Calculations in $\mathbb{Z_n}$ for three values of $n$.     

$A,\;B$ $2 \times 2$ matrices. Find eigenvalues and eigenvectors of both. Hence or otherwise, find $B^n$ for largish $n$.

Given two sets of data, sample mean and sample standard deviation, on performance on the same task, make a decision as to whether or not the mean times differ. Population variance not given, so the t test has to be used in conjunction with the pooled sample standard deviation.

Link to use of t tables and p-values in Show steps.

Finding the confidence interval at either 90%, 95% or 99% for the mean given the mean of a sample. The population variance is given and so the z values are used. Various scenarios are included.

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.

An investment of x invested today will give a return of €y in n1 years time and a further €z n2 years from today. Calculate the net present value (NPV) of the investment given that the discount rate is perc% per annum.

rebelmaths

An investment of €x invested today will give a return of €y in n years time Calculate the net present value (NPV) of the investment given that the discount rate is 3.5% per annum.

rebelmaths

To provide for retirement an employee deposits R at the end of each month in an account that earns $perc% annual interest compound monthly. What is the future value of the annuity in nyears?

rebelmaths

A 1-year lease for a company car requires a payment of €280 at the end of each month. Find the present value of these payments if the annual interest rate is 7% compounded monthly.

rebelmaths

Substitute given values into formulas.

multiple choice testing sin, cos, tan of  random(30, 45, 60) degrees

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.

Apply and combine logarithm laws in a given equation to find the value of $x$.

testing sin, cos, tan of  random(0,90,120,135,150,180,210,225,240,270,300,315,330) degrees but in radians

testing sin, cos, tan of angles that are negative or greater than 2pi radians that result in nice exact values. 

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

This question concerns the evaluation of the eigenvalues and corresponding eigenvectors of a 2x2 matrix.

Find eigenvalues and eigenvectors of a $2 \times 2$ matrix.

Using the unit circle definition of sin, cos and tan, to calculate the exact value of trig functions evaluated at angles that depend on 0, 30, 45, 60 or 90 degrees.