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Given  $P(A)$, $P(A\cup B)$, $P(B^c)$ find $P(A \cap B)$, $P(A^c \cap B^c)$, $P(A^c \cup B^c)$ etc..

Provided with information on a sample with sample mean and known population variance, use the z test to either or reject a given null hypothesis. One sided.

SPSS fat absorption question. Student downloads one of several SPSS files and carries out some analysis in SPSS, before returning to enter the answers. The analysis is a one-way analysis of variance. If there is a difference in the levels of the factor then a post hoc test (Tukey's honestly significant difference) is used to determine which pairs of variables are significantly different. 

Provided with information on a sample (>30) with sample mean and standard deviation, use the z test to either accept or reject a given null hypothesis.

You are allowed 38 minutes to complete this test.

You may use rough paper for your calculations.

You are allowed 31 minutes to complete this test.

You may use rough paper for your calculations.

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. 

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

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This questions assesses the ability to conduct an ANOVA and interpret the results.

Adaptive marking: an error in calculating F can be carried over to the calculation of the p-value as well as the test conclusion.

For practising how to recognise paired data as the first step to identify a suitable statistical analysis (such as the paired t-test or Wilcoxon test).

Show a list of the factors of a number.

Works by testing each number up to $n$ for divisibility by $n$, so won't do well with really big numbers. Certainly fast enough for numbers up to 4 or 5 digits.

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A fill-in-the-blank style question to test vocabulary within the topic of Algebra.

(Green’s theorem). $\Gamma$ a rectangle, find: $\displaystyle \oint_{\Gamma} \left(ax^2-by \right)\;dx+\left(cy^2+px\right)\;dy$.

Double integrals (2) with numerical limits

Statistics and probability. 2 questions, 1 on two sample t-test and 1 on paired t-test.

Four questions on finding least upper bounds and greatest lower bounds of various sets.

One-way ANOVA example

Two factor ANOVA example

Given a linear combination $Y$ of three independent random variables with given means and variances, find the mean of variance of $Y$.

Given sum of sample from a Normal distribution with unknown mean $\mu$ and known variance $\sigma^2$. Find MLE of $\mu$ and one of four functions of $\mu$.

Using a random sample from a population with given mean and variance, find the expectation and variance of three estimators of $\mu$. Unbiased, efficient?

LSD and Tukey yardsticks on three treatments. Also one-way Anova test on same set of data.

LSD and Tukey yardsticks on five treatments. Also two-way Anova test on same set of data.

Paired t-test to see if there is a difference between times take in a task.