Tap Maths Paper 2 Set 4[1]

8/11/2019 Tap Maths Paper 2 Set 4[1]

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Name Index No..../

121/2

MATHEMATICS Candidates Signature

Paper 2

MA! A"#"ST 2$1% &ate..

2 ' Hours

(en)a Certi*i+ate o* Se+ondar) S+,oo- Tria- Examination

MATHEMATICS

Paper 2

2 ' Hours

Instru+tions to Candidates1. Write your name and index number in the spaces provided above.

2. Sign and write the date of examination in the spaces provided above.

3. This paper consist TWOsections: sectionIand sectionII.

4. nswer a!! the "uestions in sectionIandfive"uestions from sectionII.

#. !! answers and wor$ing must be written on the "uestion paper in the spaces provided

be!ow each "uestion.

%. Show all the steps in your calculations, giving your answers at each stage in the spaces

below each question.

&. Non-programmable si!ent ca!cu!ators and N!" mathematica! tab!es may be used'except where stated otherwise.

(. "an#i#ates shoul# chec$ the question paper to ascertain that all the pages are printe#

as in#icate# an# that no questions are missing.

or Examiner use on-).

Se+tion I

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Total

Se+tion II

17 18 19 20 21 22 23 24 Total

TAP T0IA %

T,is paper +onsists o* 1 printed pages

2014 Tap Education Consultancy Ltd

P.3. 4ox 21562$$%$$7 Ce-- p,one8 $6212%956/ $6:651%$27 Emai-8 gradeplusconceptg!ail"co!" Turn o#er

#rand

Tota-
mailto:[email protected]:[email protected]


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SECTI3N 1 ;50 !ar$s%

nswer%&&the "uestions in this section in the space provided:

1. &i#en t'at () 4 is a root o* (2+$(,20)0" -ind t'e #alue o* $ and t'us ot'er roots"

.3 !ar$s%

2. /* is an acute angle *ind t'e #alue o* Cos in t'e euation 'ence *ind

4 in2,5 Cos +2)0 .3 !ar$s%

:. ationalie t'e *olloing lea#ing your anser in t'e si!pli*ied surd *or!" .2 !ar$s%1+ Tan120

1+ Tan 60



3/16

%. -ind t'e !atri( o* trans*or!ation t'at ould !ap triangle C it' #ertices at .,

52% .,32% and

C.,35% onto triangle 11C1 it' #ertices at 1.,5,2% 1.,3,2% and C1.,3,5%"

.4 !ar$s%


4/16

6" T'e ;elo s'os t'e !ar$s o;tained ;y -or! 3 students o* e'e!a econdary

c'ool in


5/16

9.-ind t'e distance in $ilo!eters ;eteen places .40o25o@% and .40o120oE% along t'e

parallel o* latitude.Ta$e radius o* t'e eart' to ;e 6370$! and A ) 22B7% correct to 2

d"p" .2 !ar$s%

5" co**ee trader ;uys to grades o* co**ee at s'" 80 and s'" 100 per par$et " -ind t'e ratio at

'ic' s'e s'ould !i( t'e! so t'at ;y selling t'e !i(ture at a s'" 120 a pro*it o* 25=

is realied" .3 !ar$s%

1$" se a calculator to or$ out t'e *olloing gi#ing your anser correct to 3 signi*icance

*igures

.2 !ar$s%



6/16


7/16

1:" /n t'e *igure ;elo T is a tangent to t'e circle CT" ) T and angle T)82o"

Calculate angle CT gi#ing reasons .3 !ar$s%

1%" T'e displace!ent !etres o* a particle *ro! a *i(ed point H a*ter ti!e t seconds is gi#en

;y ) 4t3, 3t2+2" *ind its #elocity 'en t ) 2seconds .3 !ar$s%

1


8/16

1. T'ree uantities Fand are suc' t'at #aries Iointly it' F and t'e suare o* "

i* ) 900 'en F ) 20 and ) 3

-ind .i% an euation connecting F and .2 !ar$s%

.ii% t'e #alue o* 'en F ) 10 and ) 800 .2 !ar$s%

SECTI3N II .50 !ar$s%

nswer anyfive"uestions in this section in the spaces provided.

