Given some random finite subsets of the natural numbers, perform set operations $\cap,\;\cup$ and complement.

Sample of size $24$ is given in a table. Find sample mean, sample standard deviation, sample median and the interquartile range.

Given a graph of some function $f(x)$ (a cubic), the student is asked to write the coordinates of the maximum and minimum points. The student then finds the maximum and minimum points of a second cubic function without using a graph, by finding the derivative, solving the quadratic equation that results from setting the derivative equal to zero, and finally testing the value of the second derivative.

Given two numbers, find the gcd, then use Bézout's algorithm to find $s$ and $t$ such that $as+bt=\operatorname{gcd}(a,b)$.

Finally, find all solutions of an equation $\mod b$.

Given a discrete random variable $X$ find the expectation of $1/X$ and $e^X$.

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

Given the PDF for $Y \sim \operatorname{Exp}(\lambda)$ find the CDF, $P(a \le Y \le b)$ and $\operatorname{E}[Y],\;\operatorname{Var}(Y)$

Determine if the following describes a probability mass function.

$P(X=x) = \frac{ax+b}{c},\;\;x \in S=\{n_1,\;n_2,\;n_3,\;n_4\}\subset \mathbb{R}$.

Given the pdf  $f(x)=\frac{a-bx}{c},\;r \leq x \leq s,\;f(x)=0$ else, find $P(X \gt p)$, $P(X \gt q | X \gt t)$.

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

Finding probabilities using the Poisson distribution.

rebelmaths

Tests the ability to match a quadratic function to a given parabola.

Using differentiation to find the tangent and normal to a line at a given point

Tests the ability to find the gradient and intercept of a straight line graph.

Given the original formula the student enters the transformed formula

Integration by susbtitution, no hint given

Find a regression equation given 12 months data on temperature and sales of a drink. 

Given a set of curves on axes, generated from a function and its first two derivatives, identify which curve corresponds to which derivative.

Given constant demand for a product, calculate the economic order quantity, and the minimum cost per year.

Given constant demand for a product, calculate the economic order quantity, and the minimum cost per year.

Given an oracle function that will output its value given an input: first estimate the derivative, and second calculate its shape.

Reading information from the equation of the line. Graph shown

Rebelmaths

rebelmaths

Given a random variable $X$ normally distributed as $\operatorname{N}(m,\sigma^2)$ find probabilities $P(X \gt a),\; a \gt m;\;\;P(X \lt b),\;b \lt m$.

Scores  in 20 games and frequency given -- calculate mean.

rebelmaths

Scores  in 20 games and frequency given -- calculate mean.

rebelmaths

Scores  in 20 games and frequency given -- calculate mean.

rebelmaths

Scores  in 20 games and frequency given -- calculate mean.

rebelmaths

Scores  in 20 games and frequency given -- calculate mean.

rebelmaths

Integration by susbtitution, no hint given

Implicit differentiation.

Given $x^2+y^2+ax+by=c$ find $\displaystyle \frac{dy}{dx}$ in terms of $x$ and $y$.

Implicit differentiation.

Given $x^2+y^2+ax+by=c$ find $\displaystyle \frac{dy}{dx}$ in terms of $x$ and $y$.