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

The student is asked to factorise a quadratic $x^2 + ax + b$. A custom marking script uses pattern matching to ensure that the student's answer is of the form $(x+a)(x+b)$, $(x+a)^2$, or $x(x+a)$.

To find the script, look in the Scripts tab of part a.

This is supposed to demonstrate allowing one of two different free variables in the student's answer, but only marked as correct if the same free variable is used in all gaps. The custom marking algorithm should extend to any number of gaps, and one could add more alternative answers to allow for more free variable names. It doesn't allow just any free variable name.

Instructions to candidates:-

a)        questions are to be attempted

b)       Answer questions in the spaces provided 

d)       Approved calculators are allowed

e)        Marks for each question are shown

f)       The total mark for the paper is 100.

A quick implementation of certainty-based marking: the student's score depends on how they rated their certainty in their answer before submission.

Because Numbas doesn't allow negative marking at the moment, scores are shifted upwards, so a high certainty incorrect answer scores 0, and a high certainty correct answer scores full credit.

In this question, the correct answers can't be evaluated by substituting numbers for each of the variables.

Numbas can now infer the types of variables in the answers to mathematical expression parts, so questions like this can be marked.

The student must calculate the number of digits a given decimal number would have when written in a different base. Alternative answers catch some common mal-rules and give appropriate feedback.

Based on table 2 from "diagnosing student errors in e-assessment questions" by Philip Walker, D. Rhys Gwynllyw and Karen L. Henderson.

Numbas representation of the Metacentric Height fluid mechanics laboratory for first year Engineering students. 

Students should answer this question after completing the laboratory and the associated Excel template, including the relevant plots. 

The first question tests their capacity to correctly calculate metacentric heights, the remaining questions evaluate their graph interpretation skills. 

The assessment has been designed to take no more than 2 hours to complete. You must submit the test by 10:00 am (UK time) on 13th May. Once you start the test, it has to be completed by 2 hours.

When answering the exam you should observe normal exam conditions and must not communicate/collude with other students taking the paper. The work that you submit must be your own work. Should you encounter IT difficulties that significantly affect your ability to complete this exam or when uploading your answer(s) you may submit a PEC detailing these. 

Welcome the the first stats quiz! It's very short. 

• You have 25 minutes.
• There are 3 questions (with parts). The topics are measures of central tendency and measures of spread.
• Enter all of your answers and keep 2 decimal places. 
• Submit them as you go to make sure you don't carry mistakes. You can't change your answer once you've submitted it.
  

Write down on a sheet of paper the data you are given, along with your detailed calculations. Submit a picture on google classroom. 

Let me know if you have any questions!

Good luck!

This question contains a "choose several answers" part which has an "all-or-nothing" mark scheme: the student is only awarded marks if they tick all of the correct choices, and no incorrect choices.

Find the inverse of a composite function by finding the inverses of two functions and then the composite of these; and by finding the composite of two functions then finding the inverse. The question then concludes by asking students to compare their two answers and verify they're equivalent.

No description given

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..

Download a file and scan the values into R to obtain a numeric vector of values. Then use R to explore your numeric vector in order to find the answers to these questions.

SPSS fat absorption question. Student downloads one of several SPSS files and carries out some analysis in SPSS, before returning to enter the answers. The analysis is a one-way analysis of variance. If there is a difference in the levels of the factor then a post hoc test (Tukey's honestly significant difference) is used to determine which pairs of variables are significantly different. 

Find the inverse of a composite function by finding the inverses of two functions and then the composite of these; and by finding the composite of two functions then finding the inverse. The question then concludes by asking students to compare their two answers and verify they're equivalent.

Ask the student to find a matrix corresponding to a given rotation about the origin.

Then ask them to find the determinant. Their answer is marked against the matrix they gave, not just the correct one.

Finally, ask them to find the inverse of their matrix. Marking is against the matrix and determinant they gave.

Identify parts of statistical formulas, and answer questions about how changing one variable affects the statistic.

Numbas can now understand and use several different styles of notation for numbers.

This question shows off all the supported styles, both for display in text and in the answers to number entry parts.

This question shows how to ask for a number in scientific notation, by asking for the significand and exponent separately and using a custom marking algorithm in the gap-fill part to put the two pieces together.

Answers not in standard form, i.e. with a significand not in $[1,10)$, are accepted but given partial marks.

A "match choices with answers" part where the student either gets all the marks or none. Any incorrect choice is penalised with a huge negative mark, so they end up with the minimum mark of 0.

A mathematical expression part whose answer is the product of two matrices, $X \times Y$.

By setting the "variable value generator" option for $X$ and $Y$ to produce random matrices, we can ensure that the order of the factors in the student's answer matters: $X \times Y \neq Y \times X$.