SS 1 Third Term Examination Further Mathematics

THIRD TERM

Examination malpractices may lead to a repeat of the subject or suspensions don’t be involved.   

Subject:  FURTHER MATHEMATICS            Class: SS 1     DURATION ; 2Hrs   

OBJECTIVES

Answer all questions

1. If the third term of a geometric progression (G.P) is 10 and the sixth term is 80. Find the common ratio           A. 2   B. 3   C.   4   D. 8
2. A binary operation is defined on the set R, of real numbers by a*b = ab/4. Find the value of *       A.               B.                     C.                     D.
3. Given that the straight lines kx – 5y + 6 = 0 and mx + ny – 1 = 0 are parallel, find a relationship connecting the constants m, n and k.     A. 5n – km = 0  B. kn + 5m = 0          C. 5n + km = 0          D. kn – 5m = 0
4. Given that ( find q. A. 4     B. -4   C. -5   D. -7
5. The gradient of the line passing through the points P (4, 5) and Q (x, 9) is 1/2.find the value of x.         A. -4            B. 0        C. 4            D. 12
6. Find the equation of the line that is perpendicular to 2y + 5x – 6 = 0 and bisects the line joining the points P(4,3) and Q(-6,1)    A. y + 5x + 3 = 0        B. 2y – 5x – 9 = 0        C. 5y + 2x – 8 = 0        D. 5y – 2x -12 = 0
7. If f(x) = , find f-1 (-1/2)   A. 4        B. 0       C. -2         D. -4
8. Find the coordinates of the point which divides the line joining P (-2, 3) and Q (4, 9) internally in the ratio 2:3       A. (52/5, 2/5)         B. (2/5, 52/5)          C. (2/5, 22/5)                   D. (-2/5, 52/5)
9. If P = {x: 1 x 6} and Q = {x: 2 < x < 9}, where x R, find P Q.      

1. {1, 2, 3, 4}           B. {3, 4, 5, 6}           C. {4, 2, 9, 8}     D. {1, 2, 3, 5}

1. Simplify    -2/3       A.  4                B.  -1/4                  C.  1/8              D.  –4
2. A binary operation * is defined on the set R of real numbers by a*b = ab/4. Find the value of *.      A. 3                  B.                    C.              D.                                                                         
3. Given that ( = p + q find q.  A. -4   B.  -5    C. 4        D. 7. 
4. Evaluate log0.25 8.              A. -3/2                B.  2/3                 C. -2/3             D. 3.
5. Simplify 8n x 22n 43n.           A. 21-n              B.  2n                 C. 2n+1                   D. 2-n
6. Given that log2y1/2 = log5125, find the value of y. A. 36    B. 64   C. 25         D. 16
7. All the following operations are commutative except   

1. x*y = 2xy + xy      B. x*y = x2 – y2    C. p*q = 2pq       D. a*b = 1/2ab

1.  Evaluate; log10 (1/3 + ¼) + 2log10 2 + log10 ( 3/7).   A. 0      B. 1     C. 10  D. -1.
2. Solve: 32x – 4(3x) + 3 = 0 A. x = 0 or 1     B. x = 0 or 3   C. x = 1 or 2  D. x = 1 or 3   
3. 14. For what value of x will log2 4x + log2 (x + 4) = 7?   A. 2  B. 4    C. 6       D. 8
4. 15. If  + = 7, find the value of t.     A. 6          B. 7       C. 8       D. 9
5.  A binary operation is defined on the set R, of real numbers by ab = a + b + 4. Find the identity element of the operation.  A. 4        B.  -4           C. 2             D. ¼.
6.  If log93 + 2x = 1, find x.  A. –1/2          B.  ½               C.  ¼         D. -1/4.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      
7.  If 5/ – = m, where m is a constant, find m. A.9/4    B. 2    C.  7/4     D. 5/2.
8.  Simplify    log58            A. -2               B. 2             C.-1/2                 D. 1/2

           Log5

1.  Which of the following operations is not commutative?     A. a*b = a – b + ab       B.  a*b = 1/a + 1/b C.  a*b = a + b – ab            D.  a*b = 2a + 2b + ab. 
2.   Simplify 2log28 – 3log22.      A. 3                 B. 2              C. 1          D. -1.

The table shows the number of babies born in some villages on a certain day in a district. The mean of the distribution is 6. Use this information to answer questions 9 and 10

1. Find the median of the distribution           A. 1              B. 2               C. 3          D. 6
2. Find the mode of the distribution                A. 6           B. 5              C. 4              D. 3
3. Given that p * q = p2 + q2 + pq and p * (p + 1) = 61, find the value of p?    A. 3 or 7      B. -3 or 4                   C. -4 or 5           D. -5 or 4
4. Simplify: -6)1/2      A. r/2          B. 2r            C. 1/2r           D. 2/r
5. What is the product of 27/5 , 3-3 and (1/5)-1         A. 5           B. 3           C. 1            D.1/25
6. Evaluate: (81)3/4 – (27)1/3          A. 27            B. 1            C. 1/3          D. 1/8
7. Without using tables, evaluate:

 (343)1/3 x (0.14)-1 x (25)-1/2       

1. 12    B. 10         C. 8         D. 7

1. Simplify:  (0.2)3 x 8

                            0.42         A.40                 B. 0.4              C. 0.2             D. 0.04

40. Simplify:  4(2n + 1) – 2n + 2

                    2n + 1 – 2n               A. 2n + 2            B. 2n + 1               C.2n              D. 2           

Use the information below to answer questions 35, 36 and 37.

