Determine the forces in the pistons of a hydraulicly operated excavator.

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End of chapter exercises for Engineering Statics: Open and Interactive 

Determine expressions for internal shear and bending moment as a function of $x$ for a beam with two vertical loads.

This shows how to take an expression given by the student and plot the implicit curve of points where it equals zero.

Student calculates $\bar{y}$ for a triangle.  Must use similar triangles get element $dA$.

Find the area, first moment of area, and coordinates of a general spandrel.  The area may be above or below the function.

When saving the data necessary to resume an attempt, Numbas only saves the values of variables which use the random number generator.

If you naively generate a large random sample in one variable, it'll be marked as a source of randomness so Numbas will save every value in the sample. Loading this value when you resume the attempt can be very slow.

Instead, you can generate a seed value in one variable and then use it with the seedrandom function in the variable that stores your random list. Only the value of the seed needs to be saved.

The diagram contains a line and a hidden glider on that line.

The JavaScript preamble adds a callback which shows the glider when the question advice is displayed.

Shows how to use the lpad function to format a time in HH:MM format so that leading zeros are used for numbers less than 10.

The CSS preamble adds a vertical line down the input for part b, to separate the two parts of the matrix.

Locate the centroid of a rectangle, triangle, and semi-circle on a coordinate grid.

A custom marking algorithm on the spreadsheet part changes it to interpret quantities in cells, so they can be compared to the expected answer.

In real use, you'd probably want more sophisticated logic, to give better feedback or to allow partial marks for different units, like the "quantity with units" part type does.

Find the unit vectors in the direction of four 3-dimensional vectors. Three of the vectors are given, and the fourth is expressed as a linear combination of two of the other vectors.

Find the centroid of a shape made up of a rectangle and two triangles.

Find the centroid of a shape made from a rectangle, triangle, and circle.

Draws a triangle based on 3 side lengths.

Simple Hertz contact without friction.

This question tests students knowledge of basic matrix arithmetic.

This question contains information on how Numbas works, from the beginning of an exam to the end.

Note: it was written for students who access Numbas exams through the Numbas LTI provider. Some of the information does not apply to standalone exams, or those delivered through a generic SCORM player.

HELM Book 1.1.5 exercises

Calculating the derivative of a function of the form $ax^n \ln(bx)$ using the product rule.

Do not use this: adaptive marking is the best way to access the student's answer to another part.

Shows how to retrieve the student's answer to another part from a custom marking script.

You can use LaTeX in marking comments, but remember to escape backslashes!

series of R and L and C

find Z (mag and Phase)

step find Xl

given Voltage and loads calculated all the line currents

Calculating the derivative of a function of the form $\frac{(x-a)^2}{bx}$, finding its stationary points and determining their nature.

Find the derivative of a function of the form $y=a \sin(bx+c)$ using a table of derivatives.

Practice using the log rules to add and subtract logarithms

Solve equations involving logs and exponential functions, by using inverse operations.