Exam Paper - Core (By Topic)(10).pdf

7/27/2019 Exam Paper - Core (By Topic)(10).pdf

http://slidepdf.com/reader/full/exam-paper-core-by-topic10pdf 1/21

KMOB LMOB HI^CM@J MG QEAMOHJTY EHUAJXIMO E[J@IOJXIMO

@JXKE@JXIAQAm`pucsmry ^jrt

Exj` ^jper (Dy Xmpia)Zuestimo-Joswer Dmml

Xiè jccmweh6 : kmur 1> ìoutes

IOQXTUAXIMOQ

:. Rrite ymur Ajohihjte Ojè io tke spjae prmviheh mo tke amver pjbe.4. Xkis pjper amosists mg XRM seatimos, J joh D. Qeatimo J ajrries ::> `jrls joh seatimo D

ajrries :> `jrls

1. Jtte`pt JCC questimos io tkis pjper. Rrite ymur joswers io tke spjaes prmviheh io tkis

Zuestimo-Joswer Dmml.

8. Uocess mtkerwise speaigieh, jcc wmrliob ùst de acejrcy skmwo.

5. Uocess mtkerwise speaigieh, ouèriajc joswers skmuch de eitker exjat mr amrreat tm 1 siboigiajot

gibures.

7. Xke hijbrj`s io tkis pjper jre omt oeaessjricy hrjwo tm sajce.

XMÎAQ

:. Zujhrjtia Equjtimos witk moe uolomwo4. Ou`der Qyste`

Zuestimo Om. @jrls

: / :5

4 ‑ 1 / ::

8 ‑ 5 / ::

7 / :4

2 ‑ ; / ::

9 ‑ :> / ;

:: / ::

:4 / :4:1 ‑ :8 / :4

:5 / 2

:7 ‑ 45 / :>

Xmtjc /:4>

Ajohihjte Ojè Exj` Hjte



KLHQE Exj` ̂ jper @JXKE@JXIAQ (Amre) Dy KEOTY CEUOB

Qeatimo J ‑ ::> `jrls

:. Qmcve tke gmccmwiob qujhrjtia equjtimos. (:5 ̀ jrls)

j) x ( x∔4)0>

d) (4 x∔1)4045

a) 8 x4∔8 x0∔:

h) 7 x4+2 x+40>

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

- ^jbe : -




4. Usiob tke ̀ etkmh mg am`pcetiob squjre, smcve tke gmccmwiob qujhrjtia equjtimos6 (2 `jrls)

j) x4∔4 x∔:0>

d) 4 x4

∔; x+10>

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

1. Ig 4 x4+(l +1) x+(4 l ∔4)0> kjs equjc rejc rmmt gmr smè rejc amostjot l , gioh tke vjcues

mg l . (8 `jrls)

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

- ^jbe 4 -




8. j) Gioh tke rjobe mg l suak tkjt tke equjtimo x4+7 x+(4l ∔:)0> kjs twm histioat rejc

rmmts. (1 `jrls)

d) Xjle tke `jxiù` ioteber l gmuoh io pjrt j), smcve tke equjtimo x4+7 x+(4l ∔:)0> .

(1 `jrls)

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

5. Ig x4+(4 l +:) x+l

4?> , gioh tke rjobe mg l . (5 `jrls)

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

- ^jbe 1 -




7. Ig κ joh δ jre rmmts mg x4∔; x∔70> , gioh tke vjcues mg tke gmccmwiobs. (:4 `jrls)

j) (κ +1)(δ +1)

d) κ 1+δ 1

a) κ 4+; δ ∔7

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

- ^jbe 8 -




2. Biveo tkjt κ joh δ de rmmts mg tke qujhrjtia equjtimo (l ∔:) x4∔l x+:0> joh l ?> .

Ig κ

4

+δ

4

0

5

8 ,

j) gioh tke vjcue mg l < (1 `jrls)

d) keoae, gmr` j qujhrjtia equjtimo witk rmmts κ 4 joh δ

4 . (1 `jrls)

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

;. Ig 4κ ∔: joh 4 δ ∔: jre rmmts mg x4+:> x∔;0> , gioh tke vjcues mg κ +δ joh κ δ .

