Further Mathematics Past QuestionsQuestion 801:Given that x = \(\begin{pmatrix} -4 \\ 3 \end{pmatrix}\) and y= \(\begin{pmatrix} -9 \\ 15 \end{pmatrix}\) calculate, correct to the nearest degree, the angle between the vectors Question 802:(a) A jogger is training for 15km charity race. He starts with a run of 500 metres, then he increases the distance he runs daily by 250 metres. (i) How many days will it take the jogger to reach a distance of 15km in training? (ii) Calculate the total distance he would have run in the training. (b) The second term of a Geometric Progression (GP) is -3. If its sum to infinity is 25/2, find its common ratios. Question 803:P and Q are two linear transformations in the X-Y plane defined by P: (x, y) → (-3x + 6y, 4x + y) and Q: (x, y) → (2x-3y, -4x - 6y). (a) Write down the matrices of P and Q. (b) What is the image of (-2,-3) under the transformation Q? (c) Obtain a single transformation representing the transformation Q followed by P. (d) Find the image of (1,4) when transformed by Q followed by P. (e) Find the image P\(^1\) of the point (-√2,2√2) under an anticlockwise rotation of 225° about the origin. Question 804:(a) Find the equation of the normal to the curve y = (x\(^2\) - x + 1)(x - 2) at the point where the curve cuts the X - axis. (b) The coordinates of the pints P, Q and R are (-1, 2), (5, 1) and (3, -4) respectively. Find the equation of the line joining Q and the midpoint of \(\overline{PR}\). Question 805:A box contains 5 red, 7 blue and 4 green identical bulbs. Two bulbs are picked at random from the box without replacement. Calculate the probability of picking: (a) same color of bulbs; (6) different color of bulbs (c) at least one red bulb. |
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