SS2 MATHS EXAM QUESTIONS SECOND TERM – EDUDELIGHT.COM

SECOND TERM EXAMINATION

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

SUBJECT: MATHEMATICS                           

CLASS: SSS 2       

TIME:          3HRS

Instruction: Answer all questions

SECTION A: Objectives

1.. Which of the following points lie on the line   y = 3x + 2?   A. (1,3),(-1,-1)  B. (1,5),(-1,-1)
     C. (-1,1),(0,2)     D. (-1,-1) (-2,4)Bottom of Form

2.. What is the gradient, m of  the line between the points  (-1,2)  and   (3,-4)

1. ³/₂     B. 1   C. -1    D. 2

3. According to Pythagoras theorem, distance between points (-3, 8) and  (8, -5) is

1. 19.03 units   B.11.03 units   C.15.03 units   D. 17.03 units

4.. Straight line equation y = 5x – 2 has the gradient of   A. x + y    B. xy    C. 2  D. 5

5.  if  y = 5x + c passes through point A(5, 2) then value of ‘c’ is

1. −21    B.−23     C. −25    D. −27

6. If straight line passes through points X(1. 4) and Y(3, 7) then its equation will be

1. Y=2⁄3x + 5⁄2    B. Y=⁄2x + 2⁄5   C. Y=2⁄3x – 2⁄5   D. y=3⁄2x + 5⁄2

7. Straight line equation y = x⁄2 + 1⁄4 has gradient of

1. 1⁄2     B. 1⁄4    C. x⁄4    D.  x⁄2

8.  Distance between points (2, 5) and (7, -3) is   A.6.43    B.  9.43   C12.43  D.15.43

9.  In the diagram below, find the size of the angles marked a^o.  A. 60^O  B. 80^O  C. 120^O  D. 160^O

.  

10. In gradient-intercept form of equation y = mx + c, point where line cuts y-axis is

1. (3, c)   B. (0, c)     C.   (1, c)    D. (2, c)

11.  Straight line equation y = x⁄3 + 1⁄4 cuts y-axis at point

1. (0,  x ⁄ 4)    B.  (0, 1 ⁄ 3)    C.  (0, 1 ⁄ 4)   D. (0, x ⁄ 3)

12.  In gradient-intercept form of equation y = mx + c, ‘m’ denotes

1. gradient of independent variable   B.  intercept on y-axis

C   gradient of straight line      D. intercept on x-axis

13.  If coordinates of A and B are (5, 6) and (9, 10) respectively then length of line segment AB is             
          A. 13.66    B.  9.66    C. 5.66    D. 7.66

14.  Largest part of circle divided by chord is called

1. circumference    B. quadrant   C.minor segment    D. major segment

15. Chord divides circle into  A.two segments   B. three segments

  C. four segments    D. five segments
16.  Smallest part of circle divided by chord is called

1. minor segment    B. major segment   C.major quadrant   D.radian

17.  Line segment which joins distinct points on circumference is called

1. radius     B. chord    C.  perimeter     D. length

18.  Line segment which joins distinct points on circumference is called

1.  radius    B. chord     C. perimeter    D. length

19.  The sum of angles in a semi circle is A. 180   B.90   C.45   D. 30

20. The longest chord which divides a circle into two equal segments is called

A. Diameter   B. Minor Chord   C. major segment  D. Radius

 21. By solving inequality 1⁄3(x – 3) > 1⁄2(x + 2), answer will be

A. x < -10   B. x < -12   C. x < -14 D. x < -15

22. By solving inequality 1⁄3(x + 4) > (6 – 2x), answer will be

A. x < 12⁄5   B. x < 11⁄5   C. x < 13⁄5    D. x < 14⁄5

23.  In the diagram below,  =  and <PRS = 50^O. Calculate <PQR.  A.120^O  B. 110^O  C. 100^O D. 80^O

 .

