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

Solve a Differential equation with 3 simple linear factors

Solve a Differential equation with a repeated linear factor

Solve a Differential equation having 3 simple linear factors & a delta function.

Solve a Differential equation with an irreducible quadratic factor 

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

rebelmaths

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

rebelmaths

Quiz covering basic arithmetic with complex numbers and solving roots for a quadratic with complex solutions

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

Solve a Differential equation with an irreducible quadratic factor 

Solve a Differential equation having 3 simple linear factors & a delta function.

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Solve a Differential equation with an irreducible quadratic factor 

Solve a Differential equation having 3 simple linear factors & a delta function.

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

A copy of Amy Chadwicks block question, with adaptions to provide a diagram for the student.

A block of given mass is sliding down the plane, with given acceleration. Find the normal reaction force, the coefficient of friction, and the distance travelled before reaching a given speed.

A random heating question, that randomly picks a material, and then heats it through either one or two phase changes, provides an example graph of the heating with scaled temperature ranges (though not with scaled latent and specific heats), and a table with the suitable constants.

Finding the modulus and argument (in radians) of four complex numbers; the arguments between $-\pi$ and $\pi$ and careful with quadrants!