The sum of the second and fourth terms of an AP is 15; the sum of the fifth and sixth   terms is 25.

1. Find the first term    A. 2     B. 3        C. 2     D. 3    
2. Find the common difference    A. 2    B. 3    C. 4     D. 5     
3. Find the sum of the first 20 terms of the sequence    A. 450     B. 420     C. 400     D. 380    
4. Simplify:   4(2n + 1) – 2n + 2 

                    2n + 1 – 2n               A. 2n + 2            B. 2n + 1               C.2n              D. 2     

39. In a class of 32, a student can either do Government, History or both. If 16 students do Government, 18 do History and 3 students do none of the two subjects, find how many do both. A. 2  B. 5  C. 37  D. 34.
40. Simplify;.        A. 2.
41. Solve the exponential equation; 22x – 6(2x) + 8 = 0. A. -1 or 2      B. 1 or 2      C. -2 or 1    D. -1 or -2.
42. Solve the equation; (0.25)x+1 = 16.            A. -3       B. -2        C. 3          D. ½.
43. In a class of 18, a student can either offer Biology, Economics or both. If 8 students offer Biology, 12 offer Economics and 5 students offer neither of the two subjects. 

Use the information below to answer questions 44 – 46.

44. Find how many students offer both subjects.     A. 25        B. 17      C. 7       D. 12.
45. How many students offer exactly one subject?      A. 1      B. 6      C. 12        D.
46. Find the number of students that offer at most one subject. A. 11        B. 14       C. 13      D. 5.
47. Solve the inequality:  <
48. x <       B. x >       C. x > 7       D. x < 7
49. If the domain of f: x x2 – 2 is, find its range.            A.           B.   C.           D.
50. Given that P = is the domain of g(x) = x2 + 3x – 5, find the range of g(x).     
51.           B.             C.           D.
52. Simplify: 36 ½  x 64– 1/3 x 5o (a) 0   (b) 1/24 (c) 2/3   (d) 1 ½ (e) 7 ½ 

PAPER2 (2HRS) 

              Answer only four questions in this section. (50 marks)

1.  (a)A survey carried out recently to find the number of applicants that applied for jobs in three newspaper establishments revealed that 70 applied to the Daily Times, 65 applied to the Daily Graphics and 85 applied to the Punch. 40 applied to the Daily Times only, 20 applied to the Daily Graphic only, while 45 applied to the Punch only. If 5 applied to all the three newspaper establishments, find:

1. The number that applied to both the Daily Times and the Daily Graphics.
2. The number that applied to the Daily Times and the Punch.
3. The number that applied to both the Daily Graphic and the Punch.
4. The number that applied to at least one newspaper establishment.

(b)An operation * is defined on the set R, of real numbers by x*y = x + y + 3xy. If the operation * is commutative, 

1. Find the identity element e of R under the operation *
2. Determine the inverse of the element x R, under the operation *
3. Find the value of x R, which has no inverse.

1. (a)Solve for x if 22x+1 – 5(2x) + 2 = 0.

(b) Find the values of x which satisfy the equation; log10 (x2 + 4) = 2 + log10 x – log10 20.

 (3) (a) Find the gradient of the line whose equation is given by: (a – b)x + (c – d)y = e + f

 (b) Given that p = (4i – 3j) and q=(-1 + 5j), find (i) /p+q/  (ii) /q/

(4) (a) find the acute angles between the pairs of line: 4y + 3x = 2 and x – 2y = 3

(b) Find the equation of the line which is parallel to the line 5x + 4y = 18 and makes an intercept of 2 units on the x-axis

(5)(a)The function f over the set of real number is defined by f(x) = . Find f-1(5)

(b) Find without using logarithms tables, the value of:      log327 – log1/464 

                                                          log3 1/81

(6) (a) A binary operation *is defined over R (the set of real numbers) by                        

   x * y = xy + x2 + y2 for all x, y € R.    i.    determine whether or not * is commutative    

1. If x*(x+2) = 49, find x 

(b) Solve the equation: log10(4P2 + 1) – 2log10P – log102 = 1

(7)  (a) Consider the mapping below:                        X                f          G   

                                                          p                          1

                                                                                                        q                                         

 Find the range and determine the type of mapping above

(b) 52x+1 – 26(5x) + 5= 0