24. If x > y and y > z then   A. x > z   B. x < z   C. x = 0      D. y = 0

25. Simplifying given expression 7⁄(2x – 5)+ 4⁄(x – 3) gives us

1. 23x – 31    B. (15x – 41)⁄(2x – 5)(x – 3)   C. (x – 3)(2x – 5)⁄23x  D. none of above

26.  In the diagram, O is the centre of the circle PQRS and < PSR = 86O. If <POR = x^o, find x.  A. 274^O 
B. 172^O  C. 129^O  D. 86^O

 . 27.  In the diagram below, o is the centre of the circle, <SOR = 64^O and <PSO = 36^O. Calculate <PQR. 
       A. 100^O  B. 96^O  C. 94^O  D. 86^O

28. Objective of linear programming for an objective function is to

A. maximize or minimize   B. subset or proper set modelling  C. row or column modelling   

D. adjacent modelling

29.  calculate the length of a chord 3cm away from the centre of a circle of radius 5cm

A. 16cm   B. 4cm   C.8cm    D.2cm

30.  In the diagram below, GI is  a tangent  to the circle at H. If EFI/GI, calculate the size of <EHF.           
 A. 126^O  B. 72^O  C. 54^O  D. 28^O

 .

31.P and q are simple statements. If p is true and q is false, which of the following is/are correct ?

P^q is true

p’^q’ is true

pvq is true.        A. I only B. II only C. III only D. I and III only E. I,II and III only

32.Which of these is the negation of the statement ‘ 26’  A. 2   B.   C.  2  
     D.

 Which of these is true of any two  logical statements  p and q

pq qp

p’^q’ (p^q)’

(pvq)’ p’vq’

All of the above

33. If p is a true statement and pvq is true then

       A.  q is false     B.q is true    C.q is either true or false     D.None of the above

34.Which of these is equal to the statement (pvqvr)’

A.  Pvqvr     B. P^qvr       C.P’^q’^r’        D.P’vq’^r’
35.(pvq)’ p’^q’ and (p^q)’p’vq’. This relationship is called the __________

A. Pythagoras theorem     B. De Morgan theorem    C. Fermat theorem   D.Euler’s theorem

36. If p is true and statement q is false, then q→p is

A. False B. true C. not logical  D. more information is needed to decide

37. If p is -3>0, and q is all rectangles are quadrilateral. Which of the logical statements below is true     A. pvq      B.  p’^q     C. p’vq’     D. All of the above

     38.Given the statements

X: 2 is an odd  number

Y: 2 is not an irrational number

39.Use logical connections to describe the compound statements ‘neither’  is 2 an odd number nor is it an irrational number      A. X’vY’      B. (xvy)’    C.(x^y)’     D.x^y

40. pv(q^r)(pvq)^(pvr)

The above statement made use of _______ algebraic property

1. Idempotent law    B. Absorption law    C. Distributive law    D.  Demorgan law

41. The diagram is a circle centre 0. If <SPR = 2m and <SQR =   n, express m in terms of n        A.  M = n/2  B. m = 2n  C. m = n-2  D. m = n=2

42.  In the PQR, <PQR = <PRQ = 45O. Which of the following statement is/are correct?I.  PQR is an equilateral triangle II. PQR is an isosceles triangle  III. PQR is a right – angled triangle.                        A. II only         B.I and II only            C. II and III only        D. I and III only.

43. In gradient-intercept form of equation y = mx + c, point where line cuts y-axis is

1. (3, c)    B. (0, c)   C. (1, c)    D. (2, c)

44.  Straight line equation y = x⁄3 + 1⁄4 cuts y-axis at point

1. (0, x⁄4)    B. (0, 1⁄3)    C. (0, 1⁄4)    D.(0, x⁄3)

45.  In gradient-intercept form of equation y = mx + c, ‘m’ denotes

1. gradient of independent variable    B. intercept on y-axis   C. gradient of straight line

D. intercept on x-axis

46.  If coordinates of A and B are (5, 6) and (9, 10) respectively then length of line segment AB is

1. 13.66     B. 9.66    C. 5.66    D.  7.66

47.  Largest part of circle divided by chord is called

1. Circumference    B. quadrant    C. minor segment    D. major segment

48. Chord divides circle into    A. two segments    B. three segments   C. four segments

D. five segments

49.  Smallest part of circle divided by chord is called  A. minor segment   B. major segment

C. major quadrant     D. radian

50.  Line segment which joins distinct points on circumference is called  A. radius   B. chord   C. perimeter   D. length

