Expanded Calculator Capabilities for Efofex Parameters

The built-in calculator provides a large proportion of the capabilities of Efofex Parameters. The ability to type:

{3 sin 20}

and have the expression automatically calculated is crucial to most parametized questions.

Recently we improved the capabilities of the built-in calculator in two major ways.

Improved Exact Value Calculations

The calculator can now produce exact values for expressions like {$x^5} if $x is already an exact value like 2/3.

Combinations and Permutations

The calculator can now calculate expressions involving combinations and permutations like {5C2} and {7P3}

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New Sequence Command for Efofex Parameters

If you are using Efofex Parameters, you are almost certainly using the range command.

$y=range(1, 20, 0.5)

This command will produce a random value, between 1 and 20, going up in 0.5, every time you regenerate parameters. The values that are produced might, for example, go 5.5, 7, 12, 18.5, 20, 4, 1.5… The range command is one of the main ways of adding variation to your questions.

The new sequence command works in almost exactly the same way.

$y=sequence(1, 20, 0.5)

This command will produce a value from exactly the same set of values as the previous range command. The only difference is that the numbers will be generated sequentially every time you regenerate. They values might be 17.5, 18, 18.5, 19, 19.5, 20, 0.5, 1, 1.5…

We have found this to be useful for some questions and wanted to make the facility available for everyone.

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New Greek (letter) Command

We have added a new Greek letter command to Efofex parameters. You can now define a parameter like:

$x=greek()

This will randomly select a Greek letter from a list of acceptable letters (excluding letters like pi which have specific meanings). In this case $x might be turned into al, ga or rh. This allows you to create algebraic and geometric questions with varying Greek letters.

If you define multiple Greek letters in one set of parameters, the letters will always be sequential.

$x=greek()
$y=greek()
$z=greek()

You might end up with the three Greek letters being be, ga and de.

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New ToEnglish and ToEnglishCap commands for the Inline Calculator

Often, when writing a question, you will want to include a small number in a sentence

“A bag contains five red and three blue marbles”

Creating these sorts of questions using parameters has been difficult as the parameter system only works in numerals.

The ToEnglish command allows you to turn numeric parameters into words which can be used in your Word document. In the example above, you might have created two parameters, $r and $b, which contain the number of red and blue marbles. If you just use $r and $b in your text…

A bag contains $r red and $b blue marbles

You will see…

A bag contains 5 red and 3 blue marbles”

You can turn these numbers into words by typing

A bag contains {toenglish($r)} red and {toenglish($b)} blue marbles

The ToEnglishCap command operates in exactly the same way but capitalises the first letter of the output for use at the beginning of sentences.

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New RangeEx and PrimeEx Commands

We have added two commands to Efofex Parameters that allow you to create algebraic questions with less hassle.

Often, you will want to create a question that operates with both positive and negative numbers, but you need to exclude 0 and maybe 1 and -1. For example you might want to create a question where the parameter is the used as the denominator of a fraction and need to exclude zero.

The RangeEx and PrimeEx commands allow you to create sets of possibilities that satisfy this need.

For example:

$p=rangeex(2,5) will select a value for $p from the set of values {-5, -4, -3, -2, 2, 3, 4, 5}

Notice that the numbers from 2 to 5 are included as well as the associated negative values. The values -1, 0 and 1 are excluded from the list.

The PrimeEx command operates in exactly the same way but is limited to prime numbers and their negatives.

$p=primeex(2,10) will select a value for $p from the set of values {-7, -5, -3, -2, 2, 3, 5, 7}

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New Exact Display Mode and Command

We have added a new exact display mode to Efofex parameters.

We have also added the ability to select the display mode from the Parameters toolbar in FX Equation.

Changing Display Modes

When you set FX Equation to the Exact display mode, rational numbers will be displayed as simplified fractions and surds can also be displayed.

Various Calculations in Exact Mode

If you create a calculation that parameters cannot resolve exactly, the result will be shown as a decimal. You also have the option to display exact values involving surds using only prime surds. For example, the result of the last calculation above can be shown like this.

We have also added an exact command that can display the exact result of just part of a calculation. This is useful if you need the overall display style to not be set to exact.

In the example above, the overall display style is set to decimal and we have included the exact command only for the final calculation.

The exact display style and command make creating some solutions much simpler.

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New Factor Command

We have added another way to define a parameter

$a=factor(value)
$a=factor(value,low,high)

When you regenerate a parameter defined with a factor command, $a will be allocated a random value selected from the factors of the number you have selected.

For example

$a=factor(72) will mean that $a is randomly selected from the list {1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72}

The low and high values (which are optional) allow you to restrict the factors selected.

$a=factor(72,10,40) will mean that $a is randomly selected from the list {12, 18, 24, 36}

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New Pronumerals Command

We have added a new pronumerals command to Efofex parameters. You can now define a parameter like:

$x=pronumeral()

This will randomly select a pronumeral from a list of acceptable pronumerals. In this case $x might be turned into a,b,c,… x,y,z with some options (like i and o) omitted. This allows you to create algebraic questions with varying letters.

If you define multiple pronumerals in one set of parameters, the pronumerals will always be sequential.

$x=pronumeral()
$y=pronumeral()
$z=pronumeral()

You might end up with the three pronumerals being a, b and c OR x, y and z OR f, g and h for example.

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Introducing FX Library (Beta)

As we have been working with the new parameter system to create self-modifying documents, we have created a small library of documents which would be useful for all teachers. Work on the library is slow at the moment (mainly because we keep finding ways of improving the system!) but will accelerate as the parameter system becomes more refined.

In the long run, we want the library to become a massive resource of pre-written materials, most of which will be parametised, that will be available to all FX Draw Tools subscribers. Imagine being able to access tens of thousands of questions, all able to self-modify using parameters, including fully worked solutions. We are very excited about it!

As an Efofex Insider subscriber, we are giving you early access to the library. At the moment there are only about 40 documents available but they are free to use and you can begin to see the full power of the parameters system.

You can view the library at

FX Library

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New “No Repeats” Option on Parameters

As we have been creating questions with the new parameter system, we noticed that we were often seeing issues that were caused by a parameter value repeating. For example, if we created the following parameters…

$p=range(1,10)
$q=range(1,10)

We usually wanted the variability but did NOT want the two parameters to be the same value.

We have now added a No Repeats option to the parameter screen to address this issue. No Repeats is on by default and just prevents $p and $q from being assigned the same value. It has greatly simplified the creation of many questions.

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