Using a shuffled list variable to randomise the order of all options in a multiple choice part except the last one.

Demonstrates that the marking algorithm for "match text pattern" parts doesn't put quotes around substituted strings any more.

Simple probability question. Counting number of occurrences of an event in a sample space with given size and finding the probability of the event.

A weighted coin with given $P(H),\;P(T)$ is tossed 3 times. Let $X$ be the random variable which denotes the longest string of consecutive heads that occur during these tosses. Find the Probability Mass Function (PMF), expectation and variance of $X$.

Application of the Poisson distribution given expected number of events per interval.

Finding probabilities using the Poisson distribution.

Shows how to define variables to stop degenerate examples.

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

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 $\neg q \to \neg p$.

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

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

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

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

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

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

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

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

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

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

Given a probability mass function $P(X=i)$ with outcomes $i \in \{0,1,2,\ldots 8\}$, find the expectation $E$ and $P(X \gt E)$.

The data is fitted by linear and quadratic regression.  First, find a linear regression equation for the $n$ data points, $20 \le n \le 35$.

They then are shown that the quadratic regression is often a better fit as measured by SSE. Also users can experiment with fitting polynomials of higher degree.

Given a graph of a line of the form $y=ax+b$ where $a$ and $b$ are integers, find the equation of the line. The y-intercept is given.

Given a graph of a line of the form $y=ax+b$ where $a$ and $b$ are integers, find the equation of the line. The y-intercept is given.

Solve for $x(t)$, $\displaystyle\frac{dx}{dt}=\frac{a}{(x+b)^n},\;x(0)=0$

This shows how to define a question variable whose value is a variable name with a few annotations added, so it's more convenient to use.

The question variable 'x' is defined to be the variable name vec:underline:x.

Shows how to create a simplified JME subexpression, and substitute it into a string variable.

A demonstration of how to use the "variable list of choices" option for a "choose one from a list" part to shuffle only some of the choices, and always have the same "I don't know" choice at the end of the list.

This question uses a "formatted text template" variable to define a long passage of text which is shown to the student after they submit a part. A custom marking algorithm adds the text as a comment after the standard marking algorithm has finished.

Application of the binomial distribution given probabilities of success of an event.

Finding probabilities using the binomial distribution.

Add, subtract, multiply and divide algebraic fractions.

Shows how to define variables to stop degenerate examples.

Solve for $x$ and $y$:  \[ \begin{eqnarray} a_1x+b_1y&=&c_1\\   a_2x+b_2y&=&c_2 \end{eqnarray} \]

The included video describes a more direct method of solving when, for example, one of the equations gives a variable directly in terms of the other variable.

Template question. The student is asked to perform a two factor ANOVA to test the null hypotheses that the measurement does not depend on each of the factors, and that there is no interaction between the factors.

Factorise polynomials by identifying common factors. The first expression has a constant common factor; the rest have common factors involving variables.