Julie Crowley

Annuity question as a filling in a formulae exercise

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Simple interest.

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Simple Percentages

Inverse Laplace transform if trig functions.

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Laplace transform of e^{at}

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Expansion of two brackets

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Multiplying and dividing decimals

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Order of Operations

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Rotate $y=a(\cos(x)+b)$ by $2\pi$ radians about the $x$-axis between $x=c\pi$ and $x=(c+2)\pi$. Find the volume of revolution.

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Finding areas under graphs using definite integration.

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Find $\displaystyle \int\frac{ax+b}{(1-x^2)^{1/2}} \;dx$. Solution involves inverse trigonometric functions.

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Summation Notation

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Evaluate $\int_1^{\,m}(ax ^ 2 + b x + c)^2\;dx$, $\int_0^{p}\frac{1}{x+d}\;dx,\;\int_0^\pi x \sin(qx) \;dx$, $\int_0^{r}x ^ {2}e^{t x}\;dx$

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Scores  in 20 games and frequency given -- calculate mean.

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Scores (including negatives)  in 20 games and frequency given -- calculate mean.

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Find the general solution of $y''+2py'+(p^2-q^2)y=x$ in the form  $Ae^{ax}+Be^{bx}+y_{PI}(x),\;y_{PI}(x)$ a particular integral.

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

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Find the solution of $\displaystyle \frac{dy}{dx}=\frac{1+y^2}{a+bx}$ which satisfies $y(1)=c$

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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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Basic data structures and maths/stats functionality given.

You can configure the rest.

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Expand out brackets to simplify an algebraic expression.

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Using e to solve equations involving the natural log

Transposition

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Transposing formulae

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Given random set of data (between 13 and 23 numbers all less than 100), find their stem-and-leaf plot.

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

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Match the question with the correct formula.

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

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