Advanced level 2026 west regional mock further mathematics 3
Advanced level 2026 west regional mock further mathematics 3
Three forces F1 = (−i − 3j + 4k) N, F2 = (−2i + 4j − 5k) N and F3 act on a rigid body. The force F1 acts through the point with position vector (−2j + 4k) m and the force F2 acts through the point with position vector (3i − 3j + 5k) m.
The system of three forces is in equilibrium.
a. Find a vector equation of the line of action of F3.
The force F3 is replaced by a force F4 acting through the point with position vector (i − j) m.
The system of F1, F2 and F4 is now equivalent to a single force (i − j − k) N acting through the point with position vector (2i + j + k) m, together with a couple G.
b. Determine the magnitude of the couple G.
(i) Use Simpson’s rule with 5 equally spaced ordinates to estimate the value of
is to be solved subject to the conditions y(2) = 3 and y(2.1) = 4.
Use the following approximations:
where h = 0.1 to find correct to 2 decimal places the value of y when x = 2.2.
A small smooth sphere A is moving with constant speed, in a straight line on a smooth horizontal floor. It collides obliquely with an identical sphere B which is at rest on the same horizontal floor. The direction of motion of A just before the collision is parallel to a smooth vertical wall. At the instant of impact between the two spheres, a straight line passing through the centres of the spheres makes an acute angle of 60° with the wall, as shown in the figure above. The coefficient of restitution between the two spheres is e. After the spheres collide, B collides with the vertical wall and rebounds. If the spheres now move in parallel directions, show that the coefficient of restitution between B and the wall is
