# Choose a mathematical formula question sub-type

There are ten sub-types to choose from when authoring a mathematical formula question.

Each sub-type has unique syntax requirements of how the Answer field value is defined while authoring.

NOTE: In general, the ten mathematical formula question sub-types accept equivalent responses. However, here are some special notes for equivalent responses and specific sub-types:

- The formula without logs and trig sub-type won't accept logarithmic and trigonometric functions as equivalent responses.
- The formula with physical units sub-type will accept unit equivalents as long as the units are recognized by MÃ¶bius.
- The formula that matches responses to within +C sub-type accepts two answers as equivalent if they differ by a constant number.
- The formula without simplification sub-type will only accept unsimplified responses as equivalent responses.
- The equation sub-type will accept any equation that's algebraically equivalent to the correct answer.
- The chemical formula sub-type doesn't accept equivalent responses and requires the student response to be an exact match to the defined correct answer.

TIP: Check out Author a mathematical formula question for full question authoring instructions.

## Formula

The formula sub-type accepts numbers, formulas, and operations, but not equations.

Examples of accepted syntax for defining the Answer field value for this sub-type are:

- (e^x)*sin(x^2)
- 5*x^4

Check out Author a formula sub-type.

## Formula without logs and trig

The formula without logs and trig sub-type accepts numbers and formulas without logarithms or trigonometric functions.

Examples of accepted syntax for defining the Answer field value for this sub-type are:

- 1/sqrt(2)
- (1/3)*3^(1/2)

Check out Author a formula without logs and trig sub-type.

## Formula with physical units

The formula with physical units sub-type accepts a combination of numeric quantities, algebraic formulas, unit dimensions, and physical units.

Examples of accepted syntax for defining the Answer field value for this sub-type are:

- 6 mg
- 2*t m/s
- sin(x) m/s^2
- (3*t^2+1) km/hr

Check out Author a formula with physical units sub-type.

## Formula that matches responses to within +C

The formula that matches responses to within +C sub-type accepts numbers and formulas as answers within a constant number of the defined correct answer.

Examples of accepted syntax for defining the Answer field value for this sub-type are:

- x*ln(x)
- x*ln(x) +1
- (4/3)*x^3 + (7/5)*x^5 + (11/7)*x^7

Check out Author a formula that matches responses to within +C sub-type.

## Formula without simplification

The formula without simplification sub-type accepts only the exact formula provided, and doesn't accept any simplification of student responses.

Examples of accepted syntax for defining the Answer field value for this sub-type are:

- 4*x+x
- 3*x^2+9*x+10

Check out Author a formula without simplification sub-type.

## Equation

The equation sub-type accepts responses that use an = symbol, where the equation can be expressed in terms of a single variable.

Examples of accepted syntax for defining the Answer field value for this sub-type are:

- y = 7*x+2
- y = 4*(x+1) +2
- y = 8*(x-2) + 7

Check out Author an equation sub-type.

## Unordered list of formulas

The unordered list of formulas sub-type accepts an unordered list of numbers or formulas separated by semicolons (;).

Examples of accepted syntax for defining the Answer field value for this sub-type are:

- 4; 5*x; 3
- (-5/2)+(1/2)*19^(1/2); (-5/2)-(1/2)*19^(1/2)

Check out Author an unordered list of formulas sub-type.

## Ordered lists of formulas

The ordered lists of formulas sub-type accepts an ordered list of numbers or formulas separated by commas (,).

Examples of accepted syntax for defining the Answer field value for this sub-type are:

- 2, 4, 8, 16
- sqrt(3)/2, 1/2, sqrt(3)

Check out Author an ordered lists of formulas sub-type.

## Vectors of formulas

The vectors of formulas sub-type is used for questions about Cartesian coordinates or vectors.

Examples of accepted syntax for defining the Answer field value for this sub-type are:

- (2, 5)
- (2, 4*t, 7*t+1)

Check out Author a vector of formulas sub-type.

## Chemical equation

The chemical equation sub-type is used for chemistry questions involving chemical equations.

Examples of accepted syntax for defining the Answer field value for this sub-type are:

- H_2SO_4
- 2H_2+O_2 -> 2H_2O

Check out Author a chemical equation sub-type.