exam paper - core (by topic)(10).pdf
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7/27/2019 Exam Paper - Core (By Topic)(10).pdf
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KMOB LMOB HI^CM@J MG QEAMOHJTY EHUAJXIMO E[J@IOJXIMO
@JXKE@JXIAQAm`pucsmry ^jrt
Exj` ^jper (Dy Xmpia)Zuestimo-Joswer Dmml
Xi`e jccmweh6 : kmur 1> `ioutes
IOQXTUAXIMOQ
:. Rrite ymur Ajohihjte Oj`e 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 `ust de acejrcy skmwo.
5. Uocess mtkerwise speaigieh, ou`eriajc joswers skmuch de eitker exjat mr amrreat tm 1 siboigiajot
gibures.
7. Xke hijbrj`s io tkis pjper jre omt oeaessjricy hrjwo tm sajce.
XM^IAQ
:. 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 Oj`e Exj` Hjte
7/27/2019 Exam Paper - Core (By Topic)(10).pdf
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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>
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KLHQE Exj` ̂ jper @JXKE@JXIAQ (Amre) Dy KEOTY CEUOB
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>
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1. Ig 4 x4+(l +1) x+(4 l ∔4)0> kjs equjc rejc rmmt gmr sm`e rejc amostjot l , gioh tke vjcues
mg l . (8 `jrls)
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KLHQE Exj` ̂ jper @JXKE@JXIAQ (Amre) Dy KEOTY CEUOB
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 `jxi`u` ioteber l gmuoh io pjrt j), smcve tke equjtimo x4+7 x+(4l ∔:)0> .
(1 `jrls)
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5. Ig x4+(4 l +:) x+l
4?> , gioh tke rjobe mg l . (5 `jrls)
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KLHQE Exj` ̂ jper @JXKE@JXIAQ (Amre) Dy KEOTY CEUOB
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
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KLHQE Exj` ̂ jper @JXKE@JXIAQ (Amre) Dy KEOTY CEUOB
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)
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;. Ig 4κ ∔: joh 4 δ ∔: jre rmmts mg x4+:> x∔;0> , gioh tke vjcues mg κ +δ joh κ δ .
(5 `jrls)
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KLHQE Exj` ̂ jper @JXKE@JXIAQ (Amre) Dy KEOTY CEUOB
9. Xke rmmts mg tke equjtimo x4+l x+:0> jre io tke rjtim 8 6: . Gioh tke vjcue mg l .
(5 `jrls)
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:>. Ig moe rmmt mg tke equjtimo 4 x4+5 x+o0> is tke reaiprmajc mg jomtker moe, gioh tke vjcue mg
o . (1 `jrls)
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KLHQE Exj` ̂ jper @JXKE@JXIAQ (Amre) Dy KEOTY CEUOB
::. 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 si`icjr 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)
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KLHQE Exj` ̂ jper @JXKE@JXIAQ (Amre) Dy KEOTY CEUOB
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KLHQE Exj` ̂ jper @JXKE@JXIAQ (Amre) Dy KEOTY CEUOB
:4. Qi`pcigy tke gmccmwiob expressimos. (:4 `jrls)
j) i(4∔1 i)(:+i)
d) 44∔1 i
+ 44+1i
a):4
∖ 1∔i
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KLHQE Exj` ̂ jper @JXKE@JXIAQ (Amre) Dy KEOTY CEUOB
: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)
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: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)
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KLHQE Exj` ̂ jper @JXKE@JXIAQ (Amre) Dy KEOTY CEUOB
: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)
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KLHQE Exj` ̂ jper @JXKE@JXIAQ (Amre) Dy KEOTY CEUOB
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
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KLHQE Exj` ̂ jper @JXKE@JXIAQ (Amre) Dy KEOTY CEUOB
4>. Rkiak mg tke gmccmwiob stjte`eots 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>
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KLHQE Exj` ̂ jper @JXKE@JXIAQ (Amre) Dy KEOTY CEUOB
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`
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KLHQE Exj` ̂ jper @JXKE@JXIAQ (Amre) Dy KEOTY CEUOB
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>
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KLHQE Exj` ̂ jper @JXKE@JXIAQ (Amre) Dy KEOTY CEUOB
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
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KLHQE Exj` ̂ jper @JXKE@JXIAQ (Amre) Dy KEOTY CEUOB
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> .
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KLHQE Exj` ̂ jper @JXKE@JXIAQ (Amre) Dy KEOTY CEUOB
;. 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 .
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KLHQE Exj` ̂ jper @JXKE@JXIAQ (Amre) Dy KEOTY CEUOB
::. 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
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KLHQE Exj` ̂ jper @JXKE@JXIAQ (Amre) Dy KEOTY CEUOB
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> -