# FURTHER MATHEMATICS EXAMINATION QUESTIONS FOR SS3

## FURTHER MATHEMATICS EXAMINATION QUESTIONS FOR SS3

SECOND TERM’S EXAMINATION

SUBJECT: FURTHER MATHEMATICS

CLASS: SS 3

TIME: 2½ HRS

### SECTION A (OBJECTIVES)

Find the sum of all numbers between 5 and 130 which and divisible by 4 (a) 2108 (b) 1208 (c) 8012 (d) 2810.

1. For what values of y is the expression    undefined?  (a)(1, 2) (b) (-1,2) (c) (2,3) (d)(-2,1)
2. For what values of x is the expression    equal zero?  (a)(1, -2) (b) (5,1) (c) (-5,-1) (d)(-1,2)
3. If the surface area of a sphere is increased by (a) 44 (b) 30 (c) 22 (d)20
4. Evaluate (16) 3/2 + log (0.0001) log2 32   (a) 0.065 (b) 0.650 (c) 6.50 (d) 65.0
5. Find the value of n if-   = 1  (a) 5  (b) 4 (c) 3 (d)2
6. Simplify –   (a) 4  (b)  (c) 0 (d)-4
7. How long would it take a sum of money to double itself at 5 % per annum compound interest? (a) 23  (b) 15 (c) 14  (d)20
8. What is the reminder when x3 + 5x2 – 3x -6 is divided by n+1? (a) 1  (b) 6 (c) -1 (d)-11
9. Evaluate 2* (12*27) if a*b =      a) 12  (b) 6 (c) 9 (d)2
10. If X*Y = X+Y – 3XY, what is the value of x if X*2 =13
11. The area of a triangle ABC if 9cm2 and that of ABC is y (cm2). Find the value of Y if the determination of transformation matrix is 9 a) 36cm2 (b) 1cm2 (c) 18cm2 (d)81cm2
12. The 3rd term of an AP is 4x-2y and the 9 term is 10n-8y find the common difference  (a) 2x (b) x-y (c) 8n-4y (d) 19x-17y
13. The sum of positive odd integers less than 50 is (a) 625 (b) 550 (c) 725 (d) 650
14. An AP and GP have both their 1st and 2nd terms to be 2 and 4 respectively. What is the different between the sum of their first six terms? (a) 88 (b) 84 (c) 63 (d) 53
15. Rationalize     –            b      c.      d. 5-2/6
16. Simplify           b.  c. d.
17. If  =  for  ≤ n ≤   calculate   (a)  (b)  (c)  (d) 2
18. Simplify (a)  (b) (c)  (d)
19. If What is the value of ? (a)  (b)  (c)  (d)
20. Solve for in the equation
21. Find the value of if  and  are the roots of  (a)  (b)  (c)  (d)
22. If and  are the roots of  find the equation whose toots are  and  (a)  (b)  (c)  (d)
23. If find  (a) 12 (b) 27 (c) 25 (d) 7
24. If the mean of the members . Find the mean deviation (a) 4 (b) 3 (c) 2 (d) 0
25. Which of the following is not a factor of ? (a) (b)  (c)  (d)
26. The expression has  as a factor. Find the value of the constant k. (a) -2 (b) -5 (c) 2 (d) 1
27. Find the general equation of the circle, centre (4, 1) and radius 2 units (a) (b)  (c)  (d)
28. Find the centre of the following circle (a)  (b)  (c)  (d)
29. Find the acute angle between the following pair of lines (a)  (b)  (c)  (d)
30. Find the equation of the line which make with and passes through the point  (a)  (b)  (c)  (d)
31. Find the equation of the line which is parallel to the line and passes through the point  (a)  (b)  (c)  (d)
32. Which of the following is correct? (a) (b)  (c)  (d)
33. What is the distance between the points whose coordinates are (3, -5) and (1, 2) (a) (b)  (c) 7 (d)
34. If is the midpoint  of the line joining the point  and , find the values of p and q (a) 2 and 4 (b) 3 and 1 (c) 5 and 3 (d) 6 and 2
35. Factorize (a)  (b)  (c)  (d)
36. At what rate is the area of a circle decreasing when radius is 4cm and decreasing at the rate of 0.002m/s? (a) 0.00016m/s2 ­(b) 0.016m/s2 (c) 0.0016m/s2 (d) 0.16m/s2
37. Evaluate   (a) 10 (b) 0 (c) 5 (d) 15
1. What is the critical values of the function ? (a) 0 and 2 (b) 2 and 1 (c) -1 and -2 (d) 0 and 3
2. For what value of Q will make the expression a complex square.  (b)  (c)  (d)
3. If find  if  (a)  (b)  (c)  (d)
4. Interprete with respect to  (a)  (b)  (c)  (d)
5. Evaluate (a) 2 (b) 1 (c) -1 (d) 0
6. Find the area bounded by the curve , the and the lines  (a) 12 square unit (b) 22 square unit (c) 5 square unit (d) 10 square unit
7. A curve had gradient . Find the equation of the curve if it passes (a) (b)  (c)  (d)
8. Evaluate (a) -3 (b) -1 (c) 3 (d) 1
9. Differentiate (a)  (b)  (c)  (d)
10. A particle moves in a straight line from 0 with initial velocity . Its acceleration in t s later is . Calculate its velocity after 3 seconds (a) (b)  (c)  (d)
11. Find the volume of solid of revolution generated when the region bounded by  and the is revolved about the  through
12. Find the probability that in 10 throws of a fair faced die, a square number shows up three times. (a) 0.26 (b) 0.1 (c) 1 (d) 0
13. Find the probability that when a fair coin is tossed three times, a head shows up twice (a) (b)  (c)  (d)
14. In how many ways can the word COMMISSION be arranged? (a) 226800 (b) 22800 (c) 2520 (d) 840
15. In how many ways can 5 males and 6 females be selected from 10 males and 7 females? (a) 1764 (b) 764 (c) 1760 (d) 1984
16. The arc PQ of a circle radius 6.5cm subtends an angle of at the circle 0. Find the area of sector POQ. Take  (a)  (b)  (c)  (d)
17. A chord AB of a circle, radius 9.4cm is 12.8cm. Find the angle subtended by the chord at the centre of the circle to the nearest degrees (a) (b)  (c)  (d)
18. What must be added to to make it a perfect square? (a)  (b)  (c)  (d)
19. Find the angle between the vectors and  (a)  (b)  (c)  (d)
20. What is the probability of selecting a Jack in a Park of 52 cards? (a) (b)  (c)  (d)
21. In how many ways can the letters of word BEGINNING be arranged? (a) 9 (b) 81 (c) 15120 (d) 30240
22. Given that , evaluate 3A (a) (b)  (c)

