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ST. PAULS COLLEGE

F.2 Final Examination 2001-2002

Mathematics

Time allowed: 1 hours

1. Answer ALLquestions in Section A and any FOURquestions in Section B.

2. Unless otherwise specified, numerical answers should either be exact or correct to

3 significant figures.

3.

The diagrams in this paper are not necessarily drawn to scale.

Section A (60%)

Answer ALLquestions in this section on the answer sheet provided.

For questions 1-10, choose the correct answers and put the letter A, B, C, D or E in

the spaces provided. For questions 11-20, fill in the blanks with the correct answers.

1. Round off 0.03084976 to 5 significant figures.

A. 0.0308 B. 0.03085 C. 0.030849 D. 0.030850 E.

0.0308498

2. Which of the following is/are an identity/identities ?

I. 9 ( 3x + 2 )2= ( 7 3x )2

II.

( k + 3 )( k

2 ) = ( k + 5 )( k

4 ) + 14III. ( 3 + 2x )( 3 2x ) = 9 4x2

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

3.

If 3x + 2y + 1 = 0 and 4x 3y = 27 , find the value of x y.

A. 8 B. 4 C. 2 D. 4 E. 8

4. In the figure, A = C = 900. AB = 1cm. ,AD = 7cm. and BC = CD.

Find the area of the quadrilateral ABCD.

A.32 cm2

B. 24 cm2

C. 19.5 cm2

D.16 cm2

E.9.75 cm2

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5. If the simple interest on $ 2500 for 2 years is $225, find the interest on $8000

for 9 months at the same interest rate.

A. $ 245 B. $ 270 C. $ 375 D. $ 900 E. $ 3240

6. Given 3 points A = ( 6, 4 ), B = ( 1, 6 ) and C = ( x, 4 ). If AB is

perpendicular to BC, find x.

A. 1 B. 2 C. 3 D. 4 E. 5

7.

In ABC, AB : BC = 5 : 6 and AB : CA = 3 : 4. If CA is longer than BC by

3 cm., find the length of AB.

A. 20 cm. B. 22.5 cm. C. 25 cm. D. 30 cm. E. 37.5 cm.

8.

ABCD is a square of side x cm. Arc BED is an arc of the circle centre A radius

x cm. The arc cuts the diagonal AC at E. Find, in cm

2

, the shaded area.

A.4

1x2 B. ( 2 1 ) x2 C. ( 2 2 ) x2 D.

2

)12( x2 E.(1

2

1) x2

9.

In the figure, each side of the cube is x cm. The base radius of the cylinder is r cm.

and the height is 2r cm. If the surface area of the cube is the same as the total

surface area of the cylinder, thenr

x =

A. B.

1 C. D.

3

2 E.

6

4

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10.

Travelling at x kmph., a train takes y hours for a certain journey. If the train

increases its speed by 6 kmph., the time for the journey will be shortened by 30

minutes. Express y in terms of x.

A. y = x + 6 B. y = 3x + 18 C. y = 5x +30

D. y =12

6

+

+

x

x E. y =

12

x+

2

1

11. If cos ( 2 + 100) = sin ( + 260), find the value of .

12.

In the figure, ACB = 900, AB = 5, AC = 3, BE = 3 and AEC = .

Find , correct to the nearest 0.10.

13. Simplify36

4

x

24

1

x .

14. Solve2

k

p

x

4

3+ = mx for x.

15. Factorize x2 y2+ 6y 6x .

16. Find the quotient on dividing 6x3+ 5x2+ 7 18x by 3x 2 .

17.R = ( 1, 2 ), S = (6, 3 ) and T is a point on the y-axis such that RT = ST.

Find T.

18.

Find the sum of the marked angles.

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19.

In the figure, ABCD is a rectangle with AB = 2a cm. and BC = a cm. DEC is

a semi-circle with DC as diameter. Arc EC is an arc of the circle centred at B

with BC as a radius. Find the shaded area.

20.

Express ( cos 1 )( cos + 1 ) 2 tan2 cos2 in terms of sin .

Section B (40 %)

Answer any FOURquestions on the foolscap papers provided.

Marks will be deducted for untidiness and poor presentation.

All necessary workings must be shown.

Begin a new question on a new page.

1. a) In the figure, P(0,2), Q(3,0), R(5, 4) and S( k,

2

1) are the vertices of a trapezium.

PS cuts the x-axis at T and PQ // SR.

(i) Find the value of k. (2 marks)

(ii) Find the coordinates of T. (3 marks)

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b) Given that =

TPQPQPT

sin2

area of PQT ,

find TPQ correct to 2 decimal places. (5 marks)

2. a) Given that cos 3 = sina where 900 a .

(i) Express in terms of a. (2 marks)

(ii) If2

1

3tan =

a , find the value of

)60tan(

1

+ (3 marks)

b) Find the value of 22 )1

()1

(x

x

x

x + (5 marks)

3.a) A speed boat travels at a uniform speed between two places A and B.

Water flows at a constant speed of 10 km/h from A to B. The boat takes

2

14 hours to travel from A to B and

3

15 hours to travel from B to A. Find

the distance between A and B and the speed of the boat in still water.

(5 marks)

b) Simplify

2

2

sin1

cos1

costan

sin

+

(5 marks)

4.a) If the difference between simple and compound interests calculated yearly on

$10000 atx%p.a.for 2 years is 36, find the value ofx. (5 marks)

b) In the figure, OXYis a sector with centre O. Ifzis the mid-point of YO,

find area of OXZ: area of sector OXY. (Leave your answer in terms of )

(5 marks)

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5.a) A metal solid cube of side 10 cm is melted and recast into a solid right

circular cylinder of height 10 cm. ( = 3.1416)

(i) Find the base radius of the cylinder. (2 marks)

(ii) Which solid has a greater total surface area, the cube or the cylinder?

Find the difference in their total surface areas.

(Give the answers correct to 3 significant figures.) (3 marks)

b) Change the subject of the formula to b.

a

acbbR

2

42 += (5marks)

End of paper