16. .a% Co!plete t'e ta;le ;elo ;y *illing in t'e ;lan$ spaces *or t'e *unction y)sin.( + 30%

and y)cos J ( and dra t'eir grap's on t'e sa!e a(es .6 !ar$s%

Ko

0 30 60 90 120 150 180 210y)in .( + 30% 0"5 1 0"5 ,0"87

y) cos J ( 1"00 0"71 0

.;% se your grap' to sol#e :

.i% sin.( + 30% cos J ( ) 0 .1 !ar$%



9/16

.ii% sin.( + 30% ) 0 .1 !ar$%

.iii% cos J ( ) ,0"25 .1 !ar$%

.c% tate t'e a!plitude and period o* t'e *unction y ) cos J ( .1 !ar$%

19.


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.c% /* a*ter 4 years t'e tractor is sold t'roug' a ;ro$er 'o c'arge 5=co!!ission *ind t'e a!ount recei#ed ;y


11/16

.a% erite t'e euation in t'e *or! o* y)!( + c .1 !ar$%

.;% Dra t'e straig't line grap' on t'e grid pro#ided .4 !ar$s%

.c% -ind t'e #alue o* and F " .3 !ar$s%

.d% @rite don t'e euation connecting and G .1 !ar$%

.e% -ind t'e resistance at 0"5 !Bs .1 !ar$%



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21. /n t'e *igure ;elo CD is a trapeiu! is parallel to DC diagonals C and D

intersect at K and &C)2A4" A4) a &A)d A=)$AC and &=)'&4 'ere '

and $ are constants

.a% -ind in ter!s o* aand d :

.i% 4C .2 !ar$s%

.ii% A= .2 !ar$s%

.iii% &= .1 !ar$%

.;% Deter!ine t'e #alues o* ' and $ .5 !ar$s%


a

d K

D

CD


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22" elo is a s$etc' o* area ;ounded ;y t'e cur#e y ) (2+ 3 and t'e line ( ) ,2 ()4 and

y ) 0

.a% Esti!ate t'e area o* t'e s'aded region using 6 strips ;y :

.i% Trapeoidal rule .4 !ar$s%

.ii% /ntegration .3 !ar$s%


4,2

y ) (2+ 3


14/16

.;% -ind t'e percentage error in t'e area *or t'e appro(i!ation in a .i% a;o#e i* a .ii% is

ta$en as t'e e(act area .3 !ar$s%

2:. T'e cur#e y )3(2 , 6( + 6 passes t'roug' t'e point . 23%

.a% Deter!ine t'e gradient *unction o* t'e cur#e" .1 !ar$%

.;% -ind t'e co,ordinates o* t'e turning point o* t'e cur#e" .3 !ar$s%

.c% Deter!ine 'et'er t'e point is a !ini!a or a !a(i!a" .1 !ar$%



15/16

.d% -ind t'e euation o* t'e.i% Tangent to t'e cur#e at " .3 !ar$s%

.ii% >or!al to t'e cur#e at " .2 !ar$s%

2%. ;ag contains 5 red 6 ;lue and 3 green !ar;le o* si!ilar s'ape and sie" !ar;le is

pic$ed at rando! it' out replace!ent and t'e colour noted second !ar;le is t'e

pic$ed"

.i% Dra a tree diagra! to represent t'e in*or!ation a;o#e" .2 !ar$s%

?ence *ind t'e pro;a;ility t'at

.ii% T'e *irst to !ar;les are ;ot' ed" .1 !ar$%



16/16

.iii% Hnly one o* t'e *irst to !ar;les pic$ed is ;lue" .3 !ar$s%

.i#% t leastone o* t'e *irst to !ar;les pic$ed is green" .3 !ar$s%

.#% t'e *irst pic$ed is eit'er green or ;lue" .1 !ar$%

THIS IS THE AST P0INTE& PA#E.


Tap Maths Paper 2 Set 4[1]

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