4 MAJU:CONTOH MIDYEAR EXAM PAPER

MID-YEAR EXAMINATION QUESTION                

PAPER1       ANSWER                                                                                                                                              1   Diagram 1 shows the relation between set M and set N

 set M              set N
      1------------>3
     2------------->4
     3------------>5

Diagram 1 
State  

(a)  the codomain of the relation.                 
        {3,4,5}
(b)  the type of the relation.                       [2 marks]
        one to one

2   Given f(x) = 2x – 5, find the value of q if f(q) = q.
          5                                                           [2 marks] 

3.   A function is defined by 
     f: x → 2x – 5.                                                                  
 Find                                                                                                  (a)  the object of image 7,                                    

(b)  the object which maps onto itself.              
                                                                    [3 marks]
      6,  5

4   Given the functions f : x → x – 1 and g : x →3/x , find            

(a)  the composite function gf,
        gf(x)= 3/(x-1)

(b)  the value of x if gf(x) = 9.                [3 marks]
        x = 4/3

5   Given the functions f : x → 2 – x and g : x → 4x² + 1, 
      find the     value of x if gf = –fg.        [4 marks]
     x= 9/8

6   Given the function f : x → 5x + 3, find the value of x if   
       f (x)= -7
        x = -2                                                            [3 marks]

7   It is given that x = 1 is one of the roots of the quadratic        equation 2x² – 3x + 1 = 0. Find the value of another root.                     x= 1/2                                                            [2 marks]

 8  Form a quadratic equation which has the roots of x = 3p and x = p in the form of ax² + bx + c = 0, where a, b, and c are constants. Then, find the values of p if f(x) = ax² + bx + c = 27 at the y-axis.                                                     [3 marks] 
      
9   It is given that the straight line y = c – 4x does not intersect the curve xy = 16. Find the range of c.       [3 marks]
       c <16

10  Calculate the value of k for which the line y = 5(x + 2) is a tangent to the curve y = x² – 3x + k            [3 marks]

11  The curve y² = p(x² – 1) meets the straight line y = 3 only at one point. Find the negative value of p.        
            p = -36 
12  The quadratic equation 4x + c = 16 – (2 – x)² has two equal roots. Find the value of c.   c = 13 

13  The curve y = 2x² + 2tx + 3t – 4 touches the x-axis at the values of t = a and t = b, where a < b. Find the values of a and b.                                                                                                        [3 marks]

14  Find the range of values of k for which the line y = kx + 2 does not intersect the curve x² + y² = 2.                                [4 marks]

15  Find the range of values of k for which the line y + 4(kx + 1) = 0 meets the curve y = 2x² + 7k.                                     [4 marks]

16  Solve the following simultaneous equations:

        x = y + 1

       (x – y) y = 1                                                 [2 marks]
        x= 2, y=1
17 Solve the simultaneous equations y = 4x – 1 and (x + 1)(y + 2) = 0.                                                                     [3 marks]
         x= -1, y= 5
          x= -1/4, y= -2

18  Solve the following simultaneous equations:

                  y    = 2x   and  y²  = 4x – 1

                                                                             [3 marks]
               x= 1/2, y= 1

19  Solve the simultaneous equations x – y = –1 and x² + y² = 25.

                                                                             [4 marks]
      x= -4, y= -3
       x= 3, y= 4
             

20  Solve the following simultaneous equations:

      x + 1    = 2y                    x² + xy – 26  = 0

                                                                            [4 marks]
       x= -13/3, y= -5/3
        x= 4, y= 5/2

21  Solve the following simultaneous equations:

        2 log₁₀ x  = log₁₀ (x + y)

             x – y   = 0                                              [4 marks]
        x=0, y=0

        x=2, y=2

22Solve the equation 8^x . 2^{1 – x} = 32^{1 + 2x}.                                                                                                                    [3 marks]
       x= - 1/2

23  Given that log₃ x + 1 = 2 log₉ (x + y), prove that 
       8x² – 2xy – y² = 0.                                      [4 marks]

24 Solve the equation log₂ (5x + 2) + log₂ (x – 1) = 2 + log₂
(1 – 4x).                                                        
      x= 2/5     x= -1/3                                         [4 marks]

25  Given that y = kx^m – 3 where k and m are constants. Find the values of k and m if y = 24 when x = 3 and y = 240 when  
 x = 9.            

                                                                        [4 marks]