MATHEMATICS EXAM QUESTIONS FOR SS2 THIRD TERM

SS2 MATHEMATICS EXAM QUESTIONS THIRD TERM – EDUDELIGHT.COM

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 ; what is the probability that he will fail his exam?  a)     b)        c)       d)   
2. A letter is chosen at random from the word “CONTEMPORARY”. What is the probability that it is either in the word “TEMPT” or in the word “POOR”?
3.       b)       c)      d)  

• The class width of the class intervals    , , etc is:
• 6      b) 7     c) 8      d) 9
• A bearing of 320^o expressed as a compass bearing is ____  (a) N50^oW  (b) N40^oW  (c) N50^oE  (d) N40^o E
• The average age of a group of 25 girls is 10years, 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.
• In  what  quadrat  is the  cotangent  and  cosec  of  an angle  negative?  (a) first  (b) second  (c)  third  (d) fourth 
• Convert the bearing 153^o at a point  A to  a bearing  with specified  direction  A.  N63^oW   (b)  s63^oW  (c)  S27^oW   (d)  S27^oE

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)     b)      c)   d)

9. Given  that  150-q is an  angle  in the  second  quadrant; then  cosq 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 104^o, what is the bearing of Y from X? (a) 014^o  (b) 076^o  (c) 256^o  (d) 284^o.

13. Express the true bearing of 210^o as a compass bearing. (a) S30^oW (b) S30^oE (c) S60^oE (d) S60^oW

14. A bird  flies  from  point  to  a  point B  on  a  bearing  of  151^o.  Calculate  the  bearing  of  A from  B.  (a)  S61^oW  (b)  N29^oW   (c) 209^o  (d)  None  of the  above

(10m)0   m0

0

X

Z

15.

Y

In the diagram below, O is the centre of the circle, <XOZ = 10M^o and <XWZ = M^o. Calculate the value of M.  (a) 30^o  (b) 36^o  (c) 40^o  (d) 72^o.

W

16. Suppose  the  angles  a and  b are  angles  in the  second  quadrant,   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.

Age Years            13           14           15           16           17 Frequency          10           24           8              5                3

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

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) 114^o  (b) 154^o  (c) 204^o  (d)  336^o.

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  ,  is most likely in______ quadrant    (a)1^st or 3^rd  (b)2^nd or 4^th  (c)1^st or 4^th  (d)2^nd or 3^rd

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. 156^o  B. 90^o C.120^o D. 75^o

A

B

o

N

M

D

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                  (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)       b)       c)      d)

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.  is less than  at the center O of the circle of radii OA and OB joined by only  an arc. If  and  are the only two angles at the centre, then  is  ____  (a) a major arc  (b)a minor arc (c) an isosceles triangle (d) an angle in a semi-circle

41.

V

U

               In the diagram, YW is a tangent to the circle at X, /UV/ = /VX/ and

                                      <VXW = 50^o. find the

                                       value of <UXY.

50o

W

X

Y

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

42.  Which of these angles has it cosecant and cotangent function to be negative
A. 67^O  B. 178.65^O C. 191.21^O D. 354.34^O     

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.

44. 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

45. 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.

46. 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.

8

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                                                      

SS2 MATHEMATICS EXAM QUESTIONS THIRD TERM – EDUDELIGHT.COM

  PART 2 (THEORY): ANSWER 4 QUESTIONS

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

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

Class	1-5	6-10	11-15	16-20	21-25
Frequency	5	7	10	6	2

            Find  i) the modal class      ii) the mode       iii) the mean

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

• (a)   Calculate other sides and angles of a ΔABC given that  and .

b. 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 = 52^o, find:                          

P

T

52o

O

S

Q

<SQT          (ii)  <PQT

• 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?

b.         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?

