ARE YOU READY FOR CALCULUS? 1. Simplify each of the ...

ARE YOU READY FOR CALCULUS?1. Simplify each of the following expressions:(a)x 3 − 9xx 2 − 7x +12(b)x 2 − 2x − 8x 3 + x 2 − 2x(c)1x − 1 51x − 1 2 25(d) 9 − x−23+x −12. Rationalize the denominator in each expression:(a)2√ √3+ 2(b)41 − √ 5(c)11+ √ 3 − √ 53. Write each of the following expression in the form ca p b q where, c, p and q are numbers:(a) (2a2 ) 3b(b) √ 9ab 3(c) a(2/b)3/a(d) ab − ab 2 − ba −1(e)(b −1 ) √ a(f)( ) a2/3 2 ( ) b3/2b 1/2 a 1/24. In each equation, solve for x (without using a calculator):(a) 5 (x+1) =25(b) 1 3 =32x+2(c) log 2 x =3(d) log 3 x 2 =2log 3 4 − 4log 3 51

5. Simplify each expression:(a) log 2 5+log 2 (x 2 − 1) − log 2 (x − 1)(b) 2 log 4 9 − log 2 3(c) 3 2log 3 56. Simplify each expression:(a) log 10 (10 1/2 )( ) 1(b) log 1010√ x(c) 2 log 10 x +3log10 x 1/37. Solve the following equations for the indicated variables:(a) x a + y b + z c=1, for a(b) V =2(ab + bc + ca), for a(c) A =2πr 2 +2πrh, forpositiver(d) A = P + nrP ,forP(e) 2x − 2yd = y + xd, ford(f) 2x4π + 1 − x =0,forx28. For each of the following equations, complete the square and reduce to one of thestandard forms: y − b = A(x − a) 2 or x − a = A(y − b) 2 .(a) y = x 2 +4x +3(b) 3x 2 +3x +2y =0(c) 9y 2 − 6y − 9 − x =09. Factor each expression completely:(a) x 6 − 16x 4(b) 4x 3 − 8x 2 − 25x +50(c) 8x 3 +27(d) x 4 − 110. Find all real solutions to each equation:(a) x 6 − 16x 4 =0(b) 4x 3 − 8x 2 − 25x +50=0(c) 8x 3 +27=02

11. Solve for x in each equation:(a) 3 sin 2 x =cos 2 x ; 0 ≤ x

TABLE OF CONTENTSFORWARD-LOOKING STATEMENTS ..................................................................................................... 1DEFINITION OF TERMS ........................................................................................................................... 2EXECUTIVE SUMMARY ........................................................................................................................... 7SUMMARY OF THE OFFERING ............................................................................................................ 16RISK FACTORS AND OTHER CONSIDERATIONS .............................................................................. 19PHILIPPINE TAXATION .......................................................................................................................... 28USE OF PROCEEDS .............................................................................................................................. 32DETERMINATION OF OFFER PRICE ................................................................................................... 34PLAN OF DISTRIBUTION ....................................................................................................................... 35DESCRIPTION OF THE BONDS ............................................................................................................ 39INDEPENDENT AUDITOR AND COUNSEL .......................................................................................... 60DESCRIPTION OF BUSINESS ............................................................................................................... 62DESCRIPTION OF PROPERTIES .......................................................................................................... 92CERTAIN LEGAL PROCEEDINGS ........................................................................................................ 95MARKET PRICE OF AND DIVIDENDS ON GLOBE ’S COMMON EQUITY AND RELATEDSTOCKHOLDER MATTERS ................................................................................................................... 99MANAGEMENT’S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND RESULTS OFOPERATIONS ....................................................................................................................................... 108DIRECTORS, EXECUTIVE OFFICERS AND CONTROL PERSONS ................................................ 192EXECUTIVE COMPENSATION ............................................................................................................ 200SECURITY OWNERSHIP OF MANAGEMENT AND CERTAIN RECORD AND BENEFICIALOWNERS .............................................................................................................................................. 203DESCRIPTION OF DEBT ..................................................................................................................... 205CORPORATE GOVERNANCE ............................................................................................................. 207FINANCIAL INFORMATION.................................................................................................................. 208SUPPLEMENTAL FINANCIAL INFORMATION.................................................................................... 209i

31. Write each pair of equations as a single equation in x and y:(a)(b)(c){x = t +1y = t 2 − t{ √ x =3t − 1y = t 2 − t{x =sinty =cost32. Find the inverse of each function:(a) f(x) =2x +3(b) f(x) = x +25x − 1(c) f(x) =x 2 +2x − 1, x>033. A function f(x) has the graph given below. Carefully sketch the graph of the inversefunction f −1 (x).yy = f(x)y = xx34. Express x in terms of the other variables in the picture.(a)(b)rxhthtxr6

35. Consider the following diagrams:(A)(B)rrr(a) Find the ratio of the area inside the square but outside the circle to the area ofthe square in the figure (A).(b) Find the formula for the perimeter of a window of the shape in Figure (B).(c) A water tank has the shape of a cone (like an ice cream cone without ice cream).The tank is 10m high and has a radius of 3m at the top. If the water is 5m deep(in the middle) what is the surface area of the top of the water?(d) Two cars start moving from the same point. One travels south at 100 km/hour,the other west at 50 km/hour. How far apart are they two hours later?(e) A kite is 100m above the ground. If there are 200m of string out, what is theangle between the string and the horizontal. (Assume that the string is perfectlystraight).36. You should know the following trigonometric identities.(A) sin(−x) =− sin x(B) cos(−x) =cosx(C) cos(x + y) =cosx cos y − sin x sin y(D) sin(x + y) =sinx cos y +cosx sin yUse these equalities to derive the following important trigonometric identities, whichyou should also know.(a) sin 2 x +cos 2 x = 1 (use (C) and cos 0 = 1.)(b) sin 2x =2sinx cos x(c) cos 2x =cos 2 x − sin 2 x(d) cos 2x =2cos 2 x − 1(e) cos 2x =1− 2sin 2 x(f)∣ cos x √ 1+cosx∣2= 2(g)∣ sin x √ 1 − cos x∣2= 27