode three data vectors, and decode one codeword.

Compute the minimum distance between codewords of a code, given a parity check matrix.

Divergence of vector fields.

Find $\displaystyle \int_{\Gamma} \left(x+y \right)\;dx+\left(y-x\right)\;dy,\;\Gamma$ is the line from $(0,0)$ to $(a,b)$.

Cartesian form of the parametric representation of a surface, normal vector, and magnitude.

Accuracy for part c) should be made more stringent as can be marked correct for an incorrect answer. Use a different sample range rather than 0 to 1 would help as would setting accuracy to something less than 0.001.

Determine if various combinations of vectors are defined or not.

Find the cosine of the angle between two pairs of 3D and 4D vectors.

The calculations and answers are correct, however the Advice should display the interim calculations of the lengths of vectors and their products to say 6dps. At present the student may be mislead into using 2dps at each stage - the instruction at the start of Advice is somewhat confusing.

Elementary operations on vectors; sum, modulus, unit vector, scalar multiple. 

Double integrals (2) with numerical limits

Unit normal vector to a surface, given in Cartesian form.

Cartesian form of the parametric representation of a surface, normal vector, and magnitude.

Gradient of $f(x,y,z)$.

Should warn that multiplied terms need * to denote multiplication.

Outward normals to the surfaces enclosing a region; volume of that enclosed region.

Outward normals to the surfaces enclosing a region; volume of that enclosed region.

Intersection points, tangent vectors, angles between pairs of curves, given in parametric form.

Find all points for which the gradient of a scalar field is orthogonal to the $z$-axis.

Should warn that multiplied terms need * to denote multiplication.

Curl of a vector field.

Should warn that multiplied terms need * to denote multiplication.

Find a unit vector orthogonal to two others.

Uses $\wedge$ for the cross product. The interim calculations should all be displayed to enough dps, not 3,  to ensure accuracy to 3 dps. If the cross product has a negative x component then it is not explained that the negative of the cross product is taken for the unit vector.

Find the unit vector parallel to a given vector.

Interim calculations in Advice should be presented in enough accuracy to ensure that the final calculations are to 3dps.

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Although the statement has 4 power stations and 3 pits, when the question is run sometimes 3 power stations are given and sometimes 4 pits.

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Multiple response question (4 correct out of 8) covering properties of convergent and divergent series and including questions on power series. Selection of questions from a pool.