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)

3.       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)

4.     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)

5.      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) 

6.             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?  ........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................