Just showing how to use the stdev function from the stats extension to calculate the standard deviation of a list of numbers.

rebelmaths

Just showing how to use the stdev function from the stats extension to calculate the standard deviation of a list of numbers.

rebelmaths

This question assesses the students ability to find the expected number of times an event occurs given the probability of the event occurring for a single trial and the total number of trials.

Just showing how to use the stdev function from the stats extension to calculate the standard deviation of a list of numbers.

rebelmaths

Polar form of a complex number.

This question provides practice at adding, subtracting, dividing and multiplying complex numbers in rectangular form.

Practice to decide which quadrant a complex number lies in.

Calculating complex numbers raised to an natural number exponent

Find modulus and argument of the complex number $z_1$ and find the $n$th roots of $z_1$ where $n=5,\;6$ or $7$.

Complex number multiplication & division

Calculating the square root of a complex number using De Moivre.

modulus & argument of a complex number

A very simple algebraic fraction multiplied by a whole number. No cancelling is required by design. 

A whole number divided by a very simple algebraic fraction. No cancelling is required by design.

Used for LANTITE preparation (Australia). NA = Number & Algebra strand. Students are given the total cost, insurance fee and daily hire charge (all randomly generated). They need to calculate the number of days hired.

Used for LANTITE preparation (Australia). NA = Number & Algebra strand. Students are shown a personal income tax table and given a randomly generated taxable income. They are required to calculate the tax payable.

Used for LANTITE preparation (Australia). NA = Number & Algebra strand. The total amount raised and the number of participants is supplied (and both are randomly generated). Students must calculate the average per participant. 

Used for LANTITE preparation (Australia). NA = Number & Algebra strand. Students need to calculate the proportion of calls for one given emergency, after reading the number of calls, and total number of calls from the supplied infographic. There are 4 different versions of this question.

Convert a variety of numbers from decimal to standard index form.

Simple multiplication of complex conjugates. Complex numbers are of the form $a+bi$ where $a$ and $b$ are randomised between 1 and 9 inclusive. 

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Simple multiplication including multiples of 10, with answer that can be multiples of up to 1000.

Used for LANTITE preparation (Australia). NC = Non Calculator strand. NA = Number & Algebra strand. Students need to add two fractions with different denominators, then subtract the answer from 1. There are 9 different versions of this question.

A simple test for practicing division with remainder. Numbers are randomised, and ranges for divisor and quotient can be specified.

The student is asked to find the square root of an integer of the form $\pm n^2$. If the root is not real, they should enter "nan".

A custom marking algorithm extends the built-in one to deal with "nan".

There's some custom javascript to set the expected answer correctly. In the future this will be possible in the marking algorithm - see https://github.com/numbas/Numbas/issues/856

The student must enter a number in scientific notation, with separate boxes for significand and exponent. They only get the marks if both elements are correct.

Assesses multiplying numbers

In this demo question, you can see either 2 or 3 gaps depending on the variable \(m\), and the marking algorithm doesn't penalise for the empty third gap in cases when it is not shown.

Reason to use it: for vectors or matrices containing only numbers, one can easily use matrix entry to account for a random size of an answer. But this does not work for mathematical expressions. There we have to give each entry of the vector as a separate gap, which then becomes a problem when the size varies. This solves that problem. For this reason I've included two parts: one very simple one that just shows the phenomenon of variable number of gaps, and one which is more like why I  needed it.

Note that to resolve the fact that when \(m=2\), the point for the third gap cannot be earned, I have made it so that the student only gets 0 or all points, when all shown gaps are correctly filled in.

Note the use of Ax[m-1] in the third gap "correct answer" of part b): if you use Ax[2], then it will throw an error when m=2, as then Ax won't have the correct size. So even though the marking algorithm will ignore it, the question would still not work.

Bonus demo if you look in the variables: A way to automatically generate the correct latex code for \(\var{latexAx}\), since it's a variable size. I would usually  need that in the "Advice", i.e. solutions, rather than the question text.

In this demo question, you can see either 2 or 3 gaps depending on the variable \(m\), and the marking algorithm doesn't penalise for the empty third gap in cases when it is not shown.

Reason to use it: for vectors or matrices containing only numbers, one can easily use matrix entry to account for a random size of an answer. But this does not work for mathematical expressions. There we have to give each entry of the vector as a separate gap, which then becomes a problem when the size varies. This solves that problem. For this reason I've included two parts: one very simple one that just shows the phenomenon of variable number of gaps, and one which is more like why I  needed it.

Note that to resolve the fact that when \(m=2\), the point for the third gap cannot be earned, I have made it so that the student only gets 0 or all points, when all shown gaps are correctly filled in.

Note the use of Ax[m-1] in the third gap "correct answer" of part b): if you use Ax[2], then it will throw an error when m=2, as then Ax won't have the correct size. So even though the marking algorithm will ignore it, the question would still not work.

Bonus demo if you look in the variables: A way to automatically generate the correct latex code for \(\var{latexAx}\), since it's a variable size. I would usually  need that in the "Advice", i.e. solutions, rather than the question text.

Finding a matrix from a formula for each entry, which involves the row and column numbers of that entry. Randomized size of the matrices and formula.