51.   By solving inequality a – 7 < 5 – 3a, answer will be

A. a < 3           B. a < 5   C. a < 6   D. a < 7

52.   In gradient-intercept form of equation y = mx + c, ‘c’ denotes

A.gradient of straight line     B. intercept on x-axis  C. gradient of independent variable

D. intercept on y-axis

 53.  In linear programming, constraints can be represented by

A. equalities   B. inequalities    C. ratios     D. both a and b

 54. Two lines  are said to be parallel if

1. They are of equal gradient     B. Their gradients are in ratio   C. One gradient is a negation of the other  D. One is  a multiplicative inverse of the other

 55. what is the radius of a circle with a chord of length 12cm and 8cm away from its centre?  

• A. 100cm   B.20cm   C.10cm   D.15cm

.56.  Solving expression (2a+3c)⁄3b + (a – c)⁄b gives us     A. 4a⁄3b  B. 5a⁄3b   C. 3a⁄2b   D.3b⁄5a

57.  In the diagram, POR is a circle with centre O. <QPR = 50O , <PQO = 30O and <ORP = m. Find m. 

A. 20^O  B. 25^O  C. 30^O D. 50^O.

58. In the diagram, PQS is a circle with centre O. PST is a tangent at S and <SOP = 96^O. Find <PST.             A. 42^O  B. 48^O  C. 60^O  D. 66^O

59. In the diagram, RP is a diameter of circle RSP, RP is produced to T and TS is a tangent to the circle as S. If <PRS = 24^O, calculate the value of <STR.          A. 24^O  B. 42^O  C. 48^O  D. 66^O

.

60.   In the diagram, PQRS is a circle centre O. POR is a diameter and <PRQ = 40^O. Calculate <QSR.           

A. 30^O  B. 40^O  C. 45^O  D. 50^O

      SS2 MATHS EXAM QUESTIONS SECOND TERM – EDUDELIGHT.COM

   SECTION B: THEORY

INSTRUCTION:            Answer five questions only. No 1&2 are compulsory.

1.   Given two points A(-5, 2) and B(1, -4)   
find:

  (a) mid point of the lie joining point A and B
  (b) Equation of AB

       (c)  Slope of AB

       (d)  Slope of perpendicular to AB

2     Find the maximal and minimal values of P= 3x+2y subject to the following constraints:
       x  + 4y
       2x + 3y
         x                   and ensure you graph the feasible region

3.         Solve for x and y in

• 
  
  

•    Simplify :

4.   Graph the system of the following linear  inequalities and pick at least a test point to determine that the region shaded are the solution of the given inequalities
 (a)  i.        2x+2y   -2
                3x+2y   2

        ii.       5x-2y -6
                  x-2y

       (b)    Make f the subject in

    (c)        Find the length of a chord which subtends an angle of 58° at the centre of a circle with  
                 radius 16cm .

4(a)   In the diagram  below; ABCD is a cyclic quadrilateral, <CBQ = 48^o and a = 2b. Calculate the
            numerical value of b.

  (b)     For what value of x is the expression   x² + 11x + 18   undefined?
                                                                          x²  + 3x – 10

  (c)      For what value of x is the expression    9 +  x² – 1

                                                                         x      x²-16

5a.   In the diagram, O is the centre of the circle, <OQR = 32^O and <TPQ = 15^O . Calculate:
(i) <QPR;  (ii) <TQO

.  

b.         If x= a+2 ,  express x-3   in  terms of a.
                   a-1                  x+1 

c.   .   If s:t=5:8,  evaluate:

6a.     Simplify :

6b.       Calculate the value of x in the figure below

6c.       P and Q are centres of circles with radii 9cm and 2cm respectively. PQ=17cm. R is the centre of a circle of radius xcm, which touches the above circles externally. Given that PRQ= 90^o,  find the value of x.

7a.       Find the values of x and y in the figure below

7b. Two chords    lABl=10cm and lCDl=8cm are drawn on the alternate sides of a circle of radius of 6cm. calculate their distance apart.

7c.  Mr Okirikpotor; the labourer   earns  300 naira for a one hour job, if he work 7 hours a day and spends 700 naira per day on meal(s). what is the least number of years  he must  work to earn more than 2,400,000 naira?

