Manipulate surds and rationalise the denominator of a fraction when it is a surd.

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Drug Calculations

Drug Calculations

Determine the reactions supporting a cantilever beam carrying concentrated forces and moments.

Question on drug calculations

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A really simple question which asks the student to multiply two matrices.

The human resources department of a large finance company is attempting to determine if an employee’s performance is influenced by their undergraduate degree subject. Personnel ratings are used to judge performance and the task is to use expected frequencies and the chi-squared statistic to test the null hypothesis that there is no association.

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.

Implicit differentiation.

Given $x^2+y^2+dxy +ax+by=c$ find $\displaystyle \frac{dy}{dx}$ in terms of $x$ and $y$.

Also find two points on the curve where $x=0$ and find the equation of the tangent at those points.

Paired t-test to see if there is a difference between responses after treatment.

Implicit differentiation.

Given $x^2+y^2+dxy +ax+by=c$ find $\displaystyle \frac{dy}{dx}$ in terms of $x$ and $y$.

Also find two points on the curve where $x=0$ and find the equation of the tangent at those points.

Questions involving various techniques for rearranging and solving quadratic expressions and equations

Provided with information on a sample with sample mean and standard deviation, but no information on the population variance, use the t test to either accept or reject a given null hypothesis.

Differentiation of  polynomials, cos, sin, exp, log functions. Product, quotient and chain rules.

Missing: Application with bacteria, turning points, difficult chain rule

Questions on integration using various methods such as parts, substitution, trig identities and partial fractions.

Find $\displaystyle \int x(a x ^ 2 + b)^{m}\;dx$

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

Questions on transposition

Finding the confidence interval at either 90%, 95% or 99% for the mean given the mean and standard deviation of a sample. The population variance is not given and so the t test has to be used. Various scenarios are included.

Two quadratic graphs are sketched with some area beneath them shaded. Question is to determine the area of shaded regions using integration. The first graph's area is all above the $x$-axis. The second graph has some area above and some below the $x$-axis.

Find $\displaystyle \int x\sin(cx+d)\;dx,\;\;\int x\cos(cx+d)\;dx $ and hence $\displaystyle \int ax\sin(cx+d)+bx\cos(cx+d)\;dx$

Finding the stationary points of a cubic with two turning points

This exercise will help you solve equations of type ax-b = c.

Determine the reactions supporting a cantilever beam carrying concentrated forces and moments.

Given mean and sd of 1000 sample returns on a scale of 1 to 7 together with a given score, find the z-score.

Also find the 95% confidence interval for the population mean.

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.

Refresher questions on topics in algebra that students beginning a maths undergraduate course should be familiar with.