SS 3 Mock Exams Further Maths
FURTHER MATHS
1. What is the variance of a binomial distribution?
a. (a) np (b) √npq ( c ) npq (d) p2
3. The mean (µ) of a poisson distribution is the same as
(a) Standard deviation (b) variance (c) mean (d) mean deviation
4. If number of trials is 100 and probability of success is 0.0001, what is the variance of this distribution?
5. (a) 0.00999 (b) 0.1 (c ) 0.01 (d) 0.001
6. . If the birth of a male child and that of a female child are equiprobable. Find the probability that in a family of five children exactly 3 will be male. (a) 16/5 (b) 5/16 (c) 5/32 (d) 5/21
7. If an unbiased die is thrown repeatedly, what are the chances that the first, six to be thrown will be the third throw? (a) 25/216 (b) 1/6 (c) 25/36 (d)25/31
8. Find the area between z = 0.36 and z= 1.89 (a) 0.33 (b) 0.6112 (c) 1.00
B. Use the information below to answer questions 2-4.
9. A distribution with mean 85 and standard deviation 10 is normally distributed. If x is a random variable of the distribution, find
10. . Pr (80 < x <8.9) (a) 0.9332 (b) 0.5 (c) 0.3469
11. . Pr(x >83) (a) 0.1587 (b) 0.789 (c) 0.4207
12. . Pr(x > 87) (a) 0.0047 (b) 0.35 (c) 0.4207
13. Find, with the usual notations, P (z <1.810) from the table of normal distribution. (a) 0.311 (b) 0.0288 (c) 0.9649
14. Two forces each of magnitude PN are inclined to each other at an angle of 1200. Find the magnitude of their resultant.
a. (a) P√3 N (b) P2N ( c) PN
15. Find the angle between the two forces 5N and 6N if their resultant is 8N. a. (a) 600 (b) 1200 (c) 1800
16. A force P of magnitude 60N makes an angle of 400 with the horizontal. Use the information to answer questions 3 and 4
17. Find the horizontal component of P
a. (a) 20N (b) 45.96N (c ) 38.57N
18. Find the vertical component of P
a. (a) 45.96N (b) 38.57 (d) 20N.
19. Find the resultant of forces 8N and 10N inclined at an angle 1200 to each other. a. (a) 2√61N (b) 61√2N C 39N
20. A body is in limiting equilibrium on a plane inclined at an angle to the horizontal. if Cos = 0.8, calculate the coefficient of friction.
21. THEORY
1. 20% of the total production of transistors produced by a machine are below standard. If a random sample of 6 transistors produced by the machine is taken, what is the probability of getting
b. (i) exactly 2 (ii) exactly 1 (iii) at least 2 (iv) at most 2 standard transistors?
1. A fair die is thrown five times. Calculate correct to 3 decimal places, the probability of obtaining
c. (a) at most two sixes (b) exactly three sixes