MATHEMATICS EXAM QUESTIONS FOR SS2 SECOND TERM

2ND TERM EXAMINATION CLASS: SS2 &SS3 SUBJECT: MATHEMATICS

THEORY

1. If 9 ^{2x +1} =

81x-2

3x

Find x

0.81 x 10^-5

b. Without using Mathematical Tables, evaluate

2.25 x 10⁷

2. Solve the following pair of simultaneous equations 2x + 5y = 6½

b. If Log

(2x +1) – Log10 (3x -2) = 1, Find x

5x – 2y = 9

10

3a. The angle of a sector of a circle radius 7cm is 108⁰. Calculate the perimeter of the sector. (Take π= 22/7)

b. A boat is on the same horizontal level as the foot of a cliff, and the top of the cliff is 30⁰. If the boat is 120m away from the foot of the cliff, find the height of the cliff. Correct to three significant figures.

• In a game, a fair die is rolled once and two unbiased coins are tossed once. What is the probability of obtaining 3 and a tail?

b. A box contains 10 marbles, 7 of which are black and 3 are red. Two marbles are drawn one after the other without replacement. Find the probability of getting

1. A red, then a black marble
2. Two black marbles
3. If 17x = 375 ²– 356², find the exact value of x
4. if 4^x = 2^½ X 8, find X.
5. The sum of the first 9 terms of an A.P is 72 and the sum of the next 4 term is 71. Find the A.P

6.

Calculate the area of the shaded segment of the circle shown in the diagram (Takeπ = 22/7)

b. A tin has radius 3cm and height 6cm. find the

1. total surface area of the tin
2. Volume in litres of liquid that will fill the tin to capacity, correct to two decimal places (Takeπ = 22/7)

7. Copy and complete the following table for the relation y = 5/2 + X – 4X²

X	-2.0	-1.5	-1.0	-0.5	0	0.5	1	1.5	2
Y	-15.5			1	2.5

• Using a scale of 2cm to 1 unit on the X axis and 2cm to 5 units on the y- axis, draw the graph of the relation for -2.0 ≤ X ≤2.0

• What is the maximum value of y?

from your graph obtain the roots of the equation 8x² – 2x – 5 =n 0 8a. The distribution of junior workers in an illustration is as follows:

Clerks	–	78
Drivers	–	36
Typists	–	44
Messengers Others	–	– 30	52

Represent the above information by a pie chart

b. The table below shows the frequency distribution of marks scored by 30 candidates in an aptitude test

Marks	4	5	6	7	8	9
Number of Candidates	5	8	5	6	4	2

Find the mean score to the nearest whole number

• 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. if the bearing of Q from P is 075⁰ and the bearing of R from P is 310⁰ , find the
• Distance between Q and R,
• Bearing of R and Q
• The table below shows the weekly profit in naira from a Mini- Market

Weekly     Profit (₦)	1-10	11-20	21-30	31-40	41-50	51-60
Frequency	6	6	12	11	10	5

1. Draw the Cumulative Frequency graph of the data
   1. From your graph, estimate the
      1. Median      ii. 80^th Percentile iii. What is the modal weekly profit?

OBJECTIVE

1. Find (1012)² expressing the answer in base 2(a) 10101 (b) 11001 (c) 10010 (d) 11101 (e) 10110
2. 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

3.   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

/3

4.   Simplify 0.027^-1/3(a) 3¹   (b) 3 (c) 3/10 (d)1/3 (e) 1/9

2

8

5.   Given that log^a = log⁴ , 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

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}

1. In the diagram below, the shaded portion is (a) P’nR (b) QnR (c) P’nQnR (d) (PuQ)’nR (e) (PnQ)U(P’nR)

1. Find the values of X for which the expression is undefined   6x-1     (a)

x² – 4x-5

+4 or +1 (b) -5 or +1 (c) -5 or -1 (d) +5 or -1 (e) +4 or -1

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

1. Solve the inequality

x<16

1(2x – 1)<5 (a) x< -5 (b) x<-6 (c) x<7 (d) x< 8 (e)

3

1. What is the smaller value of X for which x² – 3x + 2 = 0 (a) 1 (b) 2 9c) 3 (d) 4 (e) 5
2. 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)
3. 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

1. 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

1. 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

1. 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
2. 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

A cylindrical container closed at both ends, has a radius of 7cm and height cm.

