Guides d'étude, Notes de cours & Résumés

1 The roots of the equation 4x 4 -2x 3 -3x+2 = 0 are a, b, c and d. By using a suitable substitution, find a quartic equation whose roots are a+2, b+2, c+2 and d+2 giving your answer in the form at4 + bt3 + ct2 + dt + e = 0, where a, b, c, d, and e are integers. [5] 2 The lines L1 and L2 have the following equations. J-5N J 5 N L : r = K 6 O + m K O 1 K O K-2O L 15P K -2 O J24N J 3 N L : r = K 1 O +n K 1 O 2 K O K O L -5P L -4P (a) Show that L1 and L2 inte...

The surface S is defined for all real x and y by the equation z = x 2 +2xy. The intersection of S with the plane P gives a section of the surface. On the axes provided in the Printed Answer Booklet, sketch this section when the equation of P is each of the following. (a) x = 1 [2] (b) y = 1 [2] 2 A curve has equation y = 1+x 2 , for 0 G x G 1, where both the x- and y-units are in cm. The area of the surface generated when this curve is rotated fully about the x-axis is Acm2 . 1 (a)...

The table below shows the activities involved in a project together with the immediate predecessors and the duration of each activity. Activity Immediate predecessors Duration (hours) A – 2 B A 3 C – 4 D C 2 E B, C 2 F D, E 3 G E 2 H F, G 1 (a) Model the project using an activity network. [3] (b) Determine the minimum project completion time. [2] The start of activity C is delayed by 2 hours. (c) Determine the minimum project completion time with this delay. [2] 2 A graph is s...

1 One end of a light inextensible string of length 0.8m is attached to a particle P of mass mkg. The other end of the string is attached to a fixed point O. Initially P hangs in equilibrium vertically below O. It is then projected horizontally with a speed of 5.3ms -1 so that it moves in a vertical circular path with centre O (see diagram). 5.3ms −1 At a certain instant, P first reaches the point where the string makes an angle of 1 r radians with the downward vertical through O. (...

A certain section of a library contains several thousand books. A lecturer is looking for a book that refers to a particular topic. The lecturer believes that one-twentieth of the books in that section of the library contain a reference to that topic. However, the lecturer does not know which books they might be, so the lecturer looks in each book in turn for a reference to the topic. The first book the lecturer finds that refers to the topic is the Xth book in which the lecturer looks. ...

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