Simon Thomas

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Rationalise the denominator with increasingly difficult examples involving compound denominators. 

This question tests the student's understanding of what is and is not a surd, and on their simplification of surds.

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

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.

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

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.

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.

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.

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.

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.

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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.

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A credit card company charges compound interest at x% per month 
on unpaid balances.

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A savings account earns compound interest at 1.5% per month.
Calculate the equivalent annual rate of interest

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Find i using compound interest formula A=P(1+i)^n

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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?

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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.

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Calculate the final amount in a savings account where compound interest is earned annually 

Compare two savings accounts with different interest rates.

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Calculate the annual interest rate for a savings account where A, P and n are given.

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A savings account earns compound interest at 1.5% per month.
Calculate the equivalent annual rate of interest

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Finding x and y values for straight line graphs