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

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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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(Calculating estimate and actual value of temperature using given formulas, and hence finding the percentage error)

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indefinite integration

Find $\displaystyle \int ax ^ m+ bx^{c/n}\;dx$.

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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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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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Given a table of the number of days in which sales were between £x1000 and £(x+1)1000 find the relative percentage frequencies of these volume of sales.

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Given vectors $\boldsymbol{a,\;b}$, find $\boldsymbol{a\times b}$

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Find the mean, median and mode of a list of 10 test scores.

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Finding the exVAT price

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

Find angle and side in a right angled triangle.

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Finding surface area and volume, given formulae.

Find the stationary points of the function: $f(x,y)=a x ^ 3 + b x ^ 2 y + c y ^ 2 x + dy$ by choosing from a list of points.

Find a% of b using a calculator. Suggested method to use decimal equivalent.

Finding the stationary points of a cubic with two turning points

Finding the cost including VAT

Simple inequalities - finding values of x

Implicit differentiation.

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

Using simple substitution to find $\lim_{x \to a} bx+c$, $\lim_{x \to a} bx^2+cx+d$ and $\displaystyle \lim_{x \to a} \frac{bx+c}{dx+f}$ where $d\times a+f \neq 0$.

Simple inequalities - finding values of x

Applying trigonometry to find heughts and lengths.

Finding lengths of sides of triangles

Finding lengths of sides of triangles

A particle is projected up a rough plane at a given speed. Given the angle of the slope and the coefficient friction, find the distance the particle travels before it comes to instantaneous rest.

Three forces act on a particle. You're given the magnitude of one, and the directions of all three. Find the magnitudes of the other two forces.

A mass is hanging from a string, tethered to two points. A horizontal force applied to the mass holds it directly underneath one of the points. Given the magnitude of the force, find the tension in the string and the mass of the bag.