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.

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.

$X \sim \operatorname{Binomial}(n,p)$. Find $P(X=a)$, $P(X \leq b)$, $E[X],\;\operatorname{Var}(X)$.

rebelmaths

This question provides practice at adding, subtracting, dividing and multiplying complex numbers in rectangular form.

This question provides practice at adding, subtracting, dividing and multiplying complex numbers in rectangular form.

Multiplication and addition of complex numbers. Four parts.

The easiest type of exponential to graph where the base is greater than 1 and no transformations take place.

Given an equation or a worded formula determine if it is a function or not

Manipulation of algebraic fractions

Choose which of 5 matrices are in a) row echelon form but not reduced b) reduced row echelon form c) neither.

Some basic tasks involving vectors, including converting to/from component form, scalar product, resultant vectors.

6 questions on standard statistical distributions.

Binomial, Poisson, Normal, Uniform, Exponential.

Some basic tasks involving vectors, including converting to/from component form, scalar product, resultant vectors.

Rearrange expressions in the form $ax^2+bx+c$ to $a(x+b)^2+c$.

Find the solution of a first order separable differential equation of the form $axyy'=b+y^2$.

Find the common ratio of a given geometric sequence, write down the formula for the nth term and use it to calculate a given term in the sequence.

Polar form of a complex number.

Using the reduction formulas for products of powers or sin and cosine

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

Reduce a 5x6 matrix to row reduced form and using this find rank and nullity.

Shows how to define variables to stop degenerate examples.

Given the original formula the student enters the transformed formula.

READY TO USE

A graph is drawn. A student is to identify the derivative of this graph from four other graphs. There are four version of this question: I: cubic, II: linear, III: quadratic, IV: sinusoisal.

Students will analyze the graph of a quadratic function, and then write the equation in either Standard Form or Vertex Form.

Just what the title says, I guess. I couldn't find a 0^0 that didn't converge to 1 except things like x^(1/ln(x)) as x->0, but they just need the e^ln() transformation, not L'hopital's rule!

Just what the title says, I guess. I couldn't find a 0^0 that didn't converge to 1 except things like x^(1/ln(x)) as x->0, but they just need the e^ln() transformation, not L'hopital's rule!

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$X \sim \operatorname{Binomial}(n,p)$. Find $P(X=a)$, $P(X \leq b)$, $E[X],\;\operatorname{Var}(X)$.

rebelmaths

The assignment will assess your ability to write linear equations, re-write them in various forms, identify intercepts, and write the equations of parallel and perpendicular lines.