MATHEMATICS FIRST TERM EXAMINATION SS 3

FIRST

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

SUBJECT: MATHEMATICS              CLASS:  SS 3                        TIME:  3HRS

INSTRUCTION: Answer all questions from ONLY part A

PART A – OBJECTIVE:

1. A matrix is said to be a singular matrix when is determinant is (a) 1   (b)  2    (c) 0   (d)  3

2. In a class of 40 students, 32 offer Mathematics, 24 offer Physics and 4 offer neither Mathematics nor Physics. How many offer both Mathematics and Physics? A. 4 B. 8 C. 16 D. 20
3. Simplify log₂(256)^1/8 A.4 B.2 C. 3 D. 1
4. Calculate the curved surface area of a conical shape whose radius is 5cm and vertical
   height is 12 cm ?  A. 205.23cm² B. 104.23cm²  C. 304.23cm²  D. 204.23cm²
5. In the diagram below, = and <PRS = 50^O.Calculate<PQR. A.120^O B.110^O C.100^O D.80^O

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6. If the total surface area of a solid hemisphere is equal to its volume. Find the radius

. A. 3.0cm   B. 4.5cm   C. 5.0cm   D. 9.0cm

7. 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
8. The sum of the first n terms of an arithmetic progression is 252. If the first term is -16 and the last term is 72, find the number of terms in the series. A. 9 B. 8. C. 7 D. 6
9. A trapezium has two parallel sides of lengths 5cm and 9cm. If the area is 21cm², find the distance between the parallel sides. A. 4 cm B. 7 cm C. 3 cm D. 6 cm
10. An arc of a circle subtends an angle of 30 ^o on the circumference of a circle of radius 21cm. Find the length of the arc. A. 44 cm B. 11 cm C. 66cm D. 22cm
11. On a pie chart, there are four sectors of which three angles are 45^o, 90^o and 135^o. If the smallest sector represents N28.00, how much is the largest sector? A. N84.00 B. N42.00 C. N48.00 D. N96.00
12. 12. Find the value of the angle marked x
13. 60^o    B.  45^o     C.  17^o        D. 18^o           E.  15^o

13.The mean of the numbers 3, 6, 4, x and 7 is 5. Find x. A. 5 B. 2 C. 3 D. 2

14. By how much is the mean of 30, 56, 31, 55, 43 and 44 less than the median?
15. 0.50 B. 0.33 C. 0.17 D. 0.75
16. The range of 4, 3, 11, 9, 6, 15, 19, 23, 27, 24, 21 and 16 is A. 24 B. 23 C. 21 D. 16
17. A bearing of 320^oexpressed as a compass bearing is (a) N50^oW  (b) N40^oW  (c) N50^oE
    (d) N40^oE
18. The sum of the interior angles of a pentagon is 6x + 6y. Find y in terms of x.
19.   y = 150 – x B. y = 120 – x C. y = 60 – x D. y = 90 – x
20. The area of a rhombus is 24cm². If one of its diagonals is 6cm, find the length of the other
    diagonal.  A. 2cm      B. 4cm     C. 8cm      D. 10cm     E. 18cm
21. Given that the first and fourth terms of a G.P. are 6 and 162 respectively, find the sum of the first three terms of the progression. A. 48 B. 78 C. 27 D. 8
22. Factorize completely ac – 2bc – a² + 4b².
23. (a – 2b)(c – a + 2b) B. (a – 2b)(c + a + 2b) C. (a – 2b)(c + a – 2b) D. (a – 2b)(c – a – 2b)
24. A farmer planted 5,000 grains of maize and harvested 5,000 cobs, each bearing 500 grains. What is the ratio of the number of grains sowed to the number harvested? A. 1 : 250,000 B. 1 : 25,000 C. 1 : 5,000 D. 1 : 500
25. Three teachers shared a packet of pens. The first teacher got 2/5 of the pens and the second teacher received 2/15 of the remainder. What fraction did the third teacher receive? A. 15 8 B. 25/13 C. 25/12 D. 25/11
26. Simplify: 26+22-23 (a) 4 (b) 3+4  (c)   42     (d)  43+4
27. Find the value of x in the figure  below

