MATHEMATICS (Three hours and a quarter)

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1 MATHEMATICS (Three hours ad a quarter) (The first fiftee miutes of the eamiatio are for readig the paper oly. Cadidates must NOT start writig durig this time.) Aswer Questio from Sectio A ad questios from Sectio B. All workig, icludig rough work, should be doe o the same sheet as, ad adjacet to, the rest of the aswer. The iteded marks for questios or parts of questios are give i brackets []. Mathematical formulae are give at the ed of this questio paper. The use of calculator (f-8/ f-00) is allowed. Sectio A (0 marks) Aswer ALL the questios Directio: Read the followig questios carefully. For each questio there are four alteratives A, B, C ad D. Choose the correct alterative ad write it i your aswer sheet. Questio [50 Marks] (i) The sigma otatio of the series is 5 A ( 7 + i) 5 B ( 7i) 5 C ( 7 i) 5 D ( + 7i) BHSEC/0/00 Page of This booklet cotais pages.

2 (ii) The iverse of the matri 7 5 A 7 5 B 5 7 C 5 7 D 5 is 7 (iii) If ( + ) A B - C -9 D 9 is a factor of the polyomial 6 + m, the the value of m is (iv) The horizotal asymptote of the ratioal fuctio A - B C - D f ( ) is (v) The side of a equilateral triagle is 7cm ad is icreasig at the rate of cm/s. At what rate is the area icreasig? A 0.5cm /s B 5.6 cm /s C.5 cm /s D. cm /s BHSEC/0/00 Page of

3 (vi) The poit of the curve y si cos (vii) parallel to X- ais is A B C D If A B C D π, π, π, π, y l l + for [ π, π ] +, the the value of y' will be (viii) The itegral value of A 0.5 B 0. C 0. D 0. e l d is where the taget is (i) Area of the sector POQ i the give figure is A 8. cm B.cm C 5.6 cm D 7.7cm Q π o 6cm P BHSEC/0/00 Page of

4 () Which of the followig is the amplitude of + i? i A 69.8 B 70.6 C 65.7 D 75. (i) If + +,the the value of is A B C D (ii) The tred value of the followig data usig a three yearly movig average is Year 5 6 values A.00,., 5.06,.56 B.0, 6., 7., 0. C.00,.,., 5.66 D., 7.5, 8.5, 9.5 (iii) If A B C D y, the of the value of dy at - is d 5 5 BHSEC/0/00 Page of

5 (iv) The rectagular form of 5cis 6.9 is A i B i C + i D + i (v) The equatio of the coic give i the diagram is y A 9 5 y B y C y D 5 9 Sectio B (70 marks) Aswer ay questios. All questios i this sectio have equal marks. Uless otherwise stated, you may roud aswers to decimal places. Questio (a) Evaluate sec d [] + ta (b) Determie a quadratic fuctio f ( ) such that f () 5, f '() 7 ad f "() 0 [] Questio (a) (b) A bacteria culture starts with 000 bacteria ad after 0 hours estimated cout is 8000 bacteria. Fid the umber of bacteria after hrs. [] Fid dy d if e l y [] BHSEC/0/00 Page 5 of

6 Questio (a) Determie e d [] z (b) If z i ad z + i, fid the value of zz z [] Questio 5 (a) Fid the equatio of the circle whose cetre is (,) ad passes through the poit (, ) [] (b) If the eccetricity is 0 ad the sum of those semi-aes is, the fid the equatio of the hyperbola. [] Questio 6 (a) Determie the equatio of the plae passig through the poits A( 0,, ), B (, 5, ) ad (,,) C [] (b) Fid the derivative of y cos by usig first priciple method [] Questio 7 Prove, N by mathematical iductio method [5] i + Questio 8 The legth of slat height of a right circular coe is 6cm. Fid the radius of the base so that the volume may be maimum. [5] Questio 9 Show that the cotiued product of the four values of i + is equal to. [5] BHSEC/0/00 Page 6 of

7 Questio 0 For the equatio of the ellipse9 + 6y 5 + 6y + 0, fid the i) coordiates of the cetre ii) vertices iii) eccetricity iv) legth of major ad mior aes [5] Questio Solve the equatio by matri method + y + z, y + z, + y z [5] Questio A rectagular shoppig comple is to be built o a 80 m by 60 m rectagular plot i such a way that there is a path meter width surroudig the buildig. The buildig ca occupy up to 70% of the plot s area. What is the rage of possible itegral values for the width of the path? [5] Questio (a) (b) Simplify ad state the restrictios Epress i the simplest surd form [] 6 [] 8 Questio (a) Wagchuk ivested Nu.0,000 for 5 years at the rate of 0% compouded aually. How much moey will he get back after completio of the time period? [] (b) A ladder m log rests agaist a vertical wall. If the bottom of the ladder slides away from the wall at the speed of m/sec, how fast is the agle betwee the top of the ladder ad the wall chagig the agle whe the agle is π? [] BHSEC/0/00 Page 7 of