Use this information to answer question 21 and 22 (Take π = 22/7)

• Find the total surface area of the container (a) 35cm³ (b) 154 cm³ (c) 220 cm³ (d) 528cm² (e) 770 cm²
• What is the volume of the container (a) 35cm³ (b) 154 cm³ (c) 220 cm³(d) 528 cm³ (e) 770 cm³
• Find the total surface area of a solid circular cone with base radius 3cm and slant height 4cm (Take π = 22/7) (a) 37 ⁵/7 (b) 66cm² (c) 75 3/7 cm² (d) 78 ²/7 cm² (e) 88cm²
• A hollow sphere has a volume of K cm³ and a surface are of K cm².

Calculate the diameter of the sphere (a) 3cm (b) 6cm (c) 9 cm (d) 12 cm (e) More information is needed

• A 120^o sector of a circle of radius 21 cm is bent to form a cone. What is the base radius of the cone? (a) 3 ½ cm (b) 7 cm (c) 10 ½ cm (d) 14 cm (e) 21 cm
• The angle of a sector of a circle is 108^o. if the radius of the circle is 3

½ cm, find the perimeter of the sector (a) 6 ³/5 cm (b) 6 ⁴/5 cm (c) 7

1/10 cm (d) 10 ²/5 cm (e)13 ³/5cm

27.      In the diagram below, AO is perpendicular to OB. Find X (a) 7.5^o (b) 15⁰ (c) 22.5⁰ (d) 30⁰ (e)38.6⁰

• In the diagram above, PQ is parallel to TU, < PQR = 50⁰, <QRS = 86⁰ and < STU=64⁰. Calculate the value of x (a) 136⁰ (b) 120⁰ (c) 108⁰ (d) 100⁰ (e)96⁰

10

10

If Log    ^x = 2.3675 and Log   ^y = 2.9738, what is the value of x + y,

correct to three significant figures? (a) 0.117 (b) 0.118 (c) 0.903 (d) 0.944 (e)0.946

sin 20⁰

• Without using tables, find the value of cos 700 +

0 (d) -1 (e) -2

cos 25⁰

sin 65⁰

(a) 2 (b) 1 (c)

• In the diagram below, <PRQ = 90⁰, <QPR = 30⁰ and |PQ| = 10cm. find y
  • 6cm (b) 5 cm (c) 4 cm (d) 3 cm (e)2 cm

P           10 CM            Q

R

32. What is the mode of the numbers 8,10,9,9,10,8,11,8,10,9,8 and 14? (a) 8 (b) 9 (c) 10 (d) 11 (e) 14

• The mean of 20 0bservations in an experiment is 4, if the observed largest value is 23, find the mean of the remaining observations (a) 4 (b) 3 (c) 2.85 (d) 2.60 (e)2.56
• Find the median of the following numbers 2.64, 2.50, 2.72, 2.91 and 2.35 (a) 2.91 (b) 2.72 (c) 2.64 (d) 2.50 (e) 2.35
• From a box containing 2 red, 6 white and 5 black balls, a ball is randomly selected. What is the probability that the selected ball is black? (a) ²/13 (b) ⁵/13 (c) ⁵/11 (d) ⁵/6 (e) ¹¹/13
• The 6^th term of a G.P is -2 and its first term is 18. What is the common ratio? (a)-½ (b) –¹/3 (c) ¼ (d) 2 (e) 3

37. Simplify (2¹/6 – 1²/3) ÷ 2 ²/3 (a) ³/16 (b) ⁷/16 (c) 1¹³/24 (d) 2¹¹/24 (e) 10

2/5

38. Simplify 56X^-4 ÷ 14X^-8 (a) 2x^-12 (b) 3X^-3 (c) 4X^-4 (d) 4X^-3 (e) 4X^-4

10

10

Simplify Log  ⁴ + Log   ²⁵ (a) 1 (b) 2 (c) 3 (d) 4 (e) 5

• A boy measured the length and breadth of a rectangular lawn as 59.6m and 40.3m respectively instead of 60m and 40m. what is the percentage error in his calculation of the perimeter of the Lawn? (a) 10% (b) 1.4 % (c) 0.7% (d) 0.2% (e) 0.1%