(5 `jrls)

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

- ^jbe 5 -




9. Xke rmmts mg tke equjtimo x4+l x+:0> jre io tke rjtim 8 6: . Gioh tke vjcue mg l .

(5 `jrls)

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

:>. Ig moe rmmt mg tke equjtimo 4 x4+5 x+o0> is tke reaiprmajc mg jomtker moe, gioh tke vjcue mg

o . (1 `jrls)

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

- ^jbe 7 -




::. Io tke gibure, ^ZTQ is j reatjobce iosarideh io jo ismsaeces trijobce JDA , wkere

JD0 JA 048a` joh ∮ DJA 09>m

.

j) Ig D^ 0AZ0 x a` , dy amrrespmohiob sihes

mg siìcjr trijobces, express tke gmccmwiobs io

ter`s mg x . (5 `jrls)

i) ^Z

ii) ^Q

iii) Xke jrej mg ^ZTQ

d) Ig tke jrej mg ^ZTQ is ;>a`4 , gioh tke vjcue(s) mg x . (1 `jrls)

a) Ajo tke jrej mg ^ZTQ de :7>a`4 = Expcjio driegcy. (1 `jrls)

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

- ^jbe 2 -




..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

- ^jbe ; -




:4. Qi`pcigy tke gmccmwiob expressimos. (:4 `jrls)

j) i(4∔1 i)(:+i)

d) 44∔1 i

+ 44+1i

a):4

∖ 1∔i

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

- ^jbe 9 -




:1. j) Amovert >. 4̇ iotm j grjatimo. (1 `jrls)

d) Ig >. 4̇ is j rmmt mg tke equjtimo mg 9 x4+(:∔1l ) x+70> , gioh

i) tke vjcue mg l , joh (4 `jrls)

ii) jomtker rmmts. (4 ̀ jrls)

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

:8. Ig (4+j i)(:∔4 i)0;+d i , wkere j joh d jre rejc ou`ders joh i0∖ ∔: , gioh tke

vjcues mg j joh d . (5 `jrls)

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

- ^jbe :> -




:5. j) Express:

7 i+:io tke gmr` mg j+d i , wkere j joh d jre rejc ou`ders. (1 `jrls)

d) Ig 12

7 i+:is j rmmt mg

x

4

+ p x+q0>, wkere p joh q jre j rejc ou`der, gioh tke

vjcue mg p joh q (8 `jrls)

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

- ^jbe :: -




Qeatimo D ‑ :> `jrls

:7. Ig {κ 4∔8κ ∔70>

δ 4∔8 δ ∔70>

, gioh tke vjcue mg κ 4+δ

4 .

J. 8

D. 4;

A. ∔7

H. ∔:4

:2. Qmcve tke equjtimo (4u∔:)(u+5)01(4 u∔:) .

J. u0∔4

D. u01

A. u0∔4 mr u0:

4

H. u01 mr u0:

4

:;. Xke qujhrjtia equjtimo 4 x4+ x∔:50> kjs

J. om rejc rmmts.

D. 4 equjc rjtimojc rmmts.

A. 4 histioat rjtimojc rmmts.

H. 4 histioat irrjtimojc rmmts.

:9. Qi`pcigy ∔∖ 17+∖ ∔;Ò∖ ∔:; .

J. :;

D. ∔:;

A. ∔7∔:4 i

H. ∔7+:4 i

- ^jbe :4 -




4>. Rkiak mg tke gmccmwiob stjteèots is gjcse=

J. Xke su` mg twm rjtimojc ou`ders `jy de jo irrjtimojc ou`der.

D. Xke su` mg twm irrjtimojc ou`ders `jy de j rjtimojc ou`der.

A. Xke prmhuat mg twm irrjtimojc ou`ders `jy de j rjtimojc ou`der.

H. Xke squjre mg jo irrjtimojc ou`der ̀ jy de jo irrjtimojc ou`der.

4:. Ig κ joh δ jre rmmts mg tke equjtimo x4+8 x+40> , tkeo tke rmmts mg tke equjtimo

( x∔:)4+8( x∔:)+40> jre

J. κ ∔: joh δ ∔:

D. κ +: joh δ +:

A. κ joh δ

H. 4κ joh 4 δ

44. i:>490

J. i

D. ∔i

A. :

H. ∔:

41. Gioh j qujhrjtia equjtimo io x witk rmmts 4+∖ 2 joh 4∔∖ 2 .

J. x4∔8 x∔10>

D. x4+8 x∔10>

A. x4∔8 x∔::0>

H. x4+8 x∔::0>

- ^jbe :1 -




48. Ig κ joh δ jre rmmts mg tke equjtimo x4+9 x∔;0> , gioh tke vjcue(s) mg κ ∔ .

J. ∖ ::1

D. ∖ ::1 mr ∔∖ ::1

A. ::

H. :: mr ∔::

45. J 8>a` cmob striob is aut iotm twm pjrts joh gmr` twm squjres. Ig tke jrej mg twm squjre is

7;a`4 , gioh tke ceobtk mg tke cmober pjrt.

