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

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.

Topics: Trigonometeric equations and complex numbers
Students must complete the exam within 90 mins (standard time).
Questions have variables to produce randomised questions.

Create a truth table with 3 logic variables to see if two logic expressions are equivalent.

Demonstrates how to create variables containing LaTeX commands, and how to use them in the question text.

Solving a differential equation of the form $\frac{dy}{dx}=a \cos(x) e^{-y}$ using separation of variables.

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

Solving a differential equation of the form $\frac{dy}{dx}=\frac{a \cos(x)}{y}$ using separation of variables.

Solving a differential equation of the form $\frac{dy}{dx}=x(y-a)$ using separation of variables.

Create a truth table for a logical expression of the form $a \operatorname{op} b$ where $a, \;b$ can be the Boolean variables $p,\;q,\;\neg p,\;\neg q$ and $\operatorname{op}$ one of $\lor,\;\land,\;\to$.

For example $\neg q \to \neg p$.

Crear una tabla de verdad para una expresión lógica de la forma $ a \ {op} \ b $ donde $ a, \; b $ pueden ser las variables booleanas $ p, \; q, \; \neg p$  y  $\neg q $ y  $\ {op}$ puede ser uno de los operadores $ \lor, \; \land, \; \to $.

Por ejemplo $ \neg q \to \neg p $.

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.

No description given

Create a truth table for a logical expression of the form $a \operatorname{op} b$ where $a, \;b$ can be the Boolean variables $p,\;q,\;\neg p,\;\neg q$ and $\operatorname{op}$ one of $\lor,\;\land,\;\to$.

Student finds a basis for kernel and image of a matrix transformation. Any basis can be entered; there is a custom marking algorithm which checks if it is a correct basis.

There are options to adjust this question fairly easily, for example to get different variants for practice and for a test, by changing the options in the "pivot columns" in the variables. You should be careful to think about and test your pivot options, as some are easier or harder than others, and some don't work very well.

Educational calculation tool rather than "question".

This allows the student to input a linear system in augmented matrix form (max rows 5, but any number of variables). Then the student can decide to swap some rows, or multiply some rows, or add multiples of one row to other rows. The student only has to input what operation should be performed, and this is automatically applied to the system. This question has no marks and no feedback as it's just meant as a "calculator".

It has some rounding to 13 decimal places, as otherwise some fraction calculations become incorrectly displayed as a very small number instead of 0.

It would be possible to extend to more than 5 rows, one just has to put in a lot more variables and so on. I just had to choose some place to stop.

Educational calculation tool rather than "question".

This allows the student to input a square matrix (max rows 5). Then the student can decide to swap some rows, or multiply some rows, or add multiples of one row to other rows. The student only has to input what operation should be performed, and this is automatically applied to the matrix and the identity matrix (or what it has got to). This question has no marks and no feedback as it's just meant as a "calculator". It has some checks in so students know when they are not entering a square matrix or a valid row number etc.

It has some rounding to 13 decimal places, as otherwise some fraction calculations become incorrectly displayed as a very small number instead of 0.

It would be possible to extend to more than 5 rows, one just has to put in a lot more variables and so on. I just had to choose some place to stop.

This allows the student to input a linear system in augmented matrix form (max rows 5, but any number of variables). Then the student can decide to swap some rows, or multiply some rows, or add multiples of one row to other rows. The student only has to input what operation should be performed, and this is automatically applied to the system. This question has no marks and no feedback as it's just meant as a "calculator".

Create a truth table for a logical expression of the form $((a \operatorname{op1} b) \operatorname{op2}(c \operatorname{op3} d))\operatorname{op4}(e \operatorname{op5} f) $ where each of $a, \;b,\;c,\;d,\;e,\;f$ can be one the Boolean variables $p,\;q,\;\neg p,\;\neg q$ and each of $\operatorname{op1},\;\operatorname{op2},\;\operatorname{op3},\;\operatorname{op4},\;\operatorname{op5}$ one of $\lor,\;\land,\;\to$.

For example: $((q \lor \neg p) \to (p \land \neg q)) \to (p \lor q)$

Exercises in solving simultaneous equations with 2 variables.