SS2 MATHEMATICS EXAM QUESTIONS THIRD TERM – EDUDELIGHT.COM

CLASS:             S.S.S. 2                                     SUBJECT:         Mathematics

INSTRUCTION:            Answer all the questions

1.         Evaluate (101.5)² – (100.5)²

            a.  1                 b. 2.02 c.  20.02          d.  202             e. 2020

2.         Express the product of 0.06 and 0.09 in standard form

            a.  5.4 x 10^-3                b. 5.4 x 10^-2     c.  5.4 x 10^-1       d. 5.4 x 10²                e. 5.4 x 10³

3.         Simply 36^½ x 64^-1/3 x 5^o

            a.  0                 b. 1/24 c.  2/3              d.   1½             e. 7½

4.         Find the 8^th term of the A.p.  -3,  -1,  1 ………….

            a.  13               b.  11               c.  -8                d. -11               e. -17

Use this information to answer questions 5 and 6

5.         Calculate /PQ/ in metres

            a. 20                b.  24               c.  25               d.  31               e.  84

6.         What is the bearing of Q from P to the nearest whole degree?

            a.  16^o              b.  17^o              c. 73^o                           d. 106^o             e. 164^o

7.         Simplify (27^1/3)²   a. 4 ½          b.  6                 c. 9                  d. 18     e. 81

8.         Calculate the value of x in the diagram below

                                                __32x____________23x_

                                                                       4x

9.         A sales girl gave a change of N1.15 to a customer instead of N1.25.  Calculate her percentage error.

            a.  10% b. 8.7?%           c. 8.0%     d.  2.4%                   e.  0.10%

10.       What is the probability of hiring an odd number in a single toss of a fair die?        a.  1/6  b.  1/3  c.  ½                 d.  2/3  e.  5/6

11.       Evaluate log6₁₀ + log45₁₀  –  log27₁₀ without using logarithms tables

            a.  0                 b. 1                  c. 1.1738         d. 1.3802         e.  10

12.       What value of k makes the given expression a perfect square?

 M² – 8m + k

            a.  2                 b. 4        c.  8               d. 16                e.  64

13.       If logq¹⁰  =  2.7078,  what is q?

            A.  5102           B.  849.9                      C. 510.2           D. 84.99    E. 51.02

14.       If 3loga + 5log_a – 6log_a  =  log64, what is a?

            a.  4                 b. 6                  c.  8                 d. 16                e.  32

15.       If the second and fourth terms of a G.P are 8 and 32 res(ectove;u, what is the sum of the first four terms?

            a.  28      b.  40            c.  48               d.   60              e.  68

16.       Evaluate 0.009 divided 0.012, leaving your answer in standard form

            a.  7.5 x 10²         b.  7.5  x  10¹     c.  7.5  x 10^-1          d. 7.5 x 10^-2       e. 7.5 x 10^-3

17.       Factorize the following expression,  2x²  +  x  –  15

a.  (2x  + 5) (x – 3)    b. (2x-5)(x-3)     c. (2x -5)(x-3)     d. (2x-3)(x+5)   e. (2x+5)(x+3)

18.       If loga¹⁰ = 4;  what is a?

            a.  0.4              b. 40                c. 400              d.  1000                       e.  10,000

19.       Instead of recording the number 1.23cm, find the percentage error, correct to one decimal place

            a.  6.8%           b.  7.3%           c.  9.6%                        d. 14.4%          e. 15.4%

20.       Factorise 5y² + 2ay – 3a²

            a.  (5y – a)(y + 3a)       b.  (5y+a)(y-3a)           c. 5y2 + a(2y – 3a)   d. (y – a)(5y-3a)

            e.  (y+a)(5y-3a)

