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Julie's copy of BS2.1
Draft
Question in Julie's workspace by Julie Crowley and 2 others

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

rebelmaths
Solve an equation in modular arithmetic
Doesn't work
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Solving an equation of the form $ax \equiv b\;\textrm{mod}\;n$ where $a$ and $n$ are coprime.
Calculate probabilities from frequency table
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Simple probability question. Counting number of occurrences of an event in a sample space with given size and finding the probability of the event.
BS1.5
Draft
Question in Bill's workspace by Bill Foster

Given sample data find mean, standard deviation, median, interquartile range.

Note that there are different versions of the upper and lower quartiles, so you may want to include your own versions - see the user defined functions in the question.
When does a sequence get within $d$ of its limit?
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics and 1 other

$x_n=\frac{an^2+b}{cn^2+d}$ . Find the least integer $N$ such that $\left|x_n -\frac{a}{c}\right| < 10 ^{-r},\;n\geq N$ , $2\leq r \leq 6$ . Determine whether the sequence is increasing, decreasing or neither.
Find point when a sequence becomes strictly decreasing
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

$x_n=n^k t^n$ where $k$ is a positive integer and $t$ a real number with $0 < t<1$ . Find the smallest integer $N$ such that $(m+1)^k t^{m+1} \leq m^k t^m$ for all $m \geq N$ .
Solve a pair of congruences
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Solving two simultaneous congruences:

$\begin{eqnarray*} c_1x\;&\equiv&\;b_1\;&\mod&\;n_1\\ c_2x\;&\equiv&\;b_2\;&\mod&\;n_2\\ \end{eqnarray*}$ where $\operatorname{gcd}(c_1,n_1)=1,\;\operatorname{gcd}(c_2,n_2)=1,\;\operatorname{gcd}(n_1,n_2)=1$
Solve congruence in given range
Has some problems
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Solving an equation of the form $ax \equiv\;b\;\textrm{mod}\;n$ where $\operatorname{gcd}(a,n)|r$ . In this case we can find all solutions. The user is asked for the two greatest.
Solve three congruences with the Chinese Remainder Theorem
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Solving three simultaneous congruences using the Chinese Remainder Theorem:

$\begin{eqnarray*} x\;&\equiv&\;b_1\;&\mod&\;n_1\\ x\;&\equiv&\;b_2\;&\mod&\;n_2\\x\;&\equiv&\;b_3\;&\mod&\;n_3 \end{eqnarray*}$ where $\operatorname{gcd}(n_1,n_2,n_3)=1$
When is a sequence within d of its limit?
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

$x_n=\frac{an+b}{cn+d}$ . Find the least integer $N$ such that $\left|x_n -\frac{a}{c}\right| \le 10 ^{-r},\;n\geq N$ , $2\leq r \leq 6$ .
Calculate probability, expected value and variance of a geometric distribution,
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

$W \sim \operatorname{Geometric}(p)$ . Find $P(W=a)$ , $P(b \le W \le c)$ , $E[W]$ , $\operatorname{Var}(W)$ .
Template 1 for Workshop
Ready to use
Question in Julie's workspace by Julie Crowley

Basic data structures and maths/stats functionality given.

You can configure the rest.

rebelmaths
IP3.3
Ready to use
Question in Bill's workspace by Bill Foster

Two numbers from a set of $5$ numbers are chosen at random, without replacement. Find the distribution $X$ of their sum and $E[X]$ .

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