MATHEMATICS FIRST TERM EXAMINATION SS 2

   FIRST TERM

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

SUBJECT: MATHEMATICS                                                    SS 2   TIME:           2HRS

OBJECTIVES:     Instruction: Answer all questions

1. If f (x) = -3x – 5, what is the value of  f (2) ?            A. -11       B.  -1       C.  1
   D.11
2. simplify: A. 1+cosx B. 1     C. sin(2x)    D. cos(2x)
3. find the value of x. A. 3 B.1      C.       D.
4. Simplify:  is    A. 6(1-3k²)    B. 6(3k²-1)     C.  6(3k-1) 6(1-3k)
5. If sin x = -sin 70^o, 0^o< x <360^odetermine the two possible values of x.
   A. 110^0,   250^o     B. 250^0,290⁰     C. 110⁰, 290⁰         D. 200⁰,250⁰
6. If g (x) = 3x² – 2x – 5, what is the value of g (-1)?                                  A.  3    B. 2      C. 1     D. 5
7.  What is the value of   sin(-240)     A.      B.     C.   D.

8       Form the equations whose roots are  x=  and x = –    A.6x²+x-2  B. 6x²+x+2  C. 6x²-x+2  D. 6x²-x-2

9       What is the distance between the points  P(-1,3) and Q(2,-1)   A. 23    B.25    C.5
D. 3

10. One of the factors of (mn-nq-n²+mq) is (m-n). The other factor is :
    (a) (n-q)   (b) ( q-n)   (c) (n+q)  (d) (q-m)
11. The length of a piece of stick is 1.75m. A girl measured it as 1.80m. Find the
    percentage error.   A.     B.   C.    D. 5%
12. If and . Find      C.     D.
13. Given that   .    What is the value of ?   A. 10      B.4 C.3       D.14
14. What value of x in the interval satisfies the equation ?    A.  -30⁰    B. 30^o    C. 45^o    D. 150^o
15. Simplify: (a)  3    (b)  5    (c)         (d)
16. The height of a cylinder is equal to it’s radius. If the volume is 0.216³, calculate the radius.
    (a)  0.46m  (b) 0.60m  (c) 0.87m   (d) 1.80m
17. Which of these is a factor of       A: x+3    B: x-4    C: x+2    D: x-1
18. Suppose , then is A. 1 B.          C.               D.
19. Given that  tan x = , what is the value of sin x + cos x? A.         ¹⁷/₁₃   B.         ⁵/₁₃
    C.     ⁷/₁₃     D.         ¹²/₁₃
20. If x + y =1;  2y-x=5,  Find the value of x.   A. 3B. 2    C. 1  D. -1
21. The sum of 12 and one third of n is more than twice n. Express the statement in

the form of an equation.    A. 12n-6=0    B. 3n-16=0    C. 2n-35=0      D. 5n-33=0

22. Express   as a simple fraction   A. B. C.   D.
23. If P(x)=x²+3     Then P(x) + p(-x)    A. 6    B. C. D. 0
24. Given that , . Then is A.     B. C. 0         D. 2
25. If g (x) = 3x² – 2x – 5, what is the value of g (-1) A. -4    B. -10    C.-6     D.  0
26. What is the value of the discriminate of the quadratic equation
    A.-13    B.13   C.49   D.
27. If y varies directly as the square root of (x+1) and y=6 when x = 3, find x when y =
    9.      A. 8    B. 7   C. 6    D. 5
28. If x+1 is a factor of then the value of k is A. 2    B. 3   C. -3    D. 4
29. If ), then b is A. 0     B. 7   D.
    30.    When a number is subtracted from 2, the result equals 4 less than one-fifth of the
    number. Find the number.   (A) 11  (B)   (C) 5  (D)
30. Solve for x in 7x +4 < (4x+3) (A) x >     (B)  x  < –     (C) x >    (D) x <
31. If X= , Y = and Z = are subsets of U= ,
    Find X A.    B.   C.   D.
32. Subtract (a-b-c) from the sum of (a-b+c) and (a+b-c) A. (a+b+c)   B. (a+b-c)  C. (a-b+c)   D.  (a+b-c)
33. A man’s eye level is 1.7m above the horizontal ground and 13m from a vertical pole. If the pole is 8.3m high, calculate correct to the nearest degree, the angle of elevation of the top of the pole from his eyes.
34. 33^o       B. 32^o       C.  27^o          D.  26^o
35. If a number is selected at random from each of the sets P= and Q= , find the probability that the sum of the numbers is prime.
    A.       B.        C.      D.

