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.

Cramers Rule applied to 3 simultaneous equations

Find the determinant and inverse of three $2 \times 2$ invertible matrices.

Multiplication of $2 \times 2$ matrices.

Practice to decide which quadrant a complex number lies in.

Practice to decide which quadrant a complex number lies in.

Two parts.

Content assessed : complex arithmetic; argument and modulus of complex numbers; de Moivre's theorem.

This complex numbers in-class assesment counts 20% towards your final maths grade for WM104.

Note that although questions are randomised for each student, all questions test the same learning outcomes at the same level for each student.  

If you have any questions during the test, please put up your hand to alert the invigilator that you need attention. 

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 formulas to calculate the areas of various shapes.

Graphs are given with areas underneath them shaded. The student is asked to select the correct integral which calculates its area.

Q1. True/false questions about basic facts.

Q2 and Q3. Velocity-time graphs are given with areas underneath them shaded. The area of the shaded regions are given. From this, definite integrals of v ar eto be determined.

Simple counting exercise, with combinations

Introduction to counting with permutations and combinations

Introduction to first order recurrence relations with a simple example, including homogenous and non-homogenous solutions.

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Find the first few terms of the Maclaurin and Taylor series of given functions.

Multiple choice question. Given a randomised polynomial select the possible ways of writing the domain of the function.

Find the determinant and inverse of three $2 \times 2$ invertible matrices.

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

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Find the first 3 terms in the Taylor series at $x=c$ for $f(x)=(a+bx)^{1/n}$ i.e. up to and including terms in $x^2$.

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