Real life problems with differentiation

Finding the stationary points of a cubic with two turning points

A basic introduction to differentiation

Addition Formulas in Trigonometry. Range of Sinusoidal functions. 

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

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

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Mean, median and mode from a frequency table with classes 1(b)

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These questions are designed to give students on questions to do with statistics. They are basic but gives a small understanding on mean, variance and standard deviation. There are also some definitions.

Solve: $\displaystyle \frac{d^2y}{dx^2}+2a\frac{dy}{dx}+(a^2+b^2)y=0,\;y(0)=1$ and $y'(0)=c$. 

Solve: $\displaystyle \frac{d^2y}{dx^2}+2a\frac{dy}{dx}+(a^2+b^2)y=0,\;y(0)=1$ and $y'(0)=c$. 

This question tests the students ability to factorise simple quadratic equations (where the coefficient of the x^2 term is 1) and use the factorised equation to solve the equation when it is equal to 0.

Mean, median and mode from a frequency table with classes 1(b)

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Compare two savings accounts with different interest rates.

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Factorise three quadratic equations of the form $x^2+bx+c$.

The first has two negative roots, the second has one negative and one positive, and the third is the difference of two squares.

Match up equations with the corresponding lines on a graph.

Match up equations with the corresponding lines on a graph.

There are copious comments in the definition of the function eqnline about the voodoo needed to have a JSXGraph diagram interact with the input box for a part.

Some questions on working with surds.

Questions on powers, the laws of indices, and exponential growth.

Finding the lengths and angles within a right-angled triangle using: pythagoras theorem, SOHCAHTOA and principle of angles adding up to 180 degrees.

Find the solution of a first order separable differential equation of the form $a\sin(x)y'=by\cos(x)$.

Solve: $\displaystyle \frac{d^2y}{dx^2}+2a\frac{dy}{dx}+(a^2+b^2)y=0,\;y(0)=1$ and $y'(0)=c$. 

Solve: $\displaystyle \frac{d^2y}{dx^2}+2a\frac{dy}{dx}+a^2y=0,\;y(0)=c$ and $y(1)=d$.  (Equal roots example).

Solve for $x(t)$, $\displaystyle\frac{dx}{dt}=\frac{a}{(x+b)^n},\;x(0)=0$

Solve a Differential equation with a repeated linear factor

Solve a Differential equation with a repeated linear factor & a delta function

Solve a Differential equation with 3 simple linear factors

Solve a Differential equation with a repeated linear factor

Solve a Differential equation with a  simple irreducible quadratic factor

Solve a Differential equation with a repeated linear factor