1. 50^o    55^o    C. 45^o    D. 75^o  E.  40^o

23. A father decided to give 20% of his monthly income to his three children as their monthly allowance. The eldest child got 45% of the allowance and the youngest got 25%. How much was the father’s monthly income if the second child got #3 000? A. #33,000 B. #45,000 C. #50,000 D. #60,000
24. If the interest of #150.00 for 2½ years is #4.50, find the interest on #250.00 for 6 months at the same rate. A. #1.50 B. #7.50 C. #15.00 D. #18.00
25. Approximate 0.03457 to 1 significant figure. (a) 0.0 (b) 0.03 (c) 0.0005    (d) 0.004? A. 60 B. 54 C. 48 D. 42
26. If log₁₀2 = 0.3010 and log₁₀3 = 0.4771, evaluate log₁₀4.5 A. 0.9542 B. 0.6532 C. 0.4771 D. 0.3010
27. Simplify (1^{2 /3}) ^1/2 A. 0 B. 1/3 C. 3/5 D. 1
28. If U = {x:x is a positive integer less than 10} and P = {x:x is a prime factor of 30}, find the complement of P.
    A. {1, 2, 4, 7, 8, 9} B. {1, 2, 4, 6, 7, 8, 9} C. {1, 4, 6, 7, 8, 9)     D. { 1, 4, 7, 8, 9}
29. If m = 3, p = -3, q = 7 and r = 5/2, evaluate m (p+q+r). A. 19.50 B. 19.15 C. 18.95 D. 18.05
30. The time taken to do a piece of work is inversely proportional to the number of men employed. If it takes 30 men to do a piece of work in 6 days, how many men are required to do the work in 4 days? A. 20 B. 35 C. 45 D. 60
31. The sum of the interior angles of a regular polygon is 1800^°. Calculate the size of one exterior angle of the polygon. A. 30^° B. 24^° C. 18^° D. 12^°
32. A chord of a circle subtends an angle of 60° at the center of a circle of radius 14cm. Find the length of the chord. A. 7 cm B. 14 cm C. 21 cm D. 28 cm
33. A sector of a circle has an area of 55 cm². If the radius of the circle is 10 cm, calculate the angle of the sector. A. 45° B. 63° C. 75^° D. 90^°
34. Find the curved surface area of a cone with circular base diameter 10 cm and height 12cm. A. 25cm² B. 65 cm² C. 120 cm² D. 156 cm²
35. Subtract 16418₉ from 18630₉. A. 1121₉ B. 2112₉ C. 2113₉ D. 2211₉
36. If 55_x + 52_x = 77₁₀, find x A. 8 B. 6 C. 7 D. 10
37. 15cm³ of a metal weighs 127.5g. What is the weight of 35cm³ of the same metal if the
    mass of the metal is directly proportional to the volume?(a) 167.3g (b) 297.5g (c) 203.2g
    (d) 132g

34  When the sum of 28 and a certain number is divided by 5, the result is equal to treble the
original number. What is the number?  (a)  x=2 (b) x= 3 (c) x=4  (d) x =5

