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King Fahd University of Petroleum and Minerals Prep-Year Math Program Prep-Year Math I1 MIDTERM EXAM Semester I, Term 061 Tuesday, November 14, 2006 Net Time Allowed: 120 minutes MASTER VERSION MATH 002-TO61 (MIDTERM EXAM) 1. + If for the function f (x) = -3 sin(?rx - 2) 5, A is its amplitude, P is its period, M is its maximum value and m is its minimum vlaue, then 2. [MASTERI Page 1 of 13 A+P M+m - If f is the inverse of the function f (x) = 2- x+l - 3, then f -'(x) = + 3) - 10g2(x + log,(x - 1) -1+ 10g2(x+ 3) 3 + log, (x + 3) (b) 3 (c) (d) (e) -1 +log2(3- ezpme4tiJ -4 ?fifiM*r' -fumrCim~, M ; m y e m m o X) * ,q & r a t ~ p p l ' c * h ~ H.l r e / ~ t i mkt- my 4 MATH 002-TO61 (MIDTERM EXAM) 3. Page 2 of 13 Which one of the following statements is TRUE about the function f(x) = -21lnxl and itsgraph? N increases on ( 0 , l ) See P r a b J ~61) (b) increases on (I, w) (c) decreases on ( 2 7 2, (d) f has no maximum value (e) x = 2 is a vertical asymptote 4. The domain of f (x) = log,-, x is m'f 62 M A 67 392 MATH 002-TO61 (MIDTERM EXAM) 5. Which one of the following statements is TRUE for all x > O , y > O , b > O and b # 1 ? % p r d b l ~ 21 & Yoi P44@4 In x (plf log, 6= 2lnb - (b) + Y) =logbx+ (c) logbx ' logby = logbx (d) log, 6. I MASTER I Page 3 of 13 logby + logby -=- The value of (In 10000)(log 6) (log3 fi) (log59) is MATH 002-TO61 (MIDTERM EXAM) 7. tan 155" - cot 35" 1 tan 155" cot 35" + /- tan 80" (b) tan 20" (d) -tan 25" ( e ) tan 15" 8. If 10" - lo-" - 1 - - then x = 10" lo-" 2' + Page 4 of 13 MATH 002-TO61 (MIDTERM EXAM) 9. pixs%iq Page 5 of 13 The number of intersection points of the graphs of y 3 and y = cos 2ax, over the interval 0 x 5 -, is 4 = sin 27rx < 3 If x = - sin 9, where 0 2 12x2 simplifies to (9 - 4x2)3/2 )'pf t an26 sec 6 (b) t an28 sin 8 (c) t an28 cos 8 (d) cot 9 sec 9 (e) cot29 sin 9 7r < 8 < -, then the expression 2 MATH 002-TO61 (MIDTERM EXAM) 11. The expression i.f Page 6 of 13 sin3x - cos3x sin z - cos x + 1 sinx cosx simplifies to SQQ pmbl* 5'7 P. 561 (b) 1 + 2 s i n x c o s x (c) 1 - 2 sin x cos x (d) -1 -sinxcosx (e) -1 12. If y + sinxcosx 2 cot 22, then the number of vertical asymptotes is equal to over the interval = MATH 002-TO61 (MIDTERM EXAM) 13. Page 7 of 13 3 5 If sin a = -, a lies in second quadrant, and cos ,O = -5 13' lies in third quadrant, then sin - - a! P = (; 14. 1MASTERI P + ) If a wheel of radius 8 centimeters is rotating at 450 revolutions per minute, then the linear speed of a point on the edge of the wheel in centimeters per seconds is equal to i.fl2OT (b) 2407r (c) 1107r (d) 2207r (e) 2 3 0 ~ MATH 002-TO61 (MIDTERM EXAM) 15. Page 8 of 13 The line y = 3 intersects the graph of 37r over the interval 67r) at y = x -2 csc ; (-I, /" three points (b) one point (c) twopoints (d) four points I 4 p.529 k waqe kc pnbt- 33, mrr4 34,38) 41J p. (e) no point 16. The reference angle 0') in radians, of the angle 0 = -1656" is equal to 527 MATH 002-TO61 (MIDTERM EXAM) 17. . The expression ipif 2 csc t (b) 2sect tan t 1 sect + + I MASTER I Page 9 of 13 +sect tan t simplifies to SOP wmfle 4 P p v a b t 4q ~ 558 G 52 P 560 (c) 2 cot t (d) 2 t a n t (e) 2 sin t 18. If the terminal side of an angle 0 lies on the line 3x where x > 0, then the value of cot 0 cos 0 is + + 49 = 0, -. MATH 002-TO61 (MIDTERM EXAM) 19. I MASTER I Page 10 of 13 Which one of the following is an odd function? j d f (4= 3 cos x ~ e c j + o b k \ 4~ g~ p~-s o & x2tanx+cscx (b) f(x) = x 3 + tan2x + (') 1 xcosx f(x) = sinx + t a n x (e) f (x) = x3 csc x 20. +1 The exact value of the expression 2 cos ( '4") -- tan(240°) - h csc is see &(3& (b) 2 h (4 h (d) -h (e) - 2 h ($) p r & i6 ~5 d 66 kq4g MATH 002-TO61 (MIDTERM EXAM) 21. pGmq Page 11 of 13 The range R and the period P of the function y are given by =- [Hint: Sketch] R = [-3,0], P = 2 n see p'obl- (c) R = [-3,0], P = 4 r P=T 7r (e) R = [-3,0], P = 2 22. If L is the distance between the two points PI(cos 8, sin 8) and P2(cos28,sin28), then L2 = (b) 2+2sin6' (c) 2+2cos38 (d) 3 - cos8 (e) 3 - cos 38 3 sin - SSG 58 (b) R = [-3,3], P = 2 r (d) R=[-3,0], I I; P 527 MATH 002-TO61 (MIDTERM EXAM) - Page 12 of 13 23. If, in the given figure, the length of AC the length of BD is 24. Ifthepoints (-1,3) and (2,81) lieonthegraphofthe then b c = exponential function f (x) = bx", is 10 cm, then + pmmq MATH 002-TO61 (MIDTERM EXAM) Page 13 of 13 - 25. + If the given graph represents the function y = a tan(bx c) over the interval (- 1,3), then the values of a, b and c are given by /Blr 7r 7r a = -2, b = -, and c = -4 4 (b) a = 2 , b = - 7r and c = 4' 4 7r 37r 7r -2, b = - and c = -4' 4 (c) a = (d) a = 2, 7r 7r b = -- and c = -4 4' (e) a = -2, b=47r, and c=-47r p b l ~ l r l 50 p. 527