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## 5 Ss1 further mathematics questions

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THIRD TERM  EXAMINATION, 2009/2010 SESSION.
SUBJECT: FURHTER MATHEMATICS(1)
CLASS: SSS 1	       	         TIME ALLOWED: 2½HRS

Calculate the distance between the points P(3,5) and Q(5,6)     (A)   (B) 1  (C) 2   (D) 3
Given that    = 2 y+2 ,  find y. (A)   (B)    (C) 1  (D) 1
Given that ( )( ) = p + q    find q. (A) 4  (B) -4  (C) -5  (D) -7
Find the sum of the exponential series 96 + 24 + 6 + . . .  (A) 144  (B) 128   (C) 72 (D) 64.
Evaluate   log 0.25 8 (A)  (B)    (C)      (D)
Simplify  8n x 2 2n/ 4 3n (A) 2 –n  (B)  2 1- n   (C) 2 n (D) 2 n+1
The gradient of the line passing through the points P(4,5) and Q(x,9) is .      Find the value of x. (A) -4  (B) 0  (C) 4  (D) 12.
Simplify    (A)   (B)    (C)  3  (D)  2
If   f(x) = mx2 – 6x – 3 and  f(1) = -5, find the value of m.  (A) 9 (B) 3 (C) -3   (D) - 4.
Find the value of p which will make x2 – x + p a perfect square. (A) -       (B)   (C)   (D)  1
Given that  p = 4i + 3j ,find the unit vector in the direction of p.                     (A)   (B)    (C)  (D)  
Find the range 0f values of x for which  2x2 + 7x – 15 < 0. (A) -5< x  (B) 5< x< -  (C) -5< x< -  (D) < x <5
2x3 + x2 – 3x + p has a remainder 20 when divided by (x – 2). Find p. (A) 8  (B) 6  (C) -6  (D) -8.
Express   in surd form. (A) 2+  (B) 2 +  (C) 2 -  (D) 1 + 2
Given that sin ? = ,where ?  is acute , find the value of tan2? (A) -v3 (B) v3  (C)   (D) 
If  2x = 0.125 , find x. (A) 0  (B) -1  (C) -2 (D)  -3.
The first term of a geometric series is 350. If the sum to infinity is 250,find the common ratio. (A)  (B)  (C)  (D) 
P and q are statements such that p? q. which of the following is a valid conclusion from the implication ? (A) q?p (B) ~q?p  (C) ~q? ~p                 (D)  ~p? ~q
Find x, if log3(x – y) = 1 and  log3(2x + y) = 2  (A) 1  (B) 2 (C) 3  (D) 4

Which of the following is not a scalar ? (A) torque (B) frequency (C) power (D) length.
Find the magnitude of the resultant of the velocity 12ms -1 and 18ms -1 which are inclined at an angle of 300 to each other. (A) 17ms -1 (B)16.45ms-1 (C) 18.55ms -1 (D) 19.35ms -1.
If 9x – 3 = p(x – 2 ) + q(x + 1), find the values of p and q. (A) p = -4, q = 5     (B) p = 4, q = 5 (C) p = -4, q = -5 (D) p = 4, q = -5.
Which of the following is not a vector ? (A) velocity (B) latent heat (C) magnetic flux (D) force
If (x - 1) = x3 + 3x2 – x + 2, find f(0).   (A) 2  (B) 5 (C) 4  (D) 3.
The quadratic equation whose roots are  and   is    (A) x2 + 2x – 3        (B) 6x2 + x – 1 = 0  (C)  6x2 + x + 1 = 0 (D)  6x2 – x – 1 = 0.
If  cos ? = where 00 = ?= 900, find 1 + cot2 ?.  (A)  (B)          (C)   (D) 
The zeros of the polynomial x3 + 4x2 + x – 6 are (A)  -1, -2 and -3  (B) 1,-2 and -3  (C)  -1,2 and -3  (D)  -1,2 and 3
Find the magnitude of the vector  P = 4i + 2j – 3k   (A)   (B) 5  (C)   (D) 
Given that  =   ,find the value of A + B.  (A) 4 (B)3 (C)1 (D)7
If a = i – 3j + 2k and b = 4i + 6j – 4k find the vector 2a + 3b.(A) 8i + 14j – 12k (B) 14i + 12j -8k (C) 12i – 8j + 14k (D) 8i – 12j + 14k
If  3, p, 75,q, 1875  are five consecutive terms of a geometric progression, find  q – p (A) 375  (B) 15  (C) 350  (D)  480.
Without using tables, evaluate (A) 15  (B) 10  (C) 2  (D) 25.
Find the equation of the straight line whose intercepts on the x and y axes are (3,0) and (0, -2) respectively. (A)  3y – 2x + 6 = 0   (B)  3y + 2x – 6 = 0    (C)  6y + x – 3 = 0  (D)   2y + 3x – 6 = 0
Find x such that 3 x+1  +  3x = 108  (A) 2  (B) 3  (C) -4 (D)  5
If  f(x) = 2x2 + 1 and  g(x) = cos 2x find   g ( f(x) ).  (A) 2cos2 2x + 1                 (B) cos(4x2 + 2) (C) 2cos 4x + 1  (D) cos2 x + 1.
If  ,find the values of     (A)  (B)  (C)  (D)
When f(x) = 5x3 – 3x2 + 4x – 1 is divided by x – 3 the remainder is  ____    (A) 152  (B) 127  (C) 135  (D) 119
Simplify   (A) 2 2n+4  (B) 2 3-n  (C) 2 n+2  (D) 3 5-n
Simplify   (A) log35   (B) 1  (C)  2  (D)  3
An arithmetic progression has first term  11 and  fourth term 32. The sum of the first nine term is (A) 351  (B)  531   (C) 135  (D)  315.

THIRD TERM  EXAMINATION, 2009/2010 SESSION.
SUBJECT: FURTHER MATHEMATICS(2)
CLASS: SSS 1	       	         TIME ALLOWED: 2½HRS

EACH QUESTION CARRIES  EQUAL MARKS.
Solve  (a)  5 2x+1 – 26(5 x) + 5 = 0.  (b)  8 = 2 /  4
(a) simplify , without using  mathematical tables :                 (b) find the value of k given that:            log k – log (k – 2) = log 5
Express   in the form  p where  p and q are  rational numbers.
In an A.P, the difference between the 8th and the 4th term  is 20 and the 8th term is 1 times the fourth term. Find (i) the common difference  (ii) the first term of the sequence.
(a) When x2 + bx + 2 is divided by x + 3 the remainder is 5. Find the value of b.   (b) determine the values of  p and q if (x – 1)  and (x + 2) are factors of  2x3 + px2 – x + q.

SECTION  B  : ATTEMPT  ANY THREE QUESTION.
If    find p + q - r.
If p and q are two logical statements, in tabular form show the truth values of  ~(pvq) ^ ~p.
Find the values of ? between 00  and 3600 which satisfy the equation:        4sin?cos? +2cos? -2 sin? -  = 0
P,Q,R and S are the vertices of a quadrilateral such that A and B are the midpoints of the side  and  respectively. Show that 
If r = 2i – 5j + 7k  find (i) modulus of r  (ii) the direction cosines  (iii) the unit vector in the direction of r.

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### 5 Ss1 further mathematics guide

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