35. A chord is drawn 5cm away from the center of a circle of radius 13cm. calculate the length of the chord. A. 7cm B. 9cm C. 12cm D. 24cm
36. Find the radius of a sphere whose surface area is 154cm2.A. 7.00cm B. 3.50cm C. 3.00cm D. 1.75cm
37. Find the value of sin45° – cos30°. A. (2√2-√3)/2 B. (√3-2√2)/2 C. (√2-√3)/3 D. (√3-√2)/3
38. A cliff on the bank of a river is 300m high. If the angle of depression of a point on the opposite side of the river is 60^o, find the width of the river. A.173.2m B.183.2 C.373.2m D.172.2m
39. Given that log2 = 0.3010, log7 = 0.8451, evaluate log 112. A. 2.1461 B. 2.0491 C. 3.1461 D. 2.5441
40. Find the sum of infinity of the following series. 0.5 + 0.05 + 0.005 + 0.0005 + …
41. 85 B. 75 C.115 D.95
42. simplify: sin2x+cos2x A. 1+cosx B. 1     C. sin(2x)    D. cos(2x)
43. Given that tan x = ⁵¹², what is the value of sin x + cos x? A.¹⁷/₁₃ B.⁵/₁₃
    C. ⁷/₁₃        D. ¹²/₁₃

43 The height of a cylinder is equal to it’s radius. If the volume is 0.216πm³, calculate the radius.
(a)  0.46m  (b) 0.60m  (c) 0.87m   (d) 1.80m

44. Express the product of 0.21 and 0.34 in standard form
45. 7.14 x 10^-2 B. 7.14 x 10^-1 C. 7.14 x 10^-4 D. 7.14 x 10^-3

45. 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

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1. (-1, 3) B. (3, 1) C. (-3, 1) D. (1, 3)
2. If y varies directly as the square root of x and y = 3 when x = 16, calculate y when x=64.
3. 6 B. 12 C. 3 D. 5
4. If x is inversely proportional to y and x =2½ when y =2, find x if y = 4. (A.) 4 (B.) 5 (C.) 1 (D.)11
5. The 3rd term of an arithmetic progression is -9 and the 7th term is -29. Find the 10^th term of the progression. A. -44 B. -165 C. 165 D. 44
6. Solve the exponential equation: 2^2X + 2^X+1 – 8 = 0 (A) 1 (B) 2 (C) 3 (D) 4
7. 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

PART TWO – THEORY

Answer eight (8) questions in this part

1. The probabilities of two candidates M and N passing an examination are 23  and  45      Find the probability that:
   (i)        Only one candidate  will pass           (ii) at least one candidate will pass

2. (a)    Rationalize (3√2 – 1) / (3√2 + 1), leaving your answer in the form a+b√c.

P=   34 253-165  7              Q=    641   324-135                 R=  131652438

(b)  Find   (i) 5P + 2Q    (ii) 4Q – 2R        (iii) 2P + Q + 3R          (iv) PR     (v)  Det Of R

4. a) Draw a Table for multiplication * in modulo  8 on the set T= {2,3,5,7}

(b)  Use the table to find the solution set of : (i)  3 * n =  5          (ii)  n * n = 1

5. Students on excursion flew from Elias Airfield, A(Lat30^⁰N, Long20^⁰W) to Elias Zoological garden, B(Lat30^⁰N, Long40^⁰E). Assume the radius of the earth to be 6400km, calculate, correct to three significant figures:

(a) the length of chord AB

(b) the distance between A and B along the parallel of latitude

(c) the shortest distance between A and B.

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

7       .a. Find the total amount paid back if #10,000,000 was borrowed at 15%
(i) compound interest   (ii) simple interest, for three years.

1. A hemispherical bowl is surmounted on a metallic cylindrical tank. Calculate the volume of the object.

11.5cm              10cm

                    14cm

8. 8. Given that Sin (A+B)= sinAcosB+cosAsinB and Cos(A+B)=cosAcosB-sinAsinB, using surd form, find the value of (i) cos105= cos(45+60) (ii) sin 105 =sin (60+45)
9. 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.

9. 9. Given the tank below, calculate the (i) capacity of the tank in m³ (ii) the cost of metal needed to construct the tank if it costs £50.00 per m².

2m                         10m                                             12m

10. 10. Use crammer’s or inverse approach to solve the linear equation below,
    5x + 2y  =26
    3x – y    = 9

    b. The sum of a two digit numbers is 11,. When interchanged, the difference of the numbers is 27. Find the
    numbers.