Please use the next table for your answer choices. QUESTION 1 2 3 4 5 6 7 8 9 10 ANSWER [B] TUTOR COMPONENT Tutor Name: __________________________________________________________________________ QUESTION 1 2 3 4 5 6 7 8 9 10 MARK Total Mark [1] Directions. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Consider the set of ten (10) multiple choice questions below. From the available choices, a, b, c and d, please do write the letter, that you think solves the given question best, in the corresponding box of the tables in section 2. Should you think that the correct answer is not among the four given choices, then please write the letter, N, (for none of the above), instead. Each correct answer is worth 4 points. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> [2] Questions. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ………………………………………………………………………........... Question - 1: The fraction, (0.175175175...)/(1.767676...) is equal to: (a) 6/11 (b)111/11 (c) 11/999 (d) 11/111 ....................................................................................................................... Question - 2: Any line perpendicular to the family of lines described by the equation, y = (– 2/5) x + b, would have a slope equal to: (a) 0 (b) 5/2 (c)1/b (d) 2/5 ..……………………………………………………………………………. Question - 3: The range of the function, f (x) = , is: (a)( – , 1) (b) (0, ) (c) [0, 1) (d) ( – , 1] ………………………………………………………………………………….... ………………………………………………………………………........... Question - 4: The function f (x) = (x+3)/(x – 2), has a vertical asymptote at: (a) x = – 3 (b) x = – 2 (c) x = 2 (d) x = 0 ……………………………………………………………………………... Question - 5: The distance between the two points (7, – 8) and (3, – 5) is equal to: (a) 20 (b) 15 (c) 10 (d) 5 …...……………………………………………………………………........ Question - 6: If , then, , is equal to: (a) (b) (c) (d) ………………………………………………………………………………….... Question - 7: The solution to: logx (8) = 3, is: (a) x = 3 (b) x = 2 (c) x = 1 (d) x = 1/2 ………………………………………………………………………………….... Question - 8: Consider the sequence, an = (– 3/5) n – (3/5) n , n = 0,1,2,.., then in the long run, the sequence, an (a) goes to 0 (b) diverges (c) goes to 3/5 (d) goes to – 3/5 ……………………………………………………………………………... Question - 9: If the sequence, an, is as in Question 8, then , is equal to: (a)15/2 (b) – 15/8 (c)8/7 (d) ∞ …………………………………………………………………….........….. Question - 10: If bn = , where the sequence, an , is as in Question 8, then the sequence, bn , (a)diverges (b)goes to 0 (c) goes to – 15/8 (d) has no limit ………………………………………………………………………........... >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Please consider the five (5) questions below, having 3 subparts each. Each question subpart is worth 4 points. Answer every question, by writing the solution to each question subpart in the space provided. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ……………………………………………………………………………Question – 1: Consider the sequence, , , for n = 0,1,2,3... (a)Write down the first four terms of the sequence. Write down the closed form of this sequence, and hence calculate the 12th term of the sequence. (b)Describe the long term behaviour of the sequence, . (c)Compute the value of the sum, S = . ……………………………………………………………………… Question – 2: Consider the circle described by the equation: . (a) Rewrite the equation of the circle in the form: . Determine the centre, C, and the radius, R, of the described circle. (b) Find the points, if any at which the circle intersects the line L described by the equation: . (c) Find the area Z of the smallest square that can contain the circle. Find the area W of the largest square that can be inscribed inside the circle. …………………………………………………………………………… Question–3: Consider the points, A (2, 7), B (–2, 4), and, C (–2, 7). (a) Find the equation of the line, L1, that is parallel to the segment AB, and passing through the point C. (b) Find the equation of the line containing the segment AC. Find the length D, and the midpoint M of the segment BA. (c) Find the equation of the circle with center C, and passing through the point B. Determine the (shortest) distance of point, A, from to the circle. ……………………………………………………………………………. Question – 4: The amount of silver extracted from a small mine in an eastern African country was 19000 kg for the year 2002. This amount was only 1500 kg in 2005. (a) Assuming that the yearly amount of silver mined follows a linear model in time, find the function Y(t) describing the yearly mined silver. Find the amount of silver expected to be mined 2009. When will the mine not yield any more silver (as expected from the linear model)? (b) Repeat part (a) assuming that the yearly amount of silver mined Z(t) is an exponential function of time instead. (c) Graph the functions Y(t) and Z(t) on the same set of axes (t, y). …………………………………………………………………………....... Question - 5: Consider the functions, f and g, given by: f (x) = ln (1– x), and g(x) = cos (– 0.5 x). (a) Find the domains and ranges of the functions f and g. (b) Show that g is not one-one, and determine sub-domains on which g is one-one. Find the inverse of g on a sub-domain containing, x = 0. (c) Show that f is one-one. Find the inverse function, f –1 of f, and the corresponding domain and range. Plot the functions, f and f –1, on the same set of axes (x, y) .