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Que!"#$ 2

(a) (i) 3ifferentiate 6 x y =  with reference to  x   ( +ar!s)

(ii) 3ifferentiate ( )  .

+=   x x y  with reference to  x   ( +ar!s)

() 4i"en the qua#ratic equation ,5,6)(   −+−=   x x x  f  

(i) se the 'etho# of co'p%etin& the square0 e/press )( x  f   in the for' of

q p xa   ++  )(  where  pa0 an# q are constants. ( +ar!s)

  (ii) Fin# the "erte/ of )( x  f   fro' part (i) an# state whether its 'a/i'u' or 

  'ini'u' ( +ar!s) 

(iii) S!etch a &raph of )( x  f   an# show the − x intercepts0 − y intercepts an#

  "erte/ c%ear%y. ( +ar!s)

 

(i") State the ran&e of )( x  f   for a%% "a%ues of  x   (, +ar!)

(c) Fin# the fo%%owin& #efinite inte&ra%s:

(i) ∫   −

5.

,

,(   dx x (

+ar!s)

(ii) ∫    −*

  ,

,dx

 x(

+ar!s)

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Que!"#$ %

(a) 4i"en that [ ]0

,

−−=

−

=   Y  X  an#

−−−

=,,

,,

 Z 

(i)  X  (, +ar!)

(ii)  XY   ( +ar!s)

(iii)  Z  XY   T 

)(   + (6 +ar!s)

() Fin# the in"erse of the 'atri/ A &i"en e%ow y appropriate row operations on[ ].7  I  A   Show that  I  A A   =

−,

 

=

 A

(5 +ar!s)

(c) se the 'etho# of in"erse 'atri/ to so%"e the syste' of %inear equations:

  5   =+   y x  an# -   =+   y x   (5 +ar!s)

Que!"#$ &

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(a) Set { }6,,-6= X 

  Set { },,5,85=Y 

Set { },-.= Z 

(i) 3raw a Venn #ia&ra' to represent the ao"e sets ( +ar!s)

(ii) Fin# )(   Y  X n   ∪ ( +ar!s)

(iii) Fin# )(   Y  X n   ∩ ( +ar!s)

(i") Fin# Y  X    ′∪ ( +ar!s)

(") Fin# the e%e'ents Y  X    ′∪′ ( +ar!s)

() Fro' a co''ittee of , peop%e0

(i) In how 'any ways can we choose a chairperson0 a "ice9chairperson0

a secretary an# a treasurer0 assu'in& that one person cannot ho%#'ore than one position ( +ar!s)

(ii) In how 'any ways can we choose a suco''ittee of 1 peop%e

( +ar!s)

(c) A co'pany has 1 'a%e an# 5 fe'a%e officers. An a#9hoc co''ittee is to efor'e#. In how 'any ways can a 59officer co''ittee e for'e# so that it is

co'pose# of

(i) Any 5 officers ( +ar!s)

(ii) 'a%e officers an# fe'a%e officers ( +ar!s)

Que!"#$ '

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(a) In#icate which of the fo%%owin& "aria%es is quantitati"e an# qua%itati"e.

(i) The nu'er of fans for ;ustin <ieer (, +ar!s)

(ii) =u'er of 'otorcyc%es in +r. ;osephs house (, +ar!)

(iii) Ti'e to co''ute fro' ho'e to co%%e&e (, +ar!)

() The #ata e%ow shows the 'ar!s otaine# in a +athe'atics test y a &roup of

 pupi%s.

8 6 1 , 5 58 5- 1,

65 6* 55 5* 5 5 6 *

6, 5, 5 6 5- 5 5 6

6 55 68 6- 5 5 5* 655 58 5- * , 5 6-

(i) sin& the #ata ao"e an# a c%ass inter"a% of 5 'ar!s0 co'p%ete the ta%e e%ow.

 

+ar! +i#point Frequency

89

59* 1

( +ar!s) 

(ii) <ase# on the ta%e ao"e ca%cu%ate the 'ean 'ar! for the +athe'atics test

an# &i"e your answer correct to #eci'a% p%aces.

( +ar!s)

(iii) sin& a sca%e of c' to 5 'ar!s on the hori$onta% a/is an# c' to , pupi% onthe "ertica% a/is0 #raw a histo&ra' for the #ata.

( +ar!s)

(c) >rite the fo%%owin& in ter's of scientific notation  (i) 08880888 (, +ar!)

  (ii) 8.888 (, +ar!)

(c) ?ationa%i$e the #eno'inator of the fo%%owin& e/pressions.

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(i)1

*  ( +ar!s)

(ii)5-

6

−( +ar!s)

Que!"#$

(a) A research was 'a#e to recor# ti'e for ,- e'p%oyees to co'p%ete a particu%ar wor! 

  an# the resu%ts are recor#e# in the ta%e e%ow

Ti'e @8 89 59* 5895 5595* 6896 6596* 1891 1

 =o. of

e'p%oyee

8 6 , 8 * 8

(i) Bopy an# co'p%ete the ta%e as fo%%ows:

 

Ti'e Frequency0   f   +i#9point0  x   fx     fx

@ 8 8

 

(* +ar!s)

(ii) Fin# the 'ean of the #ata. ( +ar!s)

(iii) Fin# the 'e#ian of #ata usin& the 'e#ian for'u%a ( +ar!s)

(i") Fin# the 'o#e of #ata usin& the 'o#e for'u%a ( +ar!s)

(") Fin# the stan#ar# #e"iation of the #ata ( +ar!s)

() 4i"en y0 ,0,0,8 an# - has een arran&e# in #escen#in& or#er. If the 'ean an#'e#ian is &i"en y C'in D 'e#ian ,0 fin# y.

( +ar!s)