## SECTION B: THEORY

1a.     A particle is projected in a straight line from a point O with an initial velocity of 2m/s. Its acceleration t seconds later is given by . Calculate

(i)      Its velocity after 2 seconds

(ii)      Its distance from O after 2 secs (6 marks)

(1b)    Find the volume of the solid of revolution generated when the region bounded by the curve , the ordinates ,  and the  is revolved about the axis through  (4 marks)

1. Using appropriate substitutions, evaluate each of the following

(a)       (b)

1. One out of a thousand people reacted to a newly manufactured vaccine against an endemic disease. If 3000 people were treated with this vaccine, find the probability that:

(i)      Exactly 2 people reacted to the vaccine

(ii)      At least 3 people reacted to the vaccine

(iii)     At least 3 people reacted to the vaccine

(iv)     No one reacts to the vaccine (10 marks)

1. 95% of the heights of students in a school are between 1.2m and 1.8m. Assuming the heights of the students are normally distributed. Calculate the:

(a)      Mean

(b)     Standard deviation

(c)      Variance

(d)     Coefficient of variance (10marks)

1. Two forces P and Q act at a point. The magnitude of P is 25N and the magnitude of Q is 30N. FI P acts in the direction N300E and Q acts in the direction S600E, find

(i)      The components of P and Q

(ii)      The resultant force R of P and Q (10 marks)

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