Maths and Applied Maths: Have they ever asked any really hard questions.

sdiff

While trudging through some monotonous applied maths questions in preparation for my mocks, I did notice that there were a few questions that could be considered slightly harder than the rest. However, I'm wondering if anyone has come across any questions, either in maths or applied maths, that they found really challenging, and almost inappropriate for leaving cert students. If so, post them here please!

Wesc.

I don't know if you have the book, but Dominick Donnelly's book for applied maths has a section at the end of each chapter with really really difficult problems.. I'll post one up here sure from the chapter on A.L.M. :


A particle is moving in a straight line OD with uniform retardation leaves point O at time t=0, and comes to rest at D. On its way the particle passes points A,B and C at times t= T, 2T and 4T respectively after leaving O, where AB=BC=w
Find, in terms of w, (i) OA , and (ii) CD

The answers are: (i) 4w/3 (ii) w/24

Wesc.

Here's another one, it's not too bad if you can get your head round it!


A ball is dropped from a height h and falls vertically onto a horizontal surface. e = 3/4. Find in terms of h, the distance travelled by the ball before coming to rest.

Answer: 25h/7

finality

Monotonous applied maths questions? There's no such thing. Every question is like an emotional rollercoaster!

MathsNerd31

1990 Collisions Question

ride-the-spiral

I always found the 2002 circular motion question for applied maths to be a bastard. "A smooth uniform hoop of radius r and mass M stands in a vertical plane. The hoop two small rings of mass m which are released from the top of the hoop.
(i) Show that the reaction force that the hoop exerts on the rings when they have each fallen an angle theta on opposite sides is
mg(3cos(theta) - 2)

(ii) show that the hoop will rise if m>3M/2

(i) is fairly standard circular motion but part (ii) is just evil, I even saw practically the same question in my college mechanics book this year.

acorn1702

My applied maths teacher would be able to list you out every part of every question from the last forty years haha.