Further Mathematics SS 2 Third Term Examination

THIRD TERM

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

SUBJECT: FURTHER MATHEMATICS            Class: SS 2   DURATION ; 2Hrs

1. If X2 – KX  + 9 = 0 has equal roots, find the values of K. (a) 3,4  (b) +3  (c) +5  (d) +6
2. Find the coordinate of the centre of the circle 3x2 + 3y2 – 4x + 8y – 2 = 0. (a) (-2,4) (b) (-2/3, 4/3) (c) (2/3, -4/3)  (d) (2, -4).
3. Given that                     , find the value of M. (a) 20 (b) 12 (c) -10 (d) -22.

1. Find the coefficient of X4 in the expansion of (1 – 2x)6. (a) -320  (b) -240  (c) 240 (d) 320.
2. How many ways can six students be settled around a circular table? (a) 36  (b) 48  (c) 72  (d) 120.
3. Express Cos 150o in surd form, (a) √-3  (b) √3/2  (c) -1/2  (d) √2/2
4. Given that Sin X = 5/13 and Sin Y = 8/17, where X and Y are acute, find the value of Cos (X + Y).  (a) 130/221  (b) 140/221  (c) 140/204  (d) 220/23.
5. A circle with centre (4,5) passes through Y – intercept of the line 5x – 2y + 6 = 0. Find its equation. (a) x2 + y2 + 8x – 10y + 21 = 0  (b) x2 + y2 + 8x – 10y – 21 = 0  (c) x2 + y2 – 8x – 10y – 21 = 0  (d) x2 + y2 – 8x – 10y + 21 = 0.
6. Given that F(x) = 5x2 – 4x + 3, find the coordinates of the point where the gradient is 6. (a) (4,6)  (b) (4, -2)  (c) (1,4)  (d) (1, -2) 

1. If           find dy/dx. (a)        (b)        (c)              (d)

1. There are 7 boys in a class of 20. Find the number of ways of selecting 3 girls and 2 boys. (a) 1638  (b) 2730  (c) 6006  (d) 7520.
2. What  is the  limit  of  2x2 + x xas  x  🡪 0  (a)  0   (b)  2    (c)  1   (d) 
3. The  above  is called  (a)  the  product  rule  (b)  implicit  rule  (c)  quotient  rule
4. In a class of 10 boys and 15 girls, the average score in a biology test is 90. If the average score for the girls is X, find the average score of the boys in terms of X. (a) 200 – 2/3x  (b) 225-3/2x  (c) 250-2x  (d) 250-3x.
5. A fair die is tossed twice. What is the sample size? (a) 6 (b) 12  (c) 36  (d) 48.

The table shows the result of tossing a fair die 150 times

Use the information to answer question 18 and 19.

1. Find the probability of obtaining a 5.  (a) 1/10 (b) 1/6  (c) 1/5  (d) 3/10.
2. Find the mode  (a) 3  (b) 4  (c) 5  (d) 6.
3. Given that a = 5i + 4j and b = 3i + 7j, evaluate 3a – 8b. (a) 9i + 44j  (b) -9i + 44j  (c) -9i – 44j  

 (d) 9i – 44j.

