Mathematics Third Term Examination Questions 32019/2020 Session – Senior Secondary School Two( SSS 2)

EDUDELIGHT GROUP OF SCHOOLS

1 Benson Avenue, Lekki Phase 1, Lagos.

3RD TERM EXAMINATION 2019/2020  SESSION

SUBJECT: FURTHER MATHEMATICS CLASS: SSS 2       TIME: 2HRS

SECTION A (OBJECTIVES)

  1. Simplify:     (A) – tan θ (B) –cos θ (C) tan θ (D) cos θ
  2. If (x+1) is a factor of the polynomial: ,find the value of  p
  3. -2  (B)- 3 (C)- 4(D)15
  4. A polynomial is defined by find f (2) (A) -8 (B) -4 (C) 4 (D) 2
  5. Differentiate  with respect to x .  (A)   (B) –  (C)   (D)
  6. In computing the mean of 8 numbers, a boy mistakenly used 17 instead of 25 as one of the numbers and obtained 20 as the mean. Find the correct mean.   (A)19 (B) 21 (C) 23 (D) 24
  7. Given that nPr =90 and nCr =15, find the value of r.  (A) 2  (B) 3 (C) 5 (D) 6
  8. Which of the following options is not a measure of Central Tendency         (A) Mode  (B) Variance (C) Mean (D) Median
  9. A fair die is tossed twice. Find the probability of obtaining a3 and a5.
     (A)   (B)  (C)   (D)
  10. Find the number of different arrangements of the letters of the word IKOTITINA.  (A) 30240(B) 60840  (C) 120960  (D) 362880
  11. A box contains 4 red and 3 blue identical balls. If two balls are picked at random, one after the other without replacement, find the probability that one is red and the other is blue.(A)   (B)  (C)   (D)
  12. If y = 3e -4x, find . (A) -3e -4x  (B) -12e -4x (C) 12e -4x (D) 4e -3x
  13. The reciprocal of tanx is   (A) cosec2x (B) cot2x (C) sec2x (D) cotx
  14. Differentiate sin 5x. (A) cos 5x  (B) – 5sin 5x (C) 5 cos 5x (D) -5cos 5x
  15. The reciprocal of sin θ is  (A) sec Ѳ   (B) cot Ѳ (C) tan Ѳ (D) cosec Ѳ
  16. The reciprocal of cot θ is (A) sec Ѳ   (B) sin Ѳ (C) tan Ѳ (D) cosec Ѳ
  17. Find the standard deviation of 2,3,5 and 6 (A)  (B)  (C)  (D)
  18. If cotθ = , where θ is an acute angle, find sin θ. (A)   (B)  (C)   (D)
  19. Find the gradient of the line passing through points P(1,1), and Q (2,5). 
     (A) 4  (B) 3 (C) 2 (D) 5
  20. Solve for x and y if x – y  = 2 and x2-y2 = 8  (A) (1,3)   (B) (-1,3) (C) (3,1) (D) (-3,1)
  21. If x is inversely proportional to y and x = 2 when y = 2. Find x when y = 4      
    (A) 4  (B) 5 (C) 2(D) 1
  22. If (x-3) is a factor of 2x3+3x2+17x-30, find the remaining factors
    (A) (B)  (C) (D)
  23. Evaluate 5C3 + 5C2 (A) 40  (B) 30 (C) 20  (D) 10
  24. Polynomial is defined by (A) -8 (B)-2 (C)12  (D)14
  25. If the mid-point of the line joining  (1-k,-4) and (2,k+1) is (-k,k), find the value of k.(A) -4   (B) -3     (C)-2   (D)  -1
  26. If  find the values of x at the turning points.(A)        (B)        (C) 1, –           (D)  1,
  27. A binary operation, ∆, is defined on the set of real numbers by a  ∆ b = a + b + 4.Find the identity element of operation ∆ .  (A)4         (B)2  (C) (D) -4
  28. Express the product of 0.21 and 0.34 in standard form.
     (A) 7.14 x 10-1 (B) 7.14 x 10-2 (C) 7.14 x 10-3 (D) 7.14 x 10-4
  29. Find k if 6k78 = 5118. (A) 6 (B) 5 (C) 3 (D) 2
  30. Evaluate  . (A) 6 (B) 5 (C) 3 (D) 2
  31. Evaluate  . (A) 6 (B) 5 (C) 3 (D) 2
  32. If (3x – 1) is a factor of the polynomial f(x) = 4x3 – 4x2 – X + P, find the value of constant p.        (A) 7/27 (B) 17/27 (C) 5/27 (D) -7/27
  33. Evaluate (1012)2, leaving your answer in base two. (A) 101012 (B) 100102 (C) 110012 (D) 111012
  34. If (2x + 3)3 = 125, find the value of x. (A) 0 (B) 1 (C) 2 (D) 3
  35. Evaluate  . (A) -2 (B) 2 (C) 0 (D) 1
  36. Find the numbers of arrangement of 7 objects taking 3 at a time.
    (A) 40  (B) 30 (C) 20  (D) 10
  37. Find the numbers of arrangement possible from the word SUCCESS.   
    (A) 30  (B) 50 (C) 180 (D) 210
  38. Eight football clubs are to play in a league on home and away basis. How many matches are possible?  (A) 14  (B) 28 (C) 56  (D) 128
  39. Given that 2x = 0.125, find the value of x. (A) 0  (B) -1 (C) -2  (D) -3
  40. 40. If  p and q are the roots of the equation  3X2 – 16X + 2=0,
         find the value of  p + q(1+p).       A. – 14  B. – 6  C. – 4  D.6 

SECTION B (THEORY)

Instruction: Answer any four questions in this section.

(1a) Differentiate (x-3)(x2+5) with respect to x.                                         (5marks)
(1b) Simplify  –                                                                               (5marks)

(2a) The ratio of the coefficients of x4 to x3 in the binomial expansion of (1+2x)n is
         3:1. Find the value of n.                                                                        (4marks)

 (2b) given that A = , Show that AA-1 = I.                                     (6marks)

(3a) Find the gradient of x2 + y2 +3xy = 14 at the point (1, 3).               (5marks)

(3b)If f(x) = 6x2 , find Lim       f( x+h) – f(x) (5Marks)

 (4a) If =   , find  .                                                                        (5marks)

(4b) If   = -24. Find the value of x.                           (5marks)

(5a)Given that  Q(x) = ax2 + bx +5. If Q(1)=6 and Q(-1)=12, determine thevalues of 
       a and b.                                                                                                      (4marks)
(5b) If the first three term of the expansion of (1+kx)n in ascending powers of x
        are 1 + 20x + 160x2.       Find the value of n and k.                            (6marks)
 (6) Using Matrix method solve the equation below                                                                       

 3x – y – z = 11

x + 5y + 2z = -1

2x + 3y + z = 15.                                                 
                                                                                                                             (10marks)

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