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• Standard Form Practice
Has some problems
Question
Finding surface of a sphere and writing value in standard form
• Question

Find the reactions of a rigid body (a truss) at a pin and roller.  All loads are either horizontal or vertical.

• Exam (1 question)
This is to demonstrate an issue with choose one from a list question.
• Question

Rigid body equilibrium problem.  Easiest to solve by replacing forces on the perimiter of the pulley with equivalent forces at the axle.

• Question

Determine the reactions supporting a cantilever beam carrying concentrated forces and moments.

• Question

Given three vectors with integer components, find the corresponding magnitude and direction.

• Question

Multiplication and division of upper and lower bounds.

• Question

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

• Question in Demos

No description given

• Construct a stem-and-leaf plot
Has some problems
Question

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.

• Find gradient of scalar field
Has some problems
Question

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

Should include a warning to insert * between multiplied terms

• Question

Find the stationary points of the function: $f(x,y)=a x ^ 3 + b x ^ 2 y + c y ^ 2 x + dy$ by choosing from a list of points.

Inputting the values given into the partial derivatives to see if 0 is obtained is tedious! Could ask for the factorisation of equation 1 as the solution uses this. However there is a problem in asking for the input of the stationary points - order of input and also giving that there is two stationary points.

• Cartesian equation of a plane
Has some problems
Question

A plane goes through three given non-collinear points in 3-space. Find the Cartesian equation of the plane in the form $ax+by+cz=d$.

There is a problem in that this equation can be multiplied by a constant and be correct. Perhaps d can be given as this makes a,b and c unique and the method of the question will give the correct solution.

• Question

Find the Cartesian form $ax+by+cz=d$ of the equation of the plane $\boldsymbol{r=r_0+\lambda a+\mu b}$.

The solution is not unique. The constant on right hand side could be given to ensure that the left hand side is unique.

• Question

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

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

• Find the angle between planes
Has some problems
Question

Find angle between plane $\Pi_1$, given by three points, and the plane $\Pi_2$ given in Cartesian form.

The calculation of $cos(\alpha)$ at the end of Advice has fractionNumbers switched on and so the result is presented as a fraction, which can be misleading. Best if calculation is followed through without using fractionNumbers.

• Question

Find minimum distance between a point and a line in 3-space. The line goes through a given point in the direction of a given vector.

The correct solution is given, however the accuracy of 0.001  is not enough as in some cases answers near to the correct solution are also marked as correct.

• Question

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.

• Question

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.

• Question

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.

• Question

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.

• Question

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

Should warn that multiplied terms need * to denote multiplication.

• Question

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.

• Question

Curl of a vector field.

Should warn that multiplied terms need * to denote multiplication.

• Question

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.

• Question

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.

• Question

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.

• Question

No description given

• Transportation problems
Has some problems
Exam (3 questions)

No description given

• Exam (5 questions)

A collection of true/false questions aiming to reveal misconceptions about concepts encountered in a first year pure maths course.