Given a random variable $X$  normally distributed as $\operatorname{N}(m,\sigma^2)$ find probabilities $P(X \gt a),\; a \gt m;\;\;P(X \lt b),\;b \lt m$.

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Application of the Poisson distribution given expected number of events per interval.

Finding probabilities using the Poisson distribution.

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Given $5$ vectors in $\mathbb{R^4}$ determine if a spanning set for $\mathbb{R^4}$ or not by looking for any simple dependencies between the vectors.

Using Pythagoras' Theorem to find a missing side. Illustrated using simple Eukleides diagram

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Calculating percentages, VAT, Profit, Loss

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Profit and Loss, Percentages

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Profit and Loss, Percentages

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Laws of indices

Currency Conversion

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Currency Conversion

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No description given

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

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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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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Pythagoras' Theorem and naming sides of right angled triangle

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Find the solution of $\displaystyle x\frac{dy}{dx}+ay=bx^n,\;\;y(1)=c$

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Solve 4 first order differential equations of two types:$\displaystyle \frac{dy}{dx}=\frac{ax}{y},\;\;\frac{dy}{dx}=\frac{by}{x},\;y(2)=1$ for all 4.

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Equations which can be written in the form

\[\dfrac{\mathrm{d}y}{\mathrm{d}x} = f(x),   \dfrac{\mathrm{d}y}{\mathrm{d}x} = f(y),   \dfrac{\mathrm{d}y}{\mathrm{d}x} = f(x)f(y)\]

can all be solved by integration.

In each case it is possible to separate the $x$'s to one side of the equation and the $y$'s to the other

Solving such equations is therefore known as solution by separation of variables

5 indefinite integrals containing exponential functions

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It is estimated that 30% of all CIT students cycle to college. If a random sample of eight CIT students is chosen, calculate the probability that...

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$X \sim \operatorname{Binomial}(n,p)$. Find $P(X=a)$, $P(X \leq b)$, $E[X],\;\operatorname{Var}(X)$.

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