8 Questio 5 Fid the area of the regio bouded by the curves y 6 ad 6y [5] Questio6 (a) If f '( ) + + ad ( ) f the fid the value of f () [] (b) Fid the stadard deviatio of the followig distributio [] Class Frequecy Questio 7 For the fuctio y +, fid i) itercepts ii) critical values iii) iflectio poits, ad iv) sketch the graph [5] Questio 8 Fid the rak correlatio coefficiet for the followig data of marks obtaied by 0 studets i Physics ad Chemistry [5] Roll No Physics Chemistry BHSEC/0/00 Page 8 of

9 MATHEMATICS FORMULAE Fuctios ad Equatios () ( a ± b) a + b ± ab () () ( a ± b) a ± a b + ab ± b a b a + b a b ( )( ) () a ± b ( a ± b)( a m ab + b ) (5) ± b b ac a Sequece ad series () () i () i i ( + ) ( + )( + ) 6 ( + ) i () t ar (5) t a + ( )d. (6) S a ( r ) r ( ) where r< a r, Where r > r (7) S a + ( ) d Differetiatio f ( + h) f ( ) () f '( ) lim h 0 h () y, y, () y cf(), y cf () () y f ( ) ± g( ), y f ( ) ± g ( ) (5) F( ) f ( ) g( ), (6) F '( ) f ( ) g '( ) + f ' ( ) g( ) f ( ) F( ), g( ) g( ) f ( ) f ( ) g ( ) F '( ) g( ) [ ] (7) f o g( ) f g ( ) ( g ) (8) dy d dy du (9) v( t) h'( t) du d Coordiate Geometry y y m( ) () ( ) () ( a) ( y b) Trigoometry + r () Si( A ± B) si AcosB ± cosasib () Cos( A ± B) CosAcosBm si AsiB () ta A ± ta B ta( A ± B) m ta A ta B () si θ + cos θ Logarithmic Epoetials () y y0 ( + r) () y y0e k () A P( + r) Itegratio () d () b a f ( ) g( ) d f ( ) g( ) d f ( ) g( ) d d d b () () f ( ) d lim f ( ) V π y d A b a a yd i Measuremet () π Coe: V r h () Coe: SA π rl + π r () () (5) π Sphere: V r Sphere: SA π r Cylider: SA π rh + π r (6) Cylider: V πr h (7) Circle: A πr (8) Circle: C πr i BHSEC/0/00 Page 9 of

10 (9) Triagle: A bh, A A s( s a)( s b)( s c) (0) Rectagle: A lw, () Rectagle P l + w () Square: A s, () Square P s () Rectagular Prism: V lwh Comple Numbers () r a + b b () ta θ a θ ta b a () If z rcisθ the z r cisθ 60 () z r θ cis( + k ) f or k 0,,,,... Secod Degree Relatios () X y Ellipse : + a b () X y Hyperbola : + a b c () e a Geometry () D ( ) + ( y y) + ( z z) l + m ly + my lz + mz () (, y, z),, l + m l + m l + m () For a + b y + c z 0 ad a + b y + c z 0 () θ l π r 60 (5) θ A π r 60 Matrices () C ( ) () ij y z b c b c c a c a a b a b i + j M A A A A I () Iverse of A A adja det A ij Data & Probability () f () Media l + ( m c) () ( ) i () l l f + + d + d + (5) f ( ) i f f f N N (6) (7) m + m + P 00 P0 I p w I 00 p w (8) 0 (9) Cov ( X, Y) ( X X)( Y Y) (0) ( )( y y) r ( ) ( y y) ( )( y y) () r () () () (5) (6) b YX cov y ( X, Y) y r ( X Y ) ( ) cov, Y Y X X ( ) r X X y by by r r S τ ( ) 6 r d y ( ) y BHSEC/0/00 Page 0 of

11 Rough Work BHSEC/0/009 Page of Copyright reserved

12 Rough Work BHSEC/0/009 Page of Copyright reserved

MATHEMATICS (Three hours and quarter)

MATHEMATICS (Three hours and quarter) MTHEMTIS (Three hours ad quarter) swer Questio from Sectio ad 4 questios from Sectio. ll workig, icludig rough work, should e doe o the same sheet as, ad adjacet to, the rest of the aswer. The iteded marks