FURTHER MATHEMATICS EXAM QUESTIONS FOR SS1 THIRD TERM

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THIRD TERM SS1 FURTHER MATHEMATICS EXAMINATION QUESTIONS – EDUDELIGHT.COM

THIRD TERM EXAMINATION

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.     

A. {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   

A. 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

  •  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.
  •   Simplify 2log28 – 3log22.      A. 3                 B. 2              C. 1          D. -1.
Number of babies35678
Number of villages1X2X32

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

  • Find the median of the distribution           A. 1              B. 2               C. 3          D. 6
  • Find the mode of the distribution                     A. 6           B. 5              C. 4              D. 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
  • Simplify:  -6)1/2          A. r/2          B. 2r            C. 1/2r           D. 2/r
  • What is the product of 27/5 , 3-3 and (1/5)-1         A. 5           B. 3           C. 1            D.1/25
  • Evaluate: (81)3/4 – (27)1/3          A. 27            B. 1            C. 1/3          D. 1/8
  • Without using tables, evaluate:

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

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

  • 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.

  • Find the first term    A. 2     B. 3        C. 2     D. 3   
  • Find the common difference    A. 2    B. 3    C. 4     D. 5     
  • Find the sum of the first 20 terms of the sequence    A. 450     B. 420     C. 400     D. 380   
  • 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.

Read Also

47. Solve the inequality:   <      

 A. x <        B. x >        C. x > 7       D. x < 7

48. If the domain of f: x  x2 – 2 is, find its range.            A.            B.     C.            D.

49. Given that P =  is the domain of g(x) = x2 + 3x – 5, find the range of g(x).    

A.            B.              C.             D.

50. Simplify: 36 ½  x 64– 1/3 x 5o  (a) 0   (b) 1/24  (c) 2/3   (d) 1 ½ (e) 7 ½

THIRD TERM SS1 FURTHER MATHEMATICS EXAMINATION QUESTIONS – EDUDELIGHT.COM

PAPER2 (2HRS)

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

  •  (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:
  • The number that applied to both the Daily Times and the Daily Graphics.
  • The number that applied to the Daily Times and the Punch.
  • The number that applied to both the Daily Graphic and the Punch.
  • 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,

  • Find the identity element e of R under the operation *
  • Determine the inverse of the element x  R, under the operation *
  • Find the value of x  R, which has no inverse.
  • (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   

ii. 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 

THIRD TERM SS1 FURTHER MATHEMATICS EXAMINATION QUESTIONS – EDUDELIGHT.COM

OBJECTIVE

F/MATHS                                                                                                                                                             S.S.1

  1. Given that x= – 3 and y= – 7

Evaluate                                                     

(a)-1/11                  (b) 1/23                  (c) 4/13                  (d) 12/17.

  1. The solution of the equation  x2-2x-8 is
  2. X=0 or 12             (b) x=-2 or 4       (c) x=2                  (d) x=2 or 4
  3. Express the conjugate of 2 +
  4. 2                              (b)                    (c)   +2             (d) 2 –
  5. If f(x) = 10x-3 find f(2)
  6. 7                              (b) 20                    (c) 3                       (d) 17
  7.  Find the 4th term of an A P whose first term is 2 and the common different is 0.5
  8. 0.5                          (b) 2.5                   (c) 3.5                    (d) 4.
  9. Cot q can be express as
  10. 1/sin q                   (b) 1/cos q           (c) 1/tan q            (d)tan q
  11. Solve the inequality y+9 > 5y-7
  12. Y > 4                       (b) y > – 4             (c) y < 4                (d) y < – 4
  13.  Calculate the distance between the two point P (1,6) and Q (5,3)
  14. 6                              (b) 5                       (c) 4                       (d) 3
  15. Find the sum of the first 12 terms of the series 5 + 9 + 13 +
  16. 612                         (b) 702                  (c) 119                   (d) 324
  17. If 3x – y = 23 and 2x + 5y = 4 find the valve of y
  18. – 20                        (b) -2                     (c) 2                       (d) 7
  19. If  2x = 4 find the valve of x

