SS 2 Mathematics Third Term Examination

   THIRD TERM

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

Subject:  MATHEMATICS    DURATION ; 1Hrs   30moins

1. The probability that a student will pass his exam is 25; what is the probability that he will fail his exam?  a) 15    b)  25      c)  35     d)  25 
2. A letter is chosen at random from the word “TEMPORARILY ”. What is the probability that it is either in the word “TEMPT” or in the word “RARE”? (A) 512      b) 35      c)  712    d) 12 
3. The class width of the class intervals 134-140,  141-147, 148-154, etc is: (a) 6      b) 7     c) 8      d) 9
4. A bearing of 320o expressed as a compass bearing is ____  (a) N50oW  (b) N40oW  (c) N50oE  (d) N40o E
5. The average age of a group of 25 girls is 10 years, if one girl, aged 12 years and 4 months joins the group, find, correct to one decimal place, the new average age of the group. (a) 10.1 years (b) 9.3 years  (c) 8.7 years  (d) 8.3 years.
6. In  what  quadrat  is the  cotangent  and  cosec  of  an angle  negative?  (a) first  (b) second  (c)  third  (d) fourth  
7. Convert the bearing 153o at a point  A to  a bearing  with specified  direction  A.  N63oW   (b)  s63oW  (c)  S27oW   (d)  S27oE

8. In a school, four out of five students have calculators; if two students are picked at random, what is the probability that only one has a calculator?   a) 425   b)  825     c)  1225  d)  125
9. Given  that  150-θ is an  angle  in the  second  quadrant; then  cosθ will  be  (a)  positive  (b)  negative   (c)  can not  be  (d)  determined  (d)  zero
10. The age of Tunde and Ola are in the ratio 1 : 2. If the ratio of Ola’s age to Musa’s age is 4:5, what is the ratio of Tunde’s age to Musa’s age? (a) 1:4  (b) 1:5  (c) 2:5  (d) 5:2
11. Which of the following is not a measure of dispersion?  (a) mode (b) mean deviation (c) range  (d) standard deviation.
12. The bearing of X from Y is 104o, what is the bearing of Y from X? (a) 014o (b) 076o (c) 256o  (d) 284o.
13. Express the true bearing of 210o as a compass bearing. (a) S30oW (b) S30oE (c) S60oE (d) S60oW
14. A bird  flies  from  point  to  a  point B  on  a  bearing  of  151o.  Calculate  the  bearing  of  A from  B.  (a)  S61oW  (b)  N29oW   (c) 209o (d)  None  of the  above
15. In the diagram below, O is the centre of the circle, <XOZ = 10Mo and <XWZ = Mo. Calculate the value of M.  (a) 30o (b) 36o (c) 40o  (d) 72o.

16. Suppose  the  angles  α and  β are  angles  in the  second  quadrant,  Tan∝ cos β will  be   (a) negative  (b)  positive  (c)  zero   (d)  can not  be  determined
17. A bag contains 5 red and 4 blue identical balls. If two balls are selected at random from the bag, one after the other without replacement, find the probability that the first is red and the second is blue. (a) 2/9 (b) 5/18 (c) 20/81  (d) 5/9.

The table shows the age of students in a club. Use it to answer 18 and 19.

Age / years 13.  14. 15. 16. 17.

Frequency    10.  24.  08. 05. 03

18. How many students are in the club? (a) 50  (b) 55  (c) 60  (d) 65.
19. Find the median age.  (a) 13 (b) 14  (c) 15  (d) 16
20. Point X and Y are 20 Km north and 9km east of point O respectively, calculate, correct to the nearest degree, the bearing of Y from X.  (a) 114o (b) 154o (c) 204o  (d)  336o.
21. Find the mean of the whole numbers between 5 and 20 inclusive which are divisible by 2 or 3.        (a) 13.2  (b) 12.8  (c) 12.0  (d) 11.2.
22. Find the sum of the median and the range of these numbers: 6, 2, 4, 3, 8, 4, 2.      (a) 12 (b) 10 (c) 8 (d) 6.
23. Find the upper quartile of 2, 4, 5,7, 8, 9, 10.  (a) 10  (b) 9 (c) 8 (d) 7.
24. The average number of goals scored by a football team in 6 matches is 2.5. How many more goals  must the team score in the next match to bring the average to 3?  (a) 4 (b) 5  (c) 6  (d) 7
25. Find the mean deviation of 1, 2, 3, 4 and 5.  (a) 1.2  (b) 1.5  (c) 2.0  (d) 3.0
26. If  tan θ= -1.1918 , then θ is most likely in______ quadrant    (a)1st or 3rd (b)2nd or 4th (c)1st or 4th  (d)2nd or 3rd
27. The tangent of which of the following angles gives the same result as tan (-238 o )     a) 58 o (b) -122 o (c) 238 o (d) 302 o  

28.Calculate the mean of the following ages of 5 children: 3yrs and 4 mnths, 5 yrs and 1 mnth,  2yrs and 2 mnths, 1yr and 8mnths, 2yrs and 9months       (a) 3 yrs (b) 3yrs and 2mnths (c) 4 yrs (d) 4yrs and 3mnths

29. What is the angle formed by a radius of a circle 7cm long and a tangent 56cm long whose point of tangency is same as the point of contact of the radius and the circumference of the circle? A. 156o B. 90o C.120o D. 75o

Use  the  diagram  above  to  answer  questions  30 to  34.