1. The velocity V of a particle in MS-1 after + seconds is V = 3t2 – 2t – 1. Find the acceleration of the particle after 2 seconds. (a) 10MS2  (b) 13MS-2  (c) 14MS-2 (d) 17MS-2.
2. If (2x2 – x -3 ) is a factor of +(x) = 2x3 – 5x2 – x + 6, find the other factor. (a) (x -2) (b) (x-1) (c) x + 1)  (d) (x + 3/2)
3. Using the binominal expansion: (1 + x)6 = 1 + 6x + 15x2 + 20x3 + 15x4 + 6x5 + x6, find correct to 3 decimal place, the value of (1.98)6  (a) 64.245  (b) 61.255 (c) 60.255  (d) 60.245.
4. If (x + 2) and (3x + -1) are factors of 6x3 + x2 -19x + 6, find the third factor. (a) 2x – 3  (b) 3x + 1  (c) x – 2  (d) 3x + 2.
5. A box contains 5 red balls and K blue balls. A ball is selected at random from the box. If the probability of selecting a blue ball is 2/3, find the value of K. (a) 5  (b) 6 (c) 8 (d) 10. 
6. What  is  the  derivative  of  cos(3x)  (a)  -sin3x   (b)  +sin3x  (c)  -cos(3x)  (d)  = -3sin3x Find the equation of a circle with centre (2, -3) and radius 2 units. (a) x2 + y2 – 4x + 6y + 9 = 0  (b) x2 + y2 + 4x – 6y – 9 = 0  (c) x2 + y2 + 4x + 6y – 9 = 0  (d) x2 + y2 + 4x – 6y + 9 = 0.
7. For what value of m is ay2 + my + 4, a perfect square? (a) +2√3  (b) +6√2  (c) +6  (d) +12
8. A particle accelerates 12ms-2 and travels a distance of 250m in 6 seconds. Find the initial velocity of the particle. (a) 5.7ms-1 (b) 6.0ms-1  (c) 60.0ms-1  (d) 77.5ms-1.
9. In how many ways can 9 people be seated on a bench if only 3 places are available? (a) 1200  (b) 504  (c) 320  (d) 204.
10. Find the variance of 1,2,0,-3,5,-2,4  (a) 52/7  (b) 40/7  (c) 32/7  (d) 27/7
11. If the point (-1, t-1) (t, t-3) and (t-6,3) lies on the same line, find the value of t. (a) t = -2 and -3  (b) t = 2 and    (c) t = -2 and 3  (d) t = 2 and -3.
12. Which  of these  is true, Given  that  f(x)= sinx2 and  P(x) = sin2x  (a)  p1(x)=f1(x)   (b) f1(x)= 2sinx   (c) p1(x) = 2sinx  (d) p1(x) =f(x)
13. What is the number of elements in the sample space when two dice are thrown? (a) 12 (b) 24  (c) 36  (d) 48.
14. How many different arrangement are there for the letters of the word “ABRACADABRA”  (a) 83160 (b) 81360  (c) 86310  (d) 80316.
15.  Find the length of the tangent of the circle x2 + y2+ 5x + 4y – 20 from a point (2,3) outside the circle  (a) 15 units (b) 17 units  (c) √15 units (d) √17 units.
16. .  The  limit  as  Δx 🡪 0 of  fx+∆x-f(x)∆x    is (a)  f1(x)   (b) 0   (c)  1   (d)  3x
17. If np3/nc    = 6, find the value of n  (a) 5  (b) 6  (c) 7  (d) 8.
18. From an ordinary peck of cards, two cards are drawn at random. Find the probability that they consist of a king and a queen.  (a) 1/663  (b) 2/663  (c) 4/663  (d) 8/663.
19. Out of 5 children, the eldest is a boy; find the probability that the rest are girls. (a) 1/16  (b) 1/32  (c) 5/32  (d) 5/16.
20. A committee consists of 5 men and 3 women. In how many ways can a subcommittee consisting of 3 men and 1 woman be chosen? (a) 20 ways (b) 30 ways (c) 18 ways  (d) 36 ways. 
21. How many different arrangements are there for the letters of the word “JAGAJAGA” (a) 204  (b) 402  (c) 420  (d) 240.
22. A four-digit number is formed using the digits 1,2,3 and 5 without repetition. Find the probability that the number will be divisible by 5  (a) 1/6  (b) ¼  (c) 1/8  (d) 1/24.
23. A letter is selected from the English Alphabets. Find the probability that it is in the word “LOVELETTER”  (a) 3/13  (b) 4/13  (c)5/13  (d) 6/13.
24. How many arrangements are there for the letters of the word “DEEPLOVE”? (a) 6702  (b) 6270 (c)6072 (d) 6720.
25. A circle passes through the points (-3,1) and (-1,5). Its centre lies on the x-axis. Find the equation of the circle. (a) x2+y2-8x+34=0  (b) x2+y2+8x+34=0  (c) x2+y2-8x-34=0  (d) x2+y2+8x-34=0.
26. Which of the following is a circle? (a) x2+y2+2xy+5=0  (b) 2x2+4y2+2x+4y-5=0  (c)x3+y3+4x-5y-7=0  (d) 8x2+8xy2-24x+54y-17=0.
27. State the parametric coordinates of a circle of centre(3,-5) and radius 7 units. (a) (3+7Cos, -5+7Sin)      (b) (3 + 7Sin, -5+7Cos) (c) (-5+7Cos, 3+7Sin)  (d) (-5+7Sin, 3+7Cos).
28. Three boys and two girls randomly occupy five seats in row. What is the probability that the two girls will not sit next to each other?  (a) 2/5  (b) 1/10  (c) 3/5  (d) 3/10.
29. The probabilities of three men A, B and C winning the first prize in a competition are 1/8, 1/6 and 1/10 respectively. What is the probability that either B or C will win? (a) 2/15  (b) 1/5  (c) 4/15  (d) 1/3.
30. Given             , what values of x is to be substituted in the expansion of (1 +8x)4 (a) 0.1 (b) 0.001  (c)1    

 (d) 0.01

1. Find the equation of the tangent to the circle 3x2 + 3y2 – 8x – 6y – 61=0 at (4,5)  (a) 3y-2x-23=0  (b) 3y+2x-23=0  (c) 3y+2x+23=0  (d) 3y-2x+23=0
2. The  above  is called  (a)  the  product  rule  (b)  implicit  rule  (c)  quotient  rule

THEORY:   ANSWER FOUR QUESTIONS ONLY FROM THIS SECTION.

1a.    Write down the binomial expansion (2 – x)5 in ascending powers of x.

1. Use your expansion in a above to evaluate (1.98)5. Correct to four decimal places.

2a.    Differentiate with respect to x, the function             where x ≠2

1. Given that (x + y)2 – 3x + 2y =0 (ii)    Find value of        at point (0, 0)

3a.    the velocity VM-1 of a particle moving at any point t seconds is given by V = 3t2 – 1/3t3 – 9. Find the value of  t  at the point where acceleration of the particle is 0.

1. A particle moves in a plane such that its displacement from point 0 at time t seconds is given by  S = (t2 + t)I  +  (3t + 2)j find.  (a) velocity  (b) acceleration  (c) speed at t = 2 seconds of the particle.

4a.    Find the maximum and minimum point on the curve y = x2 (1 – x).

b.i.    Evaluate 

bii.    Evaluate

5a.    Two sides of a PQR are: PQ = 3i – 4j + 5k and  PR = i + 2j – 3k, find the area of the triangle PQR.

5b. Find the vector and scalar product of the two vectors 10i-3j+7k and 9i+5j-3k 

1. ii) What is the angle between the vectors above.
2. Given that the ratio of the coefficient of x7 and that of x5 in the expansion of 1+pxn is 40:21, find the value of p and n

6b. What is the 999th term in the expansion of 2-x1000