334 MATHS SERIES DSE MATHS PREVIEW VERSION B SAMPLE TEST & FULL SOLUTION

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1 MATHS SERIES DSE MATHS PREVIEW VERSION B SAMPLE TEST & FULL SOLUTION

2 TEST SAMPLE

3 TEST III - P APER Questio Distributio INSTRUCTIONS:. Attempt ALL questios.. Uless otherwise specified, ll worig must be clerly show.. Uless otherwise specified, umericl swers should either be ect or correct to sigifict figures.. The digrms re ot ecessrily drw to scle. Test III/

4 Sectio A): The mesured legth of bo is 5 cm. If the percetge error is %, fid ) the mimum error, b) the rge of the ctul legth. mrs) The figure shows the first regulr polygos. How my digols c be drw i regulr ) hego? b) -sided polygo? mrs) Test III/

5 If + b b = 5, fid ) : b, b) : b. mrs) Let f ) = +. Is it true, for ll rel vlues of, tht ) f ) = f )? b) f ) = [ f ) ]? Epli. mrs) Test III/

6 5 A B C D The drtbord show i the figure is divided ito 5 equl divisios. Ldig i regios A, B, C d D gets,, d poits respectively. A drt is throw d hits the drtbord. ) Fid the probbility tht it lds i i) regio D, ii) regio A or regio B or regio C. b) Joh tells you tht he epects the score obtied if he throws drt d hits the drtbord is the verge of the poits for ldig i the regios A, B, C d D. Are you gist his view? Give resos to support your swer. [Assume the drt does't ld o the boudries.] 5 mrs) Test III/

7 Sectio A): 6 The followig shows Cdy s fiished times miutes) for Eglish d Mthemtics ssigmets over the pst 0 dys. Eglish ssigmet Mthemtics ssigmet ) The followig stem-d-lef digrm represets the bove dt. Eglish Assigmet Mthemtics Assigmet Lef Stem Lef y mi) mi) y mi) 9 p q b) i) Fid d y. ii) If the miimum mr for Eglish ssigmet is 7, fid p. iii) If the mimum mr for Mthemtics ssigmet is 65, fid q. mrs) Compre the fiished times for both ssigmets. mrs) Test III/5

8 7 Give the followig lies: L : + y 8= 0, L : y + = 0, L : + y 8 + y +) = 0 L d L meet t P. ) Fid the coordites of P. mr) b) Show tht L psses through P for ll vlues of. mrs) c) Fid the equtio of L if i) its slope is, ii) it is perpediculr to L. mrs) Test III/6

9 8 A S h B C I the figure, ABC is equilterl with height h. It is iscribed i circle. S is semi-circle with AC s the dimeter. ) Epress the followig i terms of h: i) the re of ABC ii) the rdius of the circle mrs) b) Fid the re of the shded prt i terms of h. [Leve the swers i surd form, if ecessry.] mrs) Test III/7

10 Sectio B: 9 Let α d β be the roots of the qudrtic equtio + 5 =. Form equtio, with itegrl coefficiets, whose roots re α β d β α. mrs) 0 Let f )= ) Simplify f ). b). mrs) Joh clims tht f ) is defied for ll rel vlues of. Do you gree with him? Epli. mrs) Test III/8

11 The vlue of ew cr is $ The vlue $V of the cr deprecites ccordig to the formul below: V = bt where d b re costts d t is the time te i moths. ) Fid the costt. mr) b) After yers, the vlue of the cr is $00 000, fid the vlue of b, correct to sigifict figures. mrs) c) Fid the vlue of the cr fter 0 moths correct to the erest dollr. mr) d) i) For how log will the vlue of the cr be hlf of the origil? ii) Joh clims tht it tes twice the time te i i) for the vlue of the cr to be oe-fourth of the origil. Justify his clim. mrs) END OF PAPER Test III/9

12 Pper II TEST III - P APER APER Suggested Timig: 0 mi INSTRUCTIONS:. Attempt ALL questios.. Choose the best optio.. The digrms re ot ecessrily drw to scle. Sectio A: Simplify b ). b b A B b 5 C D b 5 b 5 If f )= +, f + )= A. B +. + C +. D +. Test III/0