30. The  line  OD  is a  _____to the  circle  (a)  secant  (b) tangent  (c)  radius   (d)  chord
31. The  point  D  is  the  circle  is  called  ______(a)  the  mid  point  (b)  centre  (c)  perfection  (d)  point  of  tangency 
32. The  angle  founded  by line  OD  and  DM is  (a)  an  obtuse  angle  (b)  acute  angle  (c)  zero  degrees  (d)  90  degrees
33. Line  AB  is  a    (a)  tangent  (b) chord  (c)  secant  (d)  diameter 
34. Calculate  the  length  of  a  chord  AB  of  a  circle  of  radius  which is  12cm  away  from  AB.  (a)  5cm   (b)  6cm   (c)  12cm   (d)  10cm                                  

35. Find the value of between 0 o and 180 o for which cos (20+θ) =-0.1606                 (a) 99.24 o (b) 109.24 o  (c) 89.24 o  (d) 79.24 o
36. Two fair die are thrown together once. Find the probability of obtaining at most a sum of eight  (a) 1118     b) 1318     c)  1518    d) 1718
37. What is the median height (in cm) of ten students having the following heights: 145, 163, 159, 162, 167, 149, 150, 160, 170 and 155   (a) 149.5cm  (b)154.5cm (c)159.5cm (d)164.5cm
38. The mean of 4, 8, 6, p and q is 6. Find the mean of  p+1 and q-3                              (a) 5  (b) 6 (c) 7 (d) 8
39. The line drawn from the center of a circle to bisect a _____ is _______ to the ____ (a) radius, opposite, arc (b) cyclic quadrilateral, perpendicular, tangent (c)tangent, opposite, adius (d)chord, perpendicular, chord
40. ∠X is less than ∠Y at the center O of the circle of radii OA and OB joined by only  an arc. If ∠X and ∠Y are the only two angles at the centre, then AYB is  ____  (a) a major arc  (b)a minor arc (c) an isosceles triangle (d) an angle in a semi-circle
41.               In the diagram, YW is a tangent to the circle at X, /UV/ = /VX/ and

                                      <VXW = 50o. find the 

                                       value of <UXY.   

      (a) 70o  (b) 80o (c) 105o  (d) 110o.

42. Which of these angles has it cosecant and cotangent function to be negative
    A. 67O B. 178.65O C. 191.21O D. 354.34O      43. Two bottles are drawn with replacement from a crate containing 8 coke, 12 fanta and 4 sprite bottles. What is the probability that the first is coke and the second is not coke? (a) 1/12  (b) 1/6  (c) 2/9  (d) 2/8.
43. Calculate the variance of 2,3,3,4,5,5,5,7,7 and 9.  (a) 2.2  (b) 3.4  (c) 4.0  (d) 4.2
44. A fair coin is tossed four times, what is the probability of obtaining at least one head? (a) ½  (b) ¼  (c) 13/16 (d) 15/16.
45. Calculate  the  mean deviation  of the  data 1,3,5,7,9,11. (a) 3  (b) 2  (c) -2  (d) 3.
46. The average age of ten members of a committee is the same as it was four years ago because an old member has been replaced by a young member. Find how much younger is the new member to the old member (a) 25 (b) 30 (c) 35 (d) 40
47. 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.

48.Obtain the range of the following numbers: -1.57, 2.66, 12.08, -3.45, 10.26 and -0.72  (a) 8.63  (b) 15.53  (c) -15.53  (d) -8.63.

49. A letter is chosen at random from the word “WRESTLEMANIA”. What is the word that it is in the word “MANTLE” or in the word “WASTE”? (a) 4/5 (b) 3/5 (c) 2/5  (d) 1/5
50. A coin is weighted so that a head is twice likely to appear as a tail. Find the probability of a tail not appearing (a)1  (b) 2/3 (c) 1/3 (d) 1/2                                                      

PART 2 (THEORY): ANSWER 4 QUESTIONS

1. An aeroplane leaves an airport A and flies on a bearing 035o for 3/2 hours at 600km/h to an airport B. It then flies on a bearing 130o for 3/2 hours at 400km/h to an airport C. 

  Calculate the

1. Distance from C to A
2. Bearing of C from A.

1. Draw a histogram and a frequency polygon of the frequency distribution shown below:

            Find 

i) the modal class     

ii) the mode      

iii) the mean

2b. Using the formula Median =L+ N2–fLfmedianC,

where each item stand for their usual meanings, estimate the median of the table in question 2 above.

1. (a)   Calculate other sides and angles of a ΔABC given that b=17.23cm,  c=10.86cm and B=101°15′.

1. State and prove the sine rule for acute angle

In the diagram, PQRST is a circle with centre O. if PS is   

                                                 A  diameter, RS//QT,  /QR/ = /RS/ and <QTS = 52o, find:                           

1. <SQT          (ii)  <PQT

1. A bag contains 4 red balls, 5 blue balls and 6 white balls. If two balls are picked at random, each without replacement:  What is the probability that. 
   • i) two white balls and a red ball are picked? 
   •   ii) one colour each is picked?

6. Mr. P speaks the truth 70% of the time. Mr. Q speaks the truth 80% of the time. What is the probability that both are contradicting each other?
7. If one number is chosen at random from the first 1000 positive integers, what is the probability that the number chosen is:   (i)  multiple of both 2 and 5? (ii)a multiple of 2 or 5?