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## Ss2 Further Maths questions

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FIRST TERM  EXAMINATION, 2010/2011 SESSION.
SUBJECT: FURTHER MATHEMATICS 2
CLASS:SSS 2	       	         TIME ALLOWED: 2½HRS

Theory
Section A : answer all the questions  in this part.
Find the equation of the circle with centre (-3,-2) and radius 4 units.                   	(5 marks)
Determine the centre and radius of the circle x2 + y2 -4x + 6y -3 = 0.                     	(5 marks)
The parabola x2 = 12y find (i) the focus  (ii) the directrix of the parabola.            	(5marks)
Determine the focus and the vertex of the ellipse 4y2 + 5x2 = 20.                          	(5 marks)
An operation * is defined on the set S = {0,1,2,3,4,5} by x * y = x + y – xy.                                     Find :  (a) 0 * 4  (b)  3 * 1  Is the set close under the operation * ?                        	(5 marks)
Solve the equation 32x – 30(3x) + 81 = 0.                                                                   (5 marks)
Simplify 					           		(5 marks)
If (2x+1) is a factor of the polynomial  f(x) = 2x3 + x2 -8x + k, find the value of                                     the constant k.								           		(5 marks)
Determine the vertex and the foci of the hyperbola 9x2 – 4y2 = 36.	           		(5 marks)
Resolve      into partial fractions                                                          (5 marks)

SECTION B : Answer five questions only from this part.
(a) Find the equation of the normal to the circle x2 + y2 + 3x + 5y – 18 = 0  at			  point (1,2)								            	(10marks)
110 members of a sports club play at least one of the games, football, basketball and volleyball. If 20 play football and volleyball only, 26 play  basketball and volleyball only, x play all the three games, 2x each play only one game, how many play basketball altogether ?		(10 marks)
A binary operation * is defined on the set R of real numbers by x * y = x2 + y2 + xy  for all x,y R (a) evaluate  2 * (3 * 4)   (b)  solve the equation 6 * x = 27.	             		(10 marks)
Write the equation of the parabola y2 + 4y + 4x + 16 = 0 in its canonical form. Hence determine its vertex, focus and directrix.				            			 (10 marks)
Use the truth table technique to verify that (a) ~p v q = p ? q (b) p v ~q = q ? p (c)  (p^ q) ?  (p ? q)  							             			(10 marks)
Write the equation of the ellipse 4x2 + 5y2 – 24x -20y + 36 = 0 in its canonical form and hence determine its foci and vertices.				             		(10 marks)
Given that S4 = {2, 4, 6, 8}, form the operation table for multiplication in modulo 10.		 Hence , determine the identity and the inverse elements.				(10 marks)
Find the equation of the normal to (i) the parabola  x2 = 9y at point (6,4) (ii)  the ellipse x2 + 4y2 = 4 at point (0,1)										(10 marks)

FIRST TERM  EXAMINATION, 2010/2011 SESSION.
SUBJECT:  FURTHER MATHEMATICS 1
CLASS: SSS 2	       	        TIME ALLOWED: 2½HRS