13 If is divisible by d b is divisible by 8, which of the followig is/re true? I. + b is divisible by 8. II. + b is divisible by. III. b is divisible by. A I oly B III oly C I d II oly D II d III oly I. II. Top Top Side Side III. Frot Top Frot Side Frot Which of the bove solids hve the sme top, frot d side views? A I d II oly B I d III oly C II d III oly D I, II d III Test III/

14 5 rulers d 6 pecils cost $7, while rulers d pecils cost $9. How much does rulers d pecils costs? A $ B $ C $6 D $8 6 If : b = :, A B C D + b ) b = 7 Fid the re of the give figure. A 5cm B 90 cm C 0 cm D 5cm cm cm 0 cm 8 The distce betwee,) d,) is. = A 5 or. B 5 or 5. C. D 5. Test III/

15 9 A sports groud of re 00 m hs re of 5cm whe respreseted o mp. The scle of the mp is pproimtely A : B : C : D : If vries iversely s y d y vries directly s z, z vries directly s A. B. C. D. The bse d height of trigle re icresed by 0% d 0% respectively. The re of the trigle is icresed by A 0%. B %. C 0%. D %. The figure shows the grph of y = + b + c. Which of the followig is/re true? I. > 0 II. b > 0 y III. c > 0 y = + b + c A I oly B III oly C II d III oly O D I, II d III Test III/

16 cos θ si θ= A. B. C cosθ siθ) cosθ+siθ). D cosθ siθ). I the figure, right circulr coe is cut by two ples prllel to its bse to form three prts. Their slt heights re i the rtio : :. Fid the rtio of the volumes of the three prts. A : 8 : 8 B : 8 : 7 C : 6 : 98 D : 7 : 5 5 I the figure, pper sector with cetrl gle θ is folded up to form coe with semi-verticl gle φ. The reltioship betwee θ d φ is A θ 60 = si φ. B θ 60 = si φ. θ φ C θ 60 = cosφ. D θ = si φ The polyomil + + is divisible by. Fid. A B C D Test III/

17 Sectio B: 7 log. 0= A log. 0 B log 5 C log 5 D log 5 8 Let y =. The miimum vlue of y is + A. B 9. C 7. D 7. 9 Let 000 ) = P 0) d ) = Q 0). How my prime umbers re there betwee P d Q? A 6 B 7 C 8 D K + = A B + C K + D K + ) + Test III/5

18 If y = +, + y + y = A B C D A trigle hs sides cm, 5 cm d 6 cm. The lrgest gle of the trigle is A B 56.. C 86.. D 9.8. I the figure, = A 75. B 95. C 05. D I the figure, AB d AC re the commo tgets to the three circles, the middle circle touches the other two circles. The rdii of the two lrger circles re d. Fid the rdius of the smllest circle. B C A B C D 5 A END OF PAPER Test III/6

19 FULL SOLUTION SAMPLE

20 Test III - Pper Full Solutio SECTION A): ) Mimum error 5 cm % 0.6 cm b) Upper limit cm ; Lower limit cm The rge of the ctul legth is.-5.6) cm ) Method I: Direct drwig Number of digols 9 Method II: Cocept of combitio 6 Number of digols C Note: 6 is the o. of sides b) Method I No. of Digols st Differece No. of Digols st Differece Squre Regulr Regulr Regulr Regulr 7-sided 8-sided Petgo Hego Polygo Polygo Regulr Regulr Regulr Regulr Regulr 9-sided 0-sided -sided -sided -sided Polygo Polygo Polygo Polygo Polygo By completig the bove, we c see tht: No. of digols i regulr -sided polygo = 65 Note: If you re smrt eough, you c see tht: No. of digols i regulr -sided polygo Method II No. of digols i regulr -sided polygo C

21 ) b 5 b b 5 5b 7b : b 7 : b) Method I : b ) ) b 7 b Method II : b 7 : b 7 : b : ) 7 9 : 9 9 : 9 9 : 9 ) Method I L.S. f ) R.S. f ) ) L.S. R.S. f ) f ) is ot true for ll rel vlues of Method II Whe L.S. f ) R.S. f ) ) L.S. R.S. f ) f ) is ot true for ll rel vlues of b) Method I: L.S. f ) R.S. [ f )] ) L.S. R.S. f ) f ) is ot true for ll rel vlues of Method II: Whe L.S. 5 R.S. ) 9 L.S. R.S. f ) f ) is ot true for ll rel vlues of 9

