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• Anna's copy of Maria's copy of Mario's copy of Interactive Newton-Raphson method

Write down the Newton-Raphson formula for finding a numerical solution to the equation $e^{mx}+bx-a=0$. If $x_0=1$ find $x_1$.

Included in the Advice of this question are:

6 iterations of the method.

Graph of the NR process using jsxgraph. Also user interaction allowing change of starting value and its effect on the process.

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• Finding bases for the null space and row space of a matrix

Given a matrix in row reduced form use this to find bases for the null, column and row spaces of the matrix.

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• Factorise numbers into products of prime powers

Factorising 5 to 7 digit numbers into a product of prime powers.

Uses the marking algorithms from question 1 of this CBA

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• Factorise four numbers

Pick four numbers from $1900\dots 2015$ and ask the student to factorise them.

Custom marking scripts make sure the student has entered a complete factorisation.

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• Duality of linear programming problems (2 variables)

Given a linear programming problem in standard form, write down the dual problem.

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• Classify singular points of a second order ODE

Trying out something: get the student to enter a set for each of "regular singular points" and "essential singular points".

Find and classify singular points of a second-order ordinary differential equation.  One equation is chosen from a selection of 10.

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• Probability sample mean is within d of the population mean

Given data on population mean and population standard deviation and three sampling sizes, calculate the probabilities that the sample means are within a specified distance from the population mean.

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• Probability - draw without replacement

A box contains $n$ balls, $m$ of these are red the rest white.

$r$ are drawn without replacement.

What is the probability that at least one of the $r$ is red?

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• Custom Marking version of Ex 6 Cofactors, Determinant and Inverse of a 3x3 matrix (CC)

Cofactors Determinant and inverse of a 3x3 matrix.

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• Laws of Indices [L6] Randomised

This question aims to test understanding and ability to use the laws of indices.

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