MODULE ADDMATHS F5 : ANSWER

• ANSWER OF MODULE  FORM 5
• C1: PROGRESSION
• 1)      h =5
• 2)      a= -7     d=4
• 3)      2,  5/3
• 4)      12
• 5)      291
• 6)      7
• 7)      d =4
• 8)       
•  
• C2: LINEAR LAW
•  
• C3: INTEGRATION 
•  
• C4: VECTOR
• 1)       

MATHEMATICS, ADDMATHS F4,F5

CARA GUNA KALKULATOR CASIO 570MS

LANGKAH UTK CARI PUNCA PERSAMAAN..:

1.        x ² - 3x+2 = 0

1. Tentukan         a= 1         b= -3         c=2
2. MODE
3. MODE
4. MODE
5. EQN.....1
6. Anak panah kanan --->
7. Degree....2
8. Masukkan  a?......1=
9. b?.....-3=
10. c?..........2=
11. x= 1    
12. Jawapan ke 2.... tekan  = lagi
13. x= 2

x=1  or   x =2

XDE KALKULATOR ...RUGIIIKKK!!

ADDMATH F4: ANSWER MIDYEAR PAPER 2

ANSWER MIDYEAR PAPER 2

1. 1.      -1-x
     6
   2.      (a) x²- (4+p)x+ 4p         (b) k= 1/3
   3.      (a) 1:4
   4.      (a)  p=3                          (b) k=4
   5.      x= 1,y= -2       and      x=2,y= -1
   6.       
   7.      (a)  a= 2,-2    (b)(i)  7/x    + 2   (ii)  x= -7/2
   8.       
   9.       
   10.   
   11.  (a) 0.25            (b) 14(5ⁿ)    (c)  x = ½     y=8
   12.  (a)   a = 5, b=4  (b)  4/  5-x  (c)
   13.  (a)  c <  7/4
   14.   
   15.  (a)  x= 125    

4MAJU: MIDYEAR EXAM PAPER 2

PAPER 2======> 100 MARKS

SECTION A

Answer all question

[40marks]

1 Given the function f : x → 2x + 5 and g : x → 2-3x ,    find g ^–1 f ^–1                                        [5 marks] 

2   It is given that f(x) = 0 is a quadratic equation which has the roots 4 and p.

       (a)  Write f(x) in the form of ax² + bx + c.

       (b)  The curve ky = f(x) passes through the y-axis at the point  (0, –24). 

              Given that p = –2,    calculate the value of k.                                                       [6 marks]

3   The quadratic equation px² + 5qx + 25p = 0 has two equal roots.

       (a)  Find the ratio p : q where p and q have positive values.

       (b)  Solve the equation with p : q found in (a).                                                              [6 marks]

4   It is given that point T(1, 5) is a point on the curve   f(x) = (px – 2)² + 4, where p > 1.

    (a)  Find the value of p.

    (b)  Use the value of p obtained in (a), find the range of values of k if the equation

            f(x) = k has two different roots.                                                                             [7 marks]

 5   Given that  x = p and  y = q is the solution of the simultaneous equations   

      x² + y² = 5 and  x – y = 3, find the values of p and q                                                  [8 marks]

   6   Solve the following simultaneous equations:                           

       1 + log₂ (x² + 2y²)              = log₂ 18

                       2 + log₂ y            = log₂ (9 + x)

                                                                                                                                           [8 marks]

 

 SECTION B  

Answer 4 question in this section.

[40 marks]

 

7   (a)  Given the function f : x → 5 – ax and f ^–1 (1) = a, find the values of a.

(b)  Given the functions f : x →  7/ (x-2)     and g : x → 5 + 2x. 

       Find            

          (i)   f ^–1(x)

          (ii)  the value of x such that gf(x) = 5.                                 

                                                                                                                                           [10 marks]

 8   (a)  Find the value of k for which the line 3y + kx = 6 is a tangent to the curve x² + xy = 3.

       (b)  Show that the line y + 2x = p will intersect the curve x² + xy – 5y = 12 at 

              two different points if p² + 52 > 0.

                                                                                                                                          [10 marks]

9   (a)  Find the range of values of m for which the line y = mx + 4 does not meet the curve  

            xy – 5x² = 4.

       (b)  It is given that one of the roots of equation (3x – 9)(x – 6) + p = 0 is half 

             of the another root. Find the value of p.        

                                                                                                                                            [10 marks]

10  The function f is defined for the domain –2 < x < 2 by f(x) = 2x² + 3x – 20. 

(a)  Express f(x) in the form a(x + b)² + c, where a, b, and c are constants. 

(b)  Find the range of f(x) corresponding to the given domain. 

(c)   Find the solution set of x for which f(x) > 0. 

(d)    State the coordinates of the turning point of the curve

                                                                                                                                             [10 marks]

11  (a)  Given that log₅ 2 = 0.43 and log₅ 3 = 0.68, find the value of  log₅ 1.5 without using a calculator.

      (b)  Simplify 16(5ⁿ)– 2(5ⁿ).

      (c)   Given that log₂ xy² = 4 – log₂ x, express y in terms of x.  If  y + 16x = 16,

              find the values of x and of y.               

                                                                                                                                              [10 marks]

 

  SECTION C  

Answer 2 question

[20 marks]

 12  The function h is defined as h : x → a – b /x . Given that  h(–1) = 9 and h(2) = 3.

       (a)  Find the values of a and b.

       (b)  Evaluate h^–1(–1). 

       (c)   Find the composite functions h^–1h and h^–2.                       

                                                                                                                                                [10 marks]

13  (a)  Find the range of values of c for which the equation  4cx² + 7x + c = 0 has real roots.

      (b)  Determine the value of p for which the straight line y = p(4x – 1) is a tangent to the 

             curve y = 16x² + 3.           

                                                                                                                                                [10 marks]

14  (a)  Solve the following simultaneous equations:             

                                2x + 3y    = 1

                            3x² + 4xy – y² – 6   = 0

       (b)  Find the coordinates of the intersection points of the curve x/y = 10 and the

               line x + y = 1.          

                                                                                                                                                [10 marks]

15  (a)  Find the value of     log₅ x  +   2log₅   =  5

      (b)  Given that x = log₅ p is the solution of the equation  5^{2x + 1} + 10 = 51 (5^x), 

              find the value of p.              

                                                                                                                                                [10 marks]

U OLS , PLEZ DO DIS EXERCISE K..WE'LL DISCUSS THE ANSWER IN CLASS SOON!