o               S

86

Q              R

In the diagram, O is the centre of the circle, PR is a tangent to the circle at Q and <SOQ =86^o, calculate the value of < SQR.
A. 43^o   B. 47^o  C. 54^o   D.  86^o

37. A trader bought 100 oranges at 5 for N40 and sold them at 20 for N120. Find the profit or loss percent. (a) 20% loss (b) 20% profit  (c) 25% loss (d) 25% profit
38. A letter is selected from the letters of the English alphabet. What is the probability that the letter selected is from the word MATHEMATICS?
    A.      B.      C.     D.
39. Approximate 0.03457 to 1 significant figure. (a) 0.0 (b) 0.03 (c) 0.0005 (d) 0.004.
40. Calculate 0.09 x 0.78 correct to 3 decimal places. (a) 0.070 (b) 0.071 (c) 0.007 (d)
    0.0702.
41. 41. The nth term of the sequence 6, 8, 10, 12… if n= 1- is     2n+3   B. -3n+6
    C. 2n+4  D.  –n-1
42. The sum of the infinite progression 3, 1,         (a) 4   (b)  6   (c) 2  (d) 5
43. The second and seventh term of a GP are 18 and 4374 respectively, what is the common ratio?     (a)  6   (b) 3      (c)  4     (d)  2
44. The terms that must be added to x² + 12x to make it a perfect square is
    (a)  24    (b)  -18       (c)  16      (d)  36
45. The breadth of a field is 3m less than its length. If the area is 180m²,
    What are the dimensions of the rectangle?
    (a) 15m,12m  (b)  8m, 6m  (c) 13m, 10m   (d)  9m, 6m
46. If 3^x+3y=3  and  5^2x+y=25. Find 2^x+2y    (a)  4    (b)  ¹/₂      (c)  7    (d)  2

47. The sum of two numbers x and y , is twice their difference. If the difference between the numbers is p, find x in terms of p and y.
    (a) x=y-2p    (b) x= 2y-3p    (c)  x= 2y-p   (d) x= 2p-y
48. A ………. Is the sum of the terms of a sequence (a)  finite series (b)  infinite series   (c) exponential series   (d)  series
49. A car travels a distance of 100km for 1hr 39min. Calculate the speed of the car. If the time is rounded up to the nearest hour, find the difference between the actual and the estimated speed.   (a)  11.61km/h    (b)  9.61km/h   (c)  10.61km/h   (d)  12.61km/h
50. Geometrical progression is also known as ……………..
    (a) Linear Sequence  (b) Composite Sequence (c) Constant Sequence  (d)   Exponential Sequence

SECTION B: THEORY

Answer four questions only. No 1 question is compulsory

1.         Use the table of logarithm to evaluate the following

1.     0.951³

2a.        The fourth term of a linear sequence is 37 and the 6th term is 12 more than
the fourth term . Find the (i) first term (ii) common difference (iii) twentieth term

1.      Solve the inequality:

3a.         The sum of the first three terms in an exponential sequence is 38 and their product is 1728. Find the values of the first three terms.

1. Find the constant that must be added to make each of the following expressions a perfect square,then factorize

(i)  4a² – 10a           (ii)  z² – z

4a.       The 2nd and 5th term of a Geometric Progression are -6 and 48 respectively.   Find the sum of the first four terms.

1. Use completing the square method to solve the quadratic equation
   3k²+4k+1=0

5a.         Proof: ax²+bx+c =0 is x=  -b±   using completing the square

2a

1. The breadth of a field is 5m less than the length. If its area is 36m², find the
   dimensions of the field.

6a.         Find the sum and products of the roots of the following quadratic equations.

• 8x²-2x-15=0 (ii) (x-3)(x-5) =2(x-3)

1.         Solve the equations: x-3y=2 and  x²+2y²=3 simultaneously.
   c.          Solve the pair of simultaneous equations graphically.  y=2x²-6x+2, y=x+4
   for  -3

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

SUBJECT: F/MATHEMATICS                                                    SS 2   TIME:           2HRS

Instruction:                          Answer all questions

SECTION A: Objectives

1. simplify: A. 1+cosx    B. 1   C. sin(2x)    D. cos(2x)
2. is a polynomial of what degree    A. 3    B. 1   C.   0   D. None of the above
3. If  , then is    A. 0     B. 1   C. 47
4. What is the value of the discriminate of the quadratic equation

A.-31     B.31    C.49     D.