• Find (101₂)² expressing the answer in base 2(a) 10101 (b) 11001 (c) 10010 (d) 11101 (e) 10110
• If 3 children share ₦10.50 among themselves in the ratio 6:7:8, how much is the largest share?(a) ₦ 3.00 (b) ₦3.50 (c) ₦4.00 (d) ₦4.50 (e) ₦ 5.00
• Express 0.000834 in standard form(a) 8.34 x 10^-4 (b) 8.34 x 10^-3 (c) 8.34 x 10³ (d) 8.34 x 10⁴ (e) 8.34 x 10⁶
• Simplify 0.027^-1/3(a) 3¹_/3 (b) 3 (c) 3/10 (d)1/3 (e) 1/9
• Given that log^a₂ = log⁴₈ , Find a(a) 2^1/2 (b) 4^1/3 (c) 4^2/3 (d) 2^2/3 (e) 2³
• By selling some crates of soft drinks for ₦600.00, a dealer makes a profit of 50%. How much did the dealer pay for the drinks?(a) ₦1,200.00 (b) ₦900.00 (c) ₦450.00 (d) ₦400.00 (e) ₦200.00
• Find the nth term Un of the A.P; 11, 4,-3, ­­­­­­_______(a) un= 19 + 7n (b) un= 19-7n (c)= 18-7n (d) un= 18+7n (e) un= 17-7n
• If 16/9, X, 1, y are in Geometric Progression (GP). Find the product of X and Y (a) 9/16 (b) ¾ (c) 1 (d) 4/3 (e) 16/9
• If R = { 2,4,6,8} and S= { 1, 2, 3, 4, 8}, the RUS equal (a) { 1,2,4,6,7,8} (b) {1,2,4,7,8} (c) {1,4,7,8} (d) {2,6,7} (e) {2,4}
• In the diagram below, the shaded portion is  (a) P’nR (b) QnR (c) P’nQnR (d) (PuQ)’nR (e) (PnQ)U(P’nR)

• Find the values of X for which the expression is undefined  (a) +4 or +1 (b) -5 or +1 (c) -5 or -1 (d) +5 or -1 (e) +4 or -1
• Which of the following could be the inequality illustrated in the sketch graph below? (a) y≥-2x + 1 (b) y ≤ -3x + 3 (c) y < 3x _2 (d) y ≤ x +3 (e) y ≥ 3x + 2
• Solve the inequality (2x – 1)<5 (a) x< -5 (b) x<-6 (c) x<7 (d) x< 8 (e) x<16
• What is the smaller value of X for which x² – 3x + 2 = 0  (a) 1 (b) 2 9c) 3 (d) 4 (e) 5
• Factorize the expression X(a-c) + y(c-a) (a) (a-c)(y-x) (b) (a-c)(x-y) (c) (a+c)(x-y) (d) (a+c)(x + y) (e) (a-c)(x+y)
• Solve the equation 3x² + 25x – 18 = 0 (a) x = -3 or 2 (b) x = -2 or 3 (c) x =-2 or  – 9 (d) x = -9 or 2/3 (e) -2/3, 9
• Solve the equation (x +2 )(x – 7) = 0 (a) x  = 1 or 8 (b) x  = 2 or 7 (c) x = -4 or 5 (d) x =-3 or 6 (e) x = -5 or -2
• Solve the following simultaneous equations: X +Y = 3/2, X- y = 5/2 and use your result to find the value of 2y + x (a) -2 (b) -1 (c) ½ (d) 1 (e) 3 ½
• The diagonals AC and BD of a rhombus ABCD are 16cm and 12cm long respectively. Calculate the area of the rhombus. (a) 24cm² (b) 36 cm² (c) 48 cm² (d) 60 cm² (e) 96 cm²
• A water tank of height ½ m has a square base of side 1 ½ m. if it is filled with water from a water tank holding 1500 litres, how many litres of water are left in the water tanker? (1000 Litres = 1m³) (a) 37.5 Litres (b) 375 Litres (c) 3750 Litres (d) 37500 Litres (e) 375000 Litres

41.       Mrs. Atiku sold article for N7.50 instead of N12.75.  Calculate her percentage error

• 41.2%                    (b)18.3%          (c) 5.3%           (d) 1.7%

42.       A school girl spent ¼ of her pocket money on books and 1/3 on dress.  What fraction remains?

• 5/12           (b) 5/6             (c) 7/12                       (d) 1/6

43.       Find X in      X  =  2 /                   2 – X

• 4/5             (b) 4                 (c) 5/4                         (d) ½

44.       Three numbers a, b, c are in the ratio  3 : 5 : 7 respectively.  Find the value of

            4a – b

            B + 2c              (a) 7/19                       (b)  16/21                    (c)8/11    (d) 2/3

45.       Simplify ( 16/81)

• 2/3             (b) 8/27           (c)  1/3            (d)  4/3

46.       Evaluate   Log ³⁵          +            Log 2     —      Log 7

                        ^{10                                                                   10                                           10}                  

