Maths with QTI – Help Guide for Maths Entry Questions

This is intended as a simple guide to entering mathematical expressions as answers to questions delivered using QTIWorks. Any comments about its usefulness/helpfulness would be most welcome.

Note that you can also view an input hints box by clicking on the blue question mark symbol help_questionmark next to the maths input box. You can also watch a brief video showing you how to enter mathematical answers.

This guide contains the following sections:

The Maths Input box ^ Top

When a mathematical expression is required as an answer to a question, a text box within a larger grey box is shown. When text is typed into the text box, it is interpreted mathematically, and the resulting mathematical expression is shown:


If you click on the blue question mark symbol help_questionmark, an input hints box will pop up.

Basic Operators (+ – * / =) ^ Top

The basic mathematical operators can be represented by words or symbols, as shown in the table below.

Operation Symbol Word
Addition +
Multiplication * times
Division / divide
Equals =

note that multiplication is implied between a coefficient and a variable, e.g. 2x = 2*x, and between consecutive variables, i.e. letters, unless the letters make up a special character, e.g. pa = p*a, but pi = π, not p*i.

Other Operators (± > ≥ < ≤ ≠) ^ Top

Other operatores, e.g. comparison operators, can be represented as shown in the table below.

Operation Input Interpretation
Plus or minus +- ±
Greater than > >
Greater than or equal to >=
Less than < <
Less than or equal to <=
Not equal !=

Precedence (order of operations) ^ Top

The order of precedence, i.e. the order in which operations are performed/interpreted, follows the usual rules:

  1. brackets
  2. roots and exponentials
  3. multiplication and division
  4. addition and subtraction
Input Interpretation Notes
2+3*4 precedence_nobrackets equals 14
2+(3*4) precedence_unnecessarybrackets equals 14, brackets are unnecessary
(2+3)*4 precedence_brackets equals 20, brackets are required

Special Symbols and Functions ^ Top

Generally, letters just represent variables, and multiplication between consecutive letters is implied (see Basic Operations above). However, there are certain letters or words that have special meaning, as follows:

Letter/Word Meaning
e e, the natural exponential, 2.71828…
i the imaginary number, √-1
alpha…lambda…pi…etc Greek letters, α, λ, π etc
log logarithm function
ln natural logarithm function
sin, cos, tan trigonometric functions
cap, cup, in, not, notin, subset, subseteq, to,
vee, wedge…and probably others
Logic and Set Theory operators

Fractions (a/b) ^ Top

Use the divide symbol,  ‘/’, between the numerator (top) denominator (bottom) of a fraction. Brackets may be needed to give the correct numerator and denominator.

Input Interpretation
1/2 half
2x+1/3x+2 fraction_no_brackets
(2x+1)/(3x+2) fraction_brackets

Brackets (a(b+c)) ^ Top

Brackets can be used as they normally would when writing an expression.

Input Interpretation Notes
sin(2x+30)  brackets_sin  brackets not needed for sin of single value, e.g. sinx gives sinx
5(x+1)(2x-3)  brackets_2
3(2x-(2-y))  brackets_nested equivalent to 3(2x-2+y)

Powers (x^a) ^ Top

Use ^ (hat/caret symbol) to represent powers:

Input Interpretation Notes
x^2 powers_xsquared    
x^(1/3) powers_xtothird fractional powers need brackets
x^-1 powers_xtominus1 negative powers do not need brackets
e^(x(2x+1)) powers_expbrackets
e^x(2x+1) powers_expnobrackets

Roots (sqrt(x) or x^(a/b)) ^ Top

Only a square root can be represented with the root symbol. All other roots must be represented as fractional powers:

Root Input Interpretation
Square root (√x) sqrtx or sqrt(x) roots_sqrtx
Cube root (∛x) x^(1/3) roots_cubertx

Subscripts (x_a) ^ Top

Use _ (underscore) to give a subscript (similar to using ^ for powers/superscripts)

Input Interpretation
x_1 subscript_x_1
y_a subscript_y_a

“Sorry, I could not make sense of your input” ^ Top

You will see this message in a number of situations (including, but not limited to):

  • When you have an operator (e.g. + – * / ^ _ =), that does not have a value/variable before and/or after it, e.g. ‘1+’, ‘*3’, ‘x/’, ‘y^’
  • When you have two consecutive operators, e.g. ‘+*’
  • When you have opened a bracket and not (yet) closed it, e.g. ‘2(x+3’

If you see this message when you believe you have entered a complete expression, make sure you check your expression carefully, in particular that you have closed all brackets.

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