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  1.   What is the coefficient of the term involving y -33 in the expansion of (x 2   —  y -3 ) -9 ? Ans. 3003  1( n —  r +1) —  3( r  –  1) = -33; r = 7 n-r+2= (-9)-7+2 = -14           ) (x 2 y) -9-7+1 (-y -3 ) 7-1  = 3003x -30 y 2.   Ian was twice as old as Mary is when Ian is five times as old as Mary was. Together their ages five years hence is 38. How old will Ian be next year? Ans. 21 years old (Ian  –  y) = 2 (Mary) Mary = 8 years old Ian = 5 (Mary  –  y) Ian = 20 years old (Ian+5) + (Mary+5) = 38 thus, Ian will be 21 y/o next year 3.   What is the perimeter of the ellipse with an apogee of 48 and an eccentricity of 0.6? Ans. 170.69 units apogee = a + c = 48 e =   = 0.6 =   ; a= 30, c = 18 b = √     = √     = 24 perimeter =         =         = 170. 69 units 4.   The sum and product of three numbers in arithmetic progression is 27 and 251 respectively. What is four less than twice the smallest number? Ans. 10 x=smallest number asked= 2x-4   x + (x+d) + (x+2d) = 27; (x) 2  + (x+d) 2  + (x+2d) 2  = 251 3x + 3d = 27; x+d = 9 3x 2  + 6xd + 5d 2  = 251 d= 9-x 3x 2  + 6x(9-x) 2 + 5 (9-x) 2  = 251 x = 7; d=2 2(7)  –  4 = 10 5.   What is the axis of symmetry of the parabola if the focus is at (  , –   ) and with directrix at y =  –    ? Ans. 2x  –  9 = 0 by inspection, the parabola opens upward. Vertex will be at (  , k). k=         =    thus, parabola is   ) 2 = 4a(y+  ) .   ) 2  = 0   6.   The units digit of a three digit number is three less than four times the hundreds digit. If the tens and hundreds digits are interchanged, the number will be a hundred less than thrice the srcinal number. Find the number in reverse if the sum of the digits is 14. Ans. 572.  u = 4h  –  3 h = 2 100t + 10h + u = 3(100h +10t +u) -100 t = 7 h + t + u = 14 u = 5 reversed = 572  7.   Evaluate         . Ans. 1  = )  )    ) )    = 1 8.   What is the point of inflection of the equation y=x 3 +5x 2 -x-1. Ans. (-  ,    ) y’ = 3x 2  + 10x -1   )    )        y’’ = 6x + 10 = 0  x = -5/3 p(-  ,    )   9.   To reach school, King has to ride a cab which costs six nickels and a penny per km that runs an average of 60 kph upto the bus terminal where he would then transfer. Costing two dimes a kilometer, the bus ride averages 40 mph less. It took him 41 minutes over an hour, all in all, to get to the school proper. If his total fare costs $24.702, how much does he pay for the cab going to school for the whole week of schooldays? Ans. $63.55  For cab: 6(5cents)+1cent = 31 cents For bus: 2(10 cents) = 20 cents Let x= distance travelled by cab y= distance travelled by bus Eq1: 0.31x + 0.20y = 24.702      x = 41km; y = 59.96km cab fare for five days = 5(.31)(41) = $63.55 10.   Before buying another fraction of a hectare of land, Chan srcinally had 5/4 hectares more than 82% of the bought land. If he sells 23% of his acquired land, he will have 150.14% more of what he bought. How much land did he initially have? Ans. 1.9675 hectares  x=fraction of hectare of bought land y=acquired land after buying x eq1:     ) = y eq2: y  –  0.23y = 2.5014x x =   hectare; y = 2.8425 hectares srcinal land owned = (     ( (        
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