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Equation Exercise is an answer only oriented type of Exercise. The file was specifically designed for physics problems but can be used for any answer only exercises.

The file consists of three segments: the Header, the Text and the Calculations. The separator between them is the line with --- only. In particular, the file starts with ---.

Header

The header defines respectively fields:

  • type: EqEx (static for this type of exercise)

  • name: the name of the exercise

  • img: the name of exercise’s image (optional)

type: "EqEx"
name: "Sample name"
img: "image.jpg"

Text

The text is the exercise’s content with specified types and values of all the variables.

Such specification has the format:

  • variable name: begins with a letter and can consist of Latin alphabet letters (upper- and lowercase), numbers, some special characters (') and an underscore (one per name)
    Notice that all greek letters will be replaced with the corresponding symbol.

  • =

  • value: depends on the type of the variable, specified below.

  • unit: units of the scalar commonly used in physics. They can also consist of multiplied or rased to integer power subunits. / symbol indicates the denominator part and can be used only once per unit (a/b*c will be recognised as (a)/(b*c))
    Notice that units similar to 1/s should be written as /s. In addition deg will be replaced with Unicode’s °
    e.g. g=10m/s^2, W=20kg*m^2/s^2, f=5/s

Value

There are three types of variables in the EqEx format:

  • constant (numeric): variable has a predetermined value. The value is a number written in decimal notation (1, -0.5) or scientific notation (1.234e5, 1e-3)
    e.g. x=1e-5s

  • range: variable value is between predetermined boundaries. Arguments in the range are passed between [ and ] and are separated by ; (without any whitespace between).
    range format: [ minimal value ; maximal value ; step ]
    Notice that step is optional. When omitted, the value would be rounded to 3 significant figures.
    e.g. x=[0;5;1] would yield x= one of 0, 1, 2, 3, 4, 5

  • unknown: variable defined in the calculation part. All the unknowns are in query. Unknowns are defined by ? character instead of its value.
    e.g. x=?m/s

Calculations

Each line in the Calculations is a declaration (or redeclaration) of a variable. Auxilary variables can be declared and used in the equations underneath. Every variable in the query (unknown) must be declared in the Calculation segment.

Special-use character = splits the equation into the following parts:

  • variable name

  • =

  • mathematic expression

Mathematic Expression

Operations and functions supported:

  • arytmetic operations: +, -, *, /, ^

  • brackets: (, )

  • square root: sqrt

  • absolute value (|x|): abs

  • logarithmic functions: log/log10 (base 10), ln, log2

  • exponent function (ex): exp

  • trigonometry: sin, cos, tan/tg, cot/ctg

  • hyperbolic trigonometry: use -h suffix, e.g. sinh, tanh/tgh

  • trigonometry (argument in radians): use -r suffix, e.g. sinr, tanhr/tghr

  • inverse trigonometry: use a- prefix, e.g. asin, atanh/atgh

  • inverse trigonometry (value in radians): use -r suffix, e.g. asinr, atanhr/atghr

e.g. x=-5*sinr(3.14), y=sqrt(abs(x+1))^2, z=log2(2^10)/5.

Example

type: "EqEx"
name: "Velocity 1"
img: "velocity1_img.jpg"
---
A man walks s_1=[5;10;1]km East in t_1=2h and then s_2=[2;4;0.5]km West in t_2=1h. What is the man's average speed v_1=? and velocity v_2=? for the whole journey?
---
v_1=(s_1+s_2)/(t_1+t_2)
v_2=(s_1-s_2)/(t_1+t_2)