5. What remainder does leave upon division with x+1
6. 7     10   C.  11      D.1
7. If and . Find    B.     C.     D.
8. Given that   .  What is the value of ?
9. 0 B.2         C.               D.
10. What value of x in the interval satisfies the equation

?      A.  -30^o    B. 30^o    C. 60^o    D. 150^o

9. Given that g(x)=x+2   f(x)=x-1. Calculate   g[f(1)] + f[g(1)]
10. 5   4     C. 6     D. 3
11. Given that sin(x-20)=cos70. what is x?     A. 90    B. 50     C. 40    D. 30
12. An equation of form is called the
13. Quadratic equation   B. cubic equation   C. linear equation
14. Polynomial of degree n
15. Which of these is a factor of A: x+3 B: x-5    C: x+2   D: x-1
16.  suppose, then is   A.          1  B.       C.                 D.
17. Which of these is a polynomial A.   C.  D.
18. What degree of polynomial is   3     B. 2     C.1     D.5
19. What is the value of sin(-240)    A. B.C.D.
20. Given that  tan x = ⁵/₁₂, what is the value of sin x + cos x?
21.     ¹⁷/₁₃            B.      ⁵/₁₃       C.         ⁷/₁₃              D.         ¹²/₁₃
22. In its simplified form, sin2x is equal to     A. B. sinxcosx   C. 2sinxcosx
23. tanxcosx
24. The polynomial  2x³ + x² – 3x + P has a remainder 20 when divided by (x – 2).   Find the value of constant P.   A. 8          B. 6    C. 7            D.  5
25. If P(x)=x²+3  Then P(x) + p(-x)   A. 6   B. C. D. 0
26. Given that , . Then is  A.    B. C. 0       D. 2
27. If is divided by x+1, the remainder will be   A. 0    B. 49    C.50 D.  1
28.   What is the value of the discriminate of the quadratic equation

A.-31    B.31   C.49    D.

24. If x+1 is a factor of then the value of k is    A. 2   B. 3   C. -3   D. 4
25. If ), then b is    A.  0   B. 7   D.
26. The quadratic equation whose roots are -1/2 and 3/2 is

|          A. 2x²-8x-3=0         B. 4x²-16x+8=0     C. 4x²-4x-3=0               D. 3x²-3x-4=0

27. For any 𝜃, the cos(- 𝜃) is same as   A. cos𝜃 B. –cos𝜃   C. sin𝜃         D.D. -sin𝜃
28. If , then the zero of polynomial will be
29. B.         C.    D.
30.  What  remainder  does  x²⁰¹⁹ + 2018x²⁰¹⁶ – 2016x²⁰⁰⁴  +  1  leave  upon  division  with  x + 1       A.  2015     B.  1- x²⁰¹³   C.  -2015    D.  2018
31.  If g (x) = 3x² – 2x – 5, what is the value of g (-1)   A. -4    B. -10    C.-6     D.  0

SECTION B: THEORY :   Answer four questions only. No 1 is Compulsory

1. Find the values of the following if ,
   Calculate the values of the followings: (i) (ii)  (iii)   (vi)
2. (a) Proof: Sum of roots   , =   and product of roots

(b) Construct an equation whose roots are  x=3 and  x=4

3. (a) Use “trial&error”  to factorize  x³  + 2x²  – 9x -18.
   (b)    Using Addition formulae, evaluate each of the following in surd form
   (i) cos 15^o            (ii) tan 105^o                (iii) sin 195^o
4. (a) If P₁ = 3x³+2x² + x + 5  and P₂ = 2x³-7x²+3x-2

(i) Find 3(2P₁+P₂)  (ii) P₁ x P₂    (iii) P₁ – P₂

(b)  If (x-1) and (x+3) are factors of x³ + ax²-11x+b where a and b are constant.
Find a and b and the third factor.

5. (a) Use (a+b)² formular to find the values of a²+b² and ab when a+b =6 and a-b=2
   (b) One of the root of the equation 2x²-3x+c=0 is triple the other root. Find C?
   (c)  If +5x-3=0 produce equations whose roots are
   (i)           (ii)        (iii) ,
6.  (a) What is proposition?
   (b)  Use truth table to show that (i) (ii) (p
   (c)  Divide the polynomial P₁(x) = 4x³+3x²-2x+1 by the polynomial P(x)= 2x-3