Xiaodan Leng

Dealing with functions in Numbas.

This creates a 4x4 times table grid using numbers from 2 to 9. The step gives some advice on how to work out times tables (products, multiplications) if you can't remember them.

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Multiple response question (3 correct out of 6) re properties of convergent and divergent sequences. Selection of questions from a pool.

Uses JSXGraph to generate a plot for a cubic, with given critical points, along with three other incorrect graphs with modified properties. JSXGraph code is commented.

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A graph of an (invertible) cubic is given. The question is to determine values of $f$ from graph.

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Find the solution of a first order separable differential equation of the form $(a+y)y'=b+x$.

An experiment is performed twice, each with $5$ outcomes

$x_i,\;y_i,\;i=1,\dots 5$ . Find mean and s.d. of their differences $y_i-x_i,\;i=1,\dots 5$.

A quadratic is and a graph of it is given. A tangent is also sketch. The equation of the tangent line is asked for.

For a sample of size n from a normal distribution and given the mean of the sample and the standard deviation of the distribution, find the MLE for the mean. Also the expected information and a confidence interval for the mean.

For a sample of size n from a normal distribution, given mean of the sample mean and the standard deviation , find the t-statistic corresponding to a null hypothesis $\mu=m$ and a given confidence level. Check if the result is significant at this level.

Recognising the equation of a circle.

Recognising that $(x-a)^2+(y-b)^2=r^2$ is a circle of radius $r$ with centre $(a,b)$ 

Recognising that $(x-a)^2+(y-b)^2=r^2$ is a circle of radius $r$ with centre $(a,b)$ 

Draws a triangle based on 3 side lengths.

Draws a triangle based on 2 angles and a side length.

Choosing whether given random variables are qualitative or quantitative.

Deciding whether or not three sampling methods are simple random sampling, stratified sampling, systematic or judgemental sampling. 

Finding probabilities from a survey giving a table of data on the alcohol consumption of males. This can be easily adapted to data from other types of surveys.

Solving a system of three linear equations in 3 unknowns using Gauss Elimination in 4 stages. Solutions are all integral.

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A graphical approach to aiding students in writing down a formal proof of discontinuity of a function at a given point.

Uses JSXgraph to sketch the graphs and involves some interaction/experimentation by students in finding appropriate intervals.

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Quadratic factorisation that does not rely upon pattern matching.