ANSWER ALL QUESTIONS IN THIS SECTION

1) Calculate the compound interest on Rs. 3125 for 2 ½ years at 4% p.a.                                [6]
2) A man borrows Rs.5000 at 5% compound interest for 3 years. He repays Rs.150 at the end of every year.
   What mount should be pay at the beginning of the fourth year to settle the loan?                                                        [6]
3) In the figure below A,B,C,D, is a size of transformation of ABCD with respect to O.           [6]
     Given that OA/AA¹=2/3 and AD=3. Find the scale factor , A,D, And area ABCD : area A₁B₁C₁D₁
                                      
4) i) Prove Ö1-sin q/1+sin q = Sec q-tan q                                                                               [3]
    ii) The sides of a triangle are in the ratio 1:Ö2 : Ö3. Show that it is a right angled triangle.       [3]
5) Draw an escribed circle (ex circle) to a given triangle opposite to the given vertex using ruler and compass.                                                                                                                     [8]
6) i) Given that x²+¹/_x² = 18 Find the value of x-1/x.
    ii) Solve 2x²+6x+1 = 0, giving your answer correct to 1 decimal place.                                [4]

                                                                  SECTION(B)                                                          40MARKS

ANSWER ONLY 4 QUESTIONS FROM THIS SECTION
ALL QUESTIONS CARRY EQUAL MARKS [10]

7)   i) For x, y SN and 2< x £ 5 and  4 £ y <7 express the relation R= {(x, y) : x and y  are co- prime}
       a) as a set of ordered pairs
       b) what is the range
       c) Express R as an arrow diagram
     ii) Some students wished to find the height X of a building and the height Y of the flagpole on the building.
        They made the measures as shown in diagram below. Find X and Y.

8) a) A= é16 x ù find the value of x such .  
            ë x  4 û
that A may not have a multiplicative inverse.

    b) If é a  2 ù + é -3 b ù - é -1 2 ù = é 2 -1 ù  
                      ë 3 -1 û    ë -2 2 û   ë c  d û     ë 4   3û
Find a, b, c, and d.
    c) Find mean by ' short cut method' of the following table.
            X   5   6   7   8 9 10
            F  10 12 15 11 7  5

9) a) Solve graphically 2x-y=3 and x+3y=5.
     b) Find the slope of a line parallel and perpendicular to 2y = 3x+1

10) a) find the mean of the following frequency table by "step-deviation method" method :
        

      b) In figure below A-P-B and A-Q-C such that seg PQ ôô side BC, AP=6, PB=12, AQ=9.
          Find QC.

11) a)Draw a circle radius 3 cm. Inscribe and circumscribe a rectangular octagon.
      b) From the following data draw a histogram and join the consecutive mid point of the upper  horizontal sides
        of the rectangles in histogram.
             Cost of sarees 100-200 200-300 300-400 400-500 500-600
             Sold per week   12        28           37           23           20

12) a) Prove that opposite angles of a cyclic quadrilateral are supplementary.
      b) P is the centre of a circle of radius 12. Prove that midpoints of all chords of length 18, of this circle,
         lie on a circle concentric with the given circle. Also find radius of new circle.

13) a) The radius of a sphere is 3.75 cm. Find its curved surface area.
       b) Show that line perpendicular to a radius at its outer end is a tangent to the circle.

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