Find the value of    if  a * b =  (a)  3  (b)  (c) (d)
In how many ways can 6 beads be threaded in a circular ring ?  (a)120  (b) 30  (c) 60  (d) 15
Given that  find y (a) 
Given that  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
Find the coordinates of the centre of the circle 4x2 + 4y2 – 5x + 3y – 2 = 0. (a)               (b)   (c)   (d) 
The gradient of the line passing through the points  P(4,5) and Q(x,9) is 0.5 Find the value of x. (a)  -4  (b) 0  (c)  4  (d)  12
Given that log2    = log5125, find the value of y.  (a)  16  (b) 25  (c) 36  (d) 64
The polynomial g(x) = 2x3 + 3x2 + qx – 1,has the same remainder when divided by x + 2 and          x – 1. Find the value of constant q.  (a) -11  (b) -9  (c) -3   (d) -1
Given that p=4i + 3j, find the unit vector in the direction of p.  (a) (4i + 3j)   (b)  (3i + 4j)     (c) (3i + 4j)  (d)    (4i + 3j)
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
The roots of a quadratic equation are -3 and 1. Find its equation. (a) x2 -3x + 1= 0  (b) x2 -2x + 1 = 0.  (c) x2 + 2x – 3 = 0  (d) x2 + x – 3 = 0.
Find the range of values of x for which x2 + x – 6 = 0   (a) -3 < x < 2  (b) -3 < x =  2  (c) -3= x < 2     (d) -3= x =  2.
Which of the following is not a scalar ?  (a) torque  (b) frequency  (c) power  (d) resistance
Find the length of the shortest distance between  P(3,4) and Q(-2,1)  (a) 5  (b) 3  (c)(d)
If  9x-3 P(x -2) + Q(x + 1), find the values of P and Q. (a)  -4,5  (b) 4,5  (c)  -4,-5  (d)  4,-5
Find the magnitude of the resultant of the velocities12ms-1 and 5ms-1 which are at right angle to each other.  (a) 10ms-1  (b) 7ms-1  (c( 13ms-1  (d) 17ms-1
If  f( x -1) = x3 + 3x2 – x + 2, find  f(0).  (a) 2  (b) 5  (c) 4  (d) 3

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.
Find the slope of the line 7y + 3x + 2 = 0  (a) 
What is the LCM of   ?    (a) x2 + y2  (b) x2 – y2  (c) 
Find the length of the tangent to the circle x2 + y2 – 4x + 2y – 11 = 0 drawn from the point P(6,4).  (a) 2  (b) 3  (c) 4  (d) 5
Find the number of terms in the progression 3,6,9, . . . ,93. (a) 18  (b) 27  (c) 42  (d) 19.
In how many ways can the letters of the word PRESIDENT be arranged in order ?  (a) 720          (b) 5040  (c) 362880 (d) 181440
Find the equation of the normal to the circle x2 + y2 + 4x + 8y -48 = 0 at the point (6,-2)               (a) y – 7x + 2 = 0  (b) 4y – x + 14 = 0 (c)  14y + 4x + 1 = 0  (d) y + 4x – 14 = 0.
If 3,p,75,q,1875 are five consecutive terms of a geometric progression, find q – p. (a) 375  (b) 15  (c) 360  (d) 480
If sin ? = ,   find 1 + tan2 ? (a) 
Find x such that  3 x+1 + 3 x = 108  (a) 2 (b) 3 (c) -4 (d) 5
In how many ways can a delegate of 5 people be seated round a circular table ? (a) 120  (b) 60 (c) 30 (d) 15.
Find the centre of the circle x2 + y2 – 8x – 10y + 32 = 0  (a) (4,5)  (b) (-4,5)   (c) (4,-5)  (d)  (-4,-5)
Find the equation of the normal to the parabola y2 = 8x at the point (2,4)  (a) 3x + 3y -1 = 0        (b) x + y -6 = 0  (c) x + y + 6 = 0   (d) x – y – 6 = 0.
 Is an example of (a) circle  (b)  parabola  (c) ellipse  (d) hyperbola.
If  ,find b – a (a) 0  (b) 1  (c) 3  (d) 4
Find the modulus of the vector r = 3i + 8j – 10k  (a) 
Find the centre of the ellipse  4x2 + 9y2 – 24x – 36y + 36 = 0  (a)   (-3,2)  (b)   (-2,-3)  (c)   (2,3)       (d)   (3,2)
The reciprocal of   is   (a) 
A man spent  of his monthly salary on rent and  of the remainder on household needs. If #135:00 is left,how much is his monthly salary ?  (a) #450:00  (b) #225:00 (c) #192:85 (D)#125:00
By how much is 7a greater than 10 ? if 2a + b = 7 and 3a – 2b = 3.  (a) 17  (b) 10  (c) 7  (d) 3
Find the positive number n, such that thrice its square is equal to twelve times the number.     (a) 1  (b) 2  (c)  3  (d) 4
If  x*y = xy + x + y , solve the equation  (x*3) + (2*x) = 40 (a) 4  (b) 5  (c) 6  (d) 7

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### Ss2 Further Maths guide

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