22 5 ) i) ii) P D) 5 P A or B or C) b) Score he epects to obti = Epected score Averge of the poits for ldig i A, B, C, D Obviously, 5 5 I m gist his view SECTION A): 6 ) i) 0, y ii) p 7 iii) q 5 b) For the first row, there re more dt for Mthemtics ssigmet th those for Eglish ssigmet; while for the lst row, there re more dt for Eglish ssigmet th those for Mthemtics ssigmet We my coclude tht the fiished times for Mthemtics ssigmet re shorter th those for Eglish ssigmet 7 ) L : y 8 0 ) L : y 0 ) ) ) : Sub. ito ): y 0 y P, ) b) Whe, y ) ) 8 [ ) ) ] 0 L psses through P c) y 8 y ) 0 ) ) y 8) 0 8 y *) Slope of L 0

23 i) The equtio of L is y 8 y ) 0 i.e. y 0 Note: You my lso put ii) Slope of LSlope of L ito *) to get the equtio The required equtio is y 8 y ) 0 i.e. y 0 Note: You my lso put ito *) to get the equtio 8 ) i) ii) h h CD t 60 h BC h h Are of ABC BC h h h h OD CD t 0 Rdius of the circle h r h OD h h

24 b) AC BC h Are of S h h ) 6 Are of the mior segmet AEC h 0 60 h h h 7 Are of the shded prt h 6 h h 7 ) h 5 h SECTION B: 9 5, The required equtio is: ) ) ) 0 ) 0 ) [ ] 0 5 ) ) [ ] ) f ) ) ) ) ) ) b) the deomitor of f ) cot be 0 ) ) cot be 0 i.e. d i.e. f ) is defied for ll rel vlues of ecept d Joh s clim is ot true ) )

25 ) Whe t 0, V b) V b 0 ) Whe t, V b log b log 5 b bt ) c) V d) i) Vlue of the cr = $ t ) t 0. log t t log it tes moths ii) Whe t 66 V ) Joh s clim is ot correct

26 Test III - Pper Full Solutio SECTION A: C D b b ) b 5 b 5 b 5 ) f ) ) B Let m, b 8 I, II: b m 8 m ) I d II re ot true III: b m ) 8 ) m B Top View Frot View Side View I: II: III:

27 5 5 D Let ruler cost $, pecil cost $y ) 9 ) 7 6 y y 0.5 y y rulers d pecils cost $8 6 C Method I b 6 5 ) b b b b b b b Method II Let, b ) ) ) ) b b Method III 6 5 ) ) ) b b b b b 7 B y Are 90 cm ) 0 ) 5 8 D ) ) D Scle 500 : :

28 0 C y, where is costt y y z y z, where is costt z z z ) D Let A, b, h be the origil re, bse d height respectively Let A be the ew re A bh A 0% ) b 0% ) h. ). ) bh. bh ).A Percetge chge.a A 00% A % the re icreses by % C the curve opes dowwrd 0 the is of symmetry lies o the R.S. of the y-is b 0 i.e. b 0 y-itercept > 0 c 0 C cos si cos cos ) si si ) )cos si cos si )cos si ) ) C Rtio :[ ) ] :[ ) ) ] : 6 : 98 6

29 5 A Let R d r be the rdius of the sector d the bse rdius of the coe respectively R r 60 r si R r Rsi R R si 60 si 60 6 A Let P ) P) ) 0 ) 0 SECTION B: 7 D log log 0. log log 5 log 5 5 log log log log 0. 8 C Method I y 7 ) y ttis its miimum whe its deomitor ttis its mimum, i.e. the miimum vlue of y is Method II y ) ) ) y the miimum vlue of y is 7 9 D 000 ) 0 ) P 0 ) ) 80 0 ) Q 0 ) Prime umbers betwee P d Q :, 7, 5, 59, 6, 67, 7, 7, 79 there re 9 prime umbers betwee P d Q 7

30 8 0 D ) ) C y y D The lrgest gle is opposite to the logest side ) ) 6 5 cos C B 7 6 r r r r r r r r r r r

is continuous at x 2 and g(x) 2. Oil spilled from a ruptured tanker spreads in a circle whose area increases at a

is continuous at x 2 and g(x) 2. Oil spilled from a ruptured tanker spreads in a circle whose area increases at a . Cosider two fuctios f () d g () defied o itervl I cotiig. f () is cotiuous t d g() is discotiuous t. Which of the followig is true bout fuctios f g d f g, the sum d the product of f d g, respectively?