Calculation of the length and alternative form of the parameteric representation of a curve.

Calculations of the lengths of two 3D vectors, the distance between their terminal points, their sum, difference, and dot and cross products.

Parametric form of a curve, cartesian points, tangent vector, and speed.

Parametric form of a curve, cartesian points, tangent vector, and speed.

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

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

Determine if various combinations of vectors are defined or not.

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

Double integrals (2) with numerical limits

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.

Determine the correct parametric representation of a given curve.  Curve is randomly chosen from a set of 20.

The graph of the curve was not displayed on my machine.

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

No description given

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.

$x_n=\frac{an^2+b}{cn^2+d}$. Find the least integer $N$ such that $\left|x_n -\frac{a}{c}\right| < 10 ^{-r},\;n\geq N$, $2\leq r \leq 6$. Determine whether the sequence is increasing, decreasing or neither.

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

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

Should warn that multiplied terms need * to denote multiplication.

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.

Divergence of vector fields.

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.

Curl of a vector field.

Should warn that multiplied terms need * to denote multiplication.

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.

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.

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.

No description given

Two factor ANOVA example

Four questions on finding least upper bounds and greatest lower bounds of various sets.

Two-way ANOVA example, 5 subjects, 4 treatments.

No description given