Subtracting a decimal with 3 decimal places from a decimal with 2 or 3 decimal places. borrowing is necessary. This was modified from a subtraction question using integers with each number divided by 1000 so the variables have names referring to ones, tens, hundreds etc.

The student must solve a pair of simultaneous equations in $x$ and $y$.

The variables are generated backwards: first $x$ and $y$ are picked, then values for the coefficients of the equations are chosen satisfying those values.

This question shows how to use the question's JavaScript preamble to request data from an external source, and use that data in question variables.

Note that this means the question only works when the external source is available. Use this very carefully, and avoid it if you possibly can!

This question shows how explore mode can be used to loop through several versions of the same question. The variables for each version are stored in a list of "scenarios", and a counter works through that list each time the student moves on to the next part, labelled "try the next version of this question".

Give f(x)=ax^2+b a simple function input (like 6x-3) and evaluate. Constants and variables, and the function input are all randomised.

A custom marking algorithm picks out the names of the constants of integration that the student has used in their answer, and tries mapping them to every permutation of the constants used in the expected answer. The version that agrees the most with the expected answer is used for testing equivalence.

If the student uses fewer constants of integration, it still works (but they must be wrong), and if they use too many, it's still marked correct if the other variables have no impact on the result. For example, adding $+0t$ to an expression which otherwise doesn't use $t$ would have no impact.

Rearrange an equation for a variable e in k.1/(1-e) and then evaluate for e, given values for the variables.

Rearrange a linear formula au + bv + cw = d to make one of u,v,w the subject.

Rearrange a linear function in x and y to make y the subject. Line variables are randomised.

evaluate a function (4a)/(pi*b^2cd) given random values for a,b,c,d.

Simplify (a) a fully-factorised fraction with common factors, and (b) a fraction where the numerator is a product and the denominator a sum sharing the same variables (that cannot be simplified). The variables are randomised. Part of HELM book 1.4

Simplify an algebraic fraction that is fully factorised with common factors between the numerator and denominator, and one of the variables has a larger index on the denominator. Part of HELM Book 1.4

Used for LANTITE preparation (Australia). MG = Measurement & Geometry strand. Student must calculate distance swum in km given number of laps of 50m pool, days of week and weeks in term. These variables are randomly selected.

Used for LANTITE preparation (Australia). NA = Number & Algebra strand. Students calculate the cost of the halogen globes given electricity cost, number of globes, number of years, replacement cost and lifespan of globes. Some of these variables are randomly selected. There are more than 10 different versions of this question.

Solving first order differentials by separation of variables.

Show one of several blocks of text depending on the value of a question variable.

As well as a simple check for the value of a variable, the condition to display a block of text can be a complex expression in any of the question variables - in this example, depending on the discriminant of the generated quadratic.

Given an expression in one or two variables, with two or three terms, collect like terms, if possible. Part of HELM Book 1.3

An order of operation question using +,-,* with signed integers, with up to 4 variables.

The questions are the exercises from Q3 of HELM Book 1.1.5

This exercise will help you rearrange some complex equations.

Crear una tabla de verdad para una expresión lógica de la forma :

\[[(a \ {op1}\ b) \ {op2}\ (c \ {op3}\ d)] \ {op4} [e\ {op5}\ f]]\]

donde cada una de $a, \; b, \; c, \; d, \; e, \; f $ puede ser una de las variables booleanas \[ p, \; q, \; \neg p, \; \neg q\]  y cada uno de los operados $\ {op} $  puede ser uno de los operadores $ \lor, \; \land, \; \to $.

Crear una tabla de verdad para una expresión lógica de la forma:

$$(a \ {op1}\,\  b) \ {op2}\,\ (c \ {op3} \,\ d)$$

donde $a, \;b,\;c,\;d$ pueden variables booleanas $p,\;q,\;\neg p,\;\neg q$  y cada operador  $\operatorname{op1},\;\operatorname{op2},\;\operatorname{op3}$  es uno de los conectivos $\lor,\;\land,\;\to$.

Por ejemplo: $(p \lor \neg q) \land(q \to \neg p)$.

This question assesses the learner's ability to compute a confidence interval for a difference of two means, given two samples.

Randomized variables: sample raw data and confidence level. 

Adapted from section 7.3.1 in OpenIntro Statistics (4th ed).

Solving a differential equation of the form $\frac{dy}{dx}=\frac{ax^n}{y}$ using separation of variables.

Solving a differential equation of the form $\frac{dy}{dx}=axy^2$ using separation of variables.

Solving a differential equation of the form $\frac{dy}{dx}=axy$ using separation of variables.

Subtracting a decimal with 3 decimal places from a decimal with 2 or 3 decimal places. borrowing is necessary. This was modified from a subtraction question using integers with each number divided by 1000 so the variables have names referring to ones, tens, hundreds etc.

Find $\displaystyle \int \frac{2ax + b}{ax ^ 2 + bx + c}\;dx$

Given descriptions of  3 random variables, decide whether or not each is from a Poisson or Binomial distribution.