5

  • 10.1                       (b) 10                    (c) 12                     (d) 9
  1. If the square root of 4 is 2 then find the square root of 400
  2. 20                           (b) 200                  (c) 40                     (d) 2000
  3. If P =  find the valve of p
  4. 24                           (b) 6                       (c) 48                     (d) 12
  5. Express 27-2/3
  6. 9                              (b) 1/9                    (c) 0.9                    (d) 1
  7. Express a6 x a-3
  8. a3                            (b) a4                     (c) a5                      (d) a6
  9. Find the 40th term of the linear sequence 6,11,16,21.
  10. 201                         (b) 200                  (c) 75                     (d) 150
  11. Solve (1/2)x= 8 find x.
  12. 3                              (b) 6                       (c) – 3                    (d) – 6
  13. Simplify 10g10/10g108
  14. 1/3                           (b) 1/2                    (c) 10g             (d) 1/3 10g
  15. Solve the equation (x + 2) (x + 7) = 0
  16. X = 1 or 8              (b) x = – 2 or 7    (c) x = – 4 or 5     (d) x = – 3, 6
  17. The nth term of a sequence is given by (-1) n-2 x 2n-1. Find the sum of the second term.
  18. 3                              (b) 4                       (c) 2                       (d) 10

1. Simplify (0.2)3 x 8

                       (0.4)

(a)  40     (b) 0.4        (c) 0.2    (d) 0.04

2. Express 57 x 54

(a)  5          (b) 57        (c) 511        (d) 510

3.  Solve (1/2) x =8

(a)  -3      (b) 3          (c) 1            (d) 4

4. Determine the cardinality 0f set A = (a, m, b)

 (a)  2     (b) 3              (c) 1            (d) 4

5.  Venn diagram was developed by ………………………….

(a)  Joseph venn   (b)  wolevenn  (c)  John venn  (d)  Charle’s Venn

6.  If x = (2, 4, 6, 8,) y = (2, 5, 9, 11, 12). Then find X U Y.

 (a) (2, 4, 6, 8)   (b)  (2, 5,9, 2, 4, 6)   (c)  2, 4, 5, 6, 8, 9, 11, 12 )  (d)  2, 4, 5, 11 12)

7.  Solve for x in the equation 32x – 12(3x) + 27 =0

(a)  3, a   (b) 2, 1   (c) -3, 9 (d) -1, 2

8.  Evaluate log2\3 (4\9)

    (a) 2      (b) 2\3     (c) 1         (d) 0

9.  An operation × is defined on the set of real numbers R such that

       If x, y, ER then x x y = x + y     use it to answer 10 and 11

                                        2

10.  Determine 3x 2

       (a)  2\5   (b)   3\5    (c)   5\2    (d)   1\3

Theory

  1. Determine if AB is parallel or perpendicular to PQ in each of following
  2. A (3, 1)              B (4, 3)                  P (4, 6)                  Q (5, 8)
  3. A (5,1 )             B (3,2 )                p (2,4 )                 Q(5,6  )
  4. A (4,7 )             B (6,8 )                   p (3,5 )                   Q(5,6  )
  •  Find the distance between the following pair of point.
  • A(3,2) and B (4,6)
  • C(-1,3) and D (2,-7)
  • P(5, -8) and Q (-4,-2)
  • S(-3,-2) and 7 (1,-4)
  • (a) find the equation of the straight line which passes thigh the points

P (2,-3) and Q (-4, 2)

  •  Find the common ratio in each of the following exponential sequence.
  • 6, 12, 24, 48,————————–
  • 36, 12, 4, 11/3, —————————————-
  • 4,  -8, 16, -32, ————————–
  • 54, – 18, 6,  -2, ————————–

  • (a) Evaluate  

(b) Evaluate

THIRD TERM SS1 FURTHER MATHEMATICS EXAMINATION QUESTIONS – EDUDELIGHT.COM

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