J. 8a`

D. :7a`

A. 4>a`

H. 14a`

- ^jbe :8 -




Joswer

:. j) x0> mr x04

d) (4 x∔1)4

045

4 x∔105 mr 4 x∔10∔5

x08 mr x0∔:

a) 8 x4∔8 x0∔:

8 x4∔8 x+:0>

(4 x∔:)40>

x0:

4

h) 7 x4+2 x+40>

(1 x+4)(4 x+:)0>

x0∔

4

1 mr x0∔

:

4

4. j) x4∔4 x∔:0>

( x4∔4 x+:4)∔:∔:

40>

( x∔:)4∔40>

x0:º∖ 4

d) 4 x4∔; x+10>

4( x4∔8 x)+10>

4( x4∔8 x+44)+1∔4(44)0>

4( x∔4)4∔50>

- ^jbe :5 -




x04º∖5

4

x04º∖ :>4

1. Qioae Θ0> ,

(l +1)4∔8(4)(4 l ∔4)0>

l 4+7l +9∔:7l +:70>

l 4∔:> l +450>

(l ∔5)40>

l 05

8. j) Θ?>

74∔8(:)(4 l ∔:)?>

17∔; l +8?>

l 35

d) Xjle l 08 ,

x4+7 x+20>

x0∔7º∖ 74∔8(2)

4

0∔1º∖ 4

5. Qioae Θ3> ,

(4 l +:)4∔8 l 4?>

l 3∔:

8

- ^jbe :7 -




7. κ +δ 0; mr κ δ 0∔7

j) (κ +1)(δ +1)0κ δ +1(κ +δ )+90∔7+1(;)+9042

d) κ 1

+δ 1

0(κ +δ )1

∔1κ δ (κ +δ )0;1

∔1(∔7)(;)0757

a) κ 4+; δ ∔70(;κ +7)+; δ ∔70;(;)078

2. j) κ +δ 0l

l ∔:joh κ δ 0

:

l ∔:

κ 4+δ

405

8

(κ +δ )4∔4 κ δ 058

( l

l ∔:)4

∔4

l ∔:0

5

8

8 l 4∔;(l ∔:)05(l ∔:)4

l 4∔4l ∔10>

l 01 mr l 0∔: (refeateh)

d) Qioae κ +δ 01

4joh κ δ 0

:

4,

κ 4

δ 40

:

8

Xke requireh equjtimo6 x4∔

5

8x+

:

80> .

- ^jbe :2 -




;. Qioae (4κ ∔:)+(4δ ∔:)0∔:> ,

κ +δ 0∔8

joh (4 κ ∔:)(4 δ ∔:)0∔; ,

8 κ δ ∔4 (κ +δ )+:0∔;

κ δ 0∔:2

8

9. Qioae 8κ 40: , κ 0º

:

4.

Rkeo κ 0:4

,

(:

4)4

+l (:

4)+:0>

l 01

4

Rkeo κ 0∔:

4

,

(∔:

4)4

+l (∔ :

4)+:0>

l 0∔1

4

:>. Qioae κ Ò:

κ 0:0o

4, keoae o04 .

- ^jbe :; -




::. j) Qioae DA 048 ∖ 4a` ,

i) ^Z

48∖ 4048∔ x

48

^Z0∖ 4 (48∔ x)a`

ii) ^Q 0∖ 4 x

4a`

iii) Xke jrej mg ^ZTQ 6∖ 4 x

4Ò\∖ 4(48∔ x )P0 x (48∔ x)a`4

d) x (48∔ x )0;>

x4∔48 x+;>0>

x08 mr x04>

a) Amosiher x (48∔ x )0:7> ,

x4∔48 x+:7>0>

Qioae Θ0(∔48)4∔8 (:7>)0∔783> , keoae tke jrej mg ^ZTQ ajo omt de :7>a`4 .

:4. j) i(4∔1 i)(:+i)0i(4+4 i∔1i+1)0:+5 i

d)4

4∔1 i+

4

4+1i04(4+1 i)+4(4∔1 i)(4∔1 i)(4+1 i)

0;

:1

a):4

∖ 1∔i0:4(∖ 1+i )

1+:01∖ 1+1i

:1. j)>. 4̇

0

4

9

d) i) 9(49 )4

+(:∔1l )(49)+70>

l 0∔4;

1

- ^jbe :9 -




ii)4

9δ 0

7

9

δ 01

:8. Qioae (4+j i)(:∔4 i)04∔8 i+j i+4 j

0(4+4j)+(j∔8)i

Keoae, j01 , d0∔: .

:5. j):

7 i+:0

:

:+7 iÒ:∔7 i

:∔7 i0

:

12∔

7

12i

d) Qioae 127 i+:

0:∔7 i is j rmmt mg x4+ p x+q0> , keoae,

p0(:∔7 i)+(:+7 i)04 joh q0(:∔7 i)(:+7 i)012 .

:7. D

:2. A

:;. A

:9. D

4>. J

4:. D

44. J

41. J

48. D

45. H

- ^jbe 4> -

Documents

Exam Paper - Core (By Topic)(10).pdf