Mathematics paper 2 GCE O level Past Question


SECTION A

THIS SECTION IS FOR ALL CANDIDATES
ANSWER ALL QUESTIONS IN THIS SECTION

  1.      Evaluate   14 of 14 34  of 7.                                   ……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………(5marks)                                                                                                
  2.       Given the real number B=798-7128+350
a. Express   B in the form  a2 , where a is a whole number. ………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………
b. Given that 1.732<3<1.733 and 1.414<2<1.415; write in a similar manner the bounds within which  the number   86  lies and state the amplitude of the bounds to the nearest thousandth ..……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………....................(6marks)
  1.       A polynomial function is defined by gx=x3+x2-9x-9 .
a. Evaluate  g-3 ………………………………………………………………………………………………………………………………………………………………………………………………
b. Write gx in the form  gx=x+3x2+ax+b, a,b∈Z . ………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………
c. Solve the in equation: x+3x-1x-3<0   ……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………........        (5marks)



  1.     a. Given that x = 1 is a root of fx=x2+kx-5 , calculate the value of k and write fx completely. .................................................................................................................................................................................................................................................................................................................................................................... 
       b.Solve in R the equation f(x) = 0 .............................................................................................................................................................................................................................................................................................................................................................(6marks)
  1.      To produce a fruit punch during a practical class, 13 litres of pawpaw juice, 34 litres of pineapple juice, 56 litres               of orange juice and 12 litres of carrot juice were used by the HE department of a certain school.
a. What quantity of punch was produced during this practical lesson. .....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................
b. If  12 litres of punch is sold at 1200FRS. How much money did the HE department realize on the sales of punch? .............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................                       (6 marks) 
  1.             Solve  in R  :
a. x-32=2x-33 ........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................
b.   2x-334x-75    ...............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................                                                 (6marks)
         





7.          A roof has dimensions as shown below:
Figure   1

               Calculate the number of roofing sheets to be used to roof the house if each roofing sheet is 3m 1m: 
a. If the gabbled ends are not roofed.  ...........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................
       (b).    If the gabbled ends are roofed .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................                                                    (6marks)

  8.        Calculate P=2-2335-3375235-6723   and give the answer as a fraction in its lowest form.  ................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. …………………………………………………………………                                                      ( 5marks)
    9.         In a right-angled triangle, where angle x  is acute and cos x=513   , find:
a. sin x     ....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................  
b. cot x   .........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................                                                       (5marks)
     



 10.       Given the vectors p=4i-j ,q=-3i-4j and r=5i+μj . Find
                    a. p-2q ..............................................................................................................................................................................................................................................................................................................................................................................................
                    b. magnitude of p-2q   .............................................................................................................................................................................................................................................................................................................................................................................................
                   c.  the value of the scalar for which r is parallel to p-2q.  ...............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................                                                                              (6marks) 
11.       Find the volume of the cone shown below:  
    
   
Figure   2
.........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................                                                                                (4marks)
12.      The table below represents the performance of students in a Mathematics test, marked out of 20:
  Marks   
5
7
8
10
14
15
18
20
No of students
2
3
5
7
6
2
3
2
  
i.   a. How many students wrote the test? ........................................................................................................................................................................................................................................................................................................................................
            b. What is the modal mark?  ........................................................................................................................................................................................................................................................................................................................................................
        
                 ii.    What is the probability that a student scores at least 15marks for the test. ...............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................                                                                                              (5marks)
13.     The figure below represents a circle and a square, both having the same centre O. The area of the square is 
    1225 cm2.

Figure   3
a. Calculate the length of the side of the square.  ..............................................................................................................................................................................................................................................................................................................................................................................................................................................................
b.  Calculate the radius of the circle. ...................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................                                                                                                 (4marks)
14.             a. Find the midpoint of the line segment AB given that A-4;-7 and B-6;-2. .....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................
        b.  Find the equation of the line  AB.  .......................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(6marks)                                                                                              

15.    A woman sold fourteen(14) cartons of fish for 168,000FCFA. 
               a. What is the selling price of one carton? ......................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................
         b. If the cost price of one carton is 10500FCFA. What was her gain after selling all the cartons?  ........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................
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