47.       Express 0.00562 in standard form

• 5.62  X  10^-3           (b) 562  x  10^-2             (c) 5.62  x  10²    (d) 0.562 x10-²        

48.       Find the value of   X for which 312₄  +  52_x  =  96₁₀

            (a)        8                      (b) 10               (c)  12              (d) 14

49.       A pair of fair dice with each face numbered 1 to 6 are thrown once.  Find the probability of scoring 2 on one die and a 5 on the other

            (a)  1/36                      (b)1/18                        (c)7/36            (d)1/3

                                                                                    _(1/7)

50.       Find the numerical value of  Log⁴⁹   +   Log

                                                                                                     ^{7                                              7}                

            (a) 1                 (b) 2                 (c)  3                (4)  4

51.       Given that   P  +  10  =  2p – 2,  find p

•  12             (b)13                (c)14                (d)15

52.       Given square root of 64000 is                       

            (a)80                (b)8                  (c)36                (d)  18

53.       What fraction must be subtracted from the sum of 2 1/6 and 2 7/12 to give 3¼

            (a) 1 ½             (b) 1/3             (c) ½                (d) 1 1/6

54.       The square of 20 is

            (a) 400             (b) 40               (c) 240             (d) 80

55.       A house bought for N100,000.00 was later auctioned for N80,000.00. Find the loss percentage

            (a) 20%            (b) 30%            (c) 40%            (d) 50%

PART II            Answer four question in this part

The number of items produced by a company over a five – year period is given below –

Year	1978	1979	1980	1981	1982
Number produced	4100	2500	1500	1800	9200

1 (i)      Plot a bar chart for this information

  (ii)      What is the average production for the five year period?

2a.       The subject A, B and C of a universal set are defined as follows:

            A =  {m, a p e},            B = {a, e, i, o, u}    C  =    {I, m, n, o, p, q, r, s, t, u}

            List the elements of the following sets                                                               

•  AUB      (ii)   AUC      (iii)  AU(B  C)

2B.       Out of the 400 students in the final year in a senior secondary school, 300 are offering Biology and 190 are offering Chemistry.

• How many students are offering both Biology and Chemistry?  If only 70 students Are offering neither Biology nor Chemistry?
• How many students are offering at least one of Biology or Chemistry?

3.         The table below is for the relation  y = 2 + x – x²

X	-2	-1.5	-1	-0.5	0	0.5	1	1.5	2	2.5	3
y	-4	-1.5	0	1.25	2	2.25	2	1.25	0	-1.75	-4

a.         Using a scale of 2cm to 1 unit on each axis, draw the graph of the relation

            in the interval – -2 < x < 3.

b.         From your graph, find the greatest value of y and the value of x for which this occurs.

c.         Using the same scale and axis, draw the graph of y = 1 – x

d.         Use your graph to solve the equation 1 + 2x – x² = 0

4a.       Using logarithm table, evaluate

                _____

            3\/1.376

            4\/0.007          correct to three significant figures.

b.         Without using mathematical tables, find the value of log81

                                                                                                                log1/3

5ai.      A man has 9 identical balls in a bag.  Out of these, 3 are black, 2 are blue and the remaining are red.

  ii.       If a ball is drawn at random, what is the probability that it is  (i) not blue

• not red

b.         If 2 balls are drawn at random, one after the other, what is the probability that both of them will be –

• black if there is no replacement
• blue if there is a replacement

6.         Three towns P, Q and R are such that the distance between P and Q

Is 50km and the distance between P and R is 90km us 90km.  If the bearing of Q and P is 075^o and the bearing of R from P is 310^o, find the

1. distance between Q and R
   1. Bearing of R and Q

7.         A test was given to 50 students.  The results are given in the table below

Marks	2	3	4	5	6	7	8	9	10
Frequency	4	4	10	11	5	7	6	2	1

1. Find the range
2. Calculate the mean deviation
3. Calculate the standard deviation

SS2 MATHEMATICS EXAM QUESTIONS THIRD TERM – EDUDELIGHT.COM