FORM 5 MATH PAPER 2

8/18/2019 FORM 5 MATH PAPER 2

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Section A

[52 marks]

Answer all questions in this section

1 Using factorisation, solve the following quadratic equation :

h2 = 9( h – 1)

2

[4 marks]

Answer :

2 Calculate the value of v dan w taht satisfy the following simultaneous linear equations :

2 1v w+ = and 4 1!v w− = −

[4 marks]

Answer :

3 "enn #iagram in diagram 1$a% and 1$&% shows set ξ, P , Q dan R ' (n diagram )rovided in the

answer s)ances' shade

$a% %$ ′∪∩ RQ P $&% %$ RQ P ∩∩′ Jawapan :

$a% $&%

[ marks]

ξ P

R

Q P

ξ

P

R

Q P

#iagram 1$a%

#iagram 1$&%



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4 *he diagram shows a solid formed &y +oining a cone with hemisfere

*he height of the con is cm, #iameter of the cone and the hemisfere is - cm

#iagram 2

Using,

22=π ,Calculate the volume, in cm , of the solid

.nswer :

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5'

/$ 0, %

(n #iagram 2, is the origin' traight line 3 is )arallel to straight line /' *he equation of

straight line 3 is 26 7 y 8 4

*he )oints and lie on the y0 a6is

9ind

$a% *he equation of straight line /

$&% *he x interce)t of the straight line /

[5 marks]

Jawapan : $a%

$&%

-% $a% / is a 2 ; 2 matri6 where / 4 1 <

2 5 < 1

= ÷ ÷

, find the matri6 of /

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6

y

3



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$&% =rite the following simultaneous linear equations as matri6 equation :

4 5

2 5 !

p q

p q

+ =

+ =

>ence, using matri6 method, calculate the value of ) and q

[- marks]

Answer :

$a%

$&%

'

' #iagram 4 shows the s)eed0time gra)h of a )article for a )eriod of 1! seconds

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a% tate the the length time, in seconds, the )article moves with uniform s)eed

&% Calculate the rate of change, in ms02, in the first - seconds

c% Calculate the value of u, if the average s)eed of the )article in the last 12 seconds

[5marks]

.nswer :

a%

&%

c%

! #iagram 5 shows the distance time of the +ourney of a car from ?ulau ?inang to @ohor Aahru over a

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*ime$s%

)eed$msBs%

u

4

1< 1!

22

#iagram 4

-

5



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)eriod of t hours' #istance $m%

!<<

<<

*ime $hour%

< 4 2 t

$a% tate the length of time, that car is stationary

$&% tate the distance in m, from @ohor Aahru when the car is stationary

$c% Calculate the car average s)eed, in m h01, during the - first hours

$d% (f the average s)eed of the car for the whole +ourney is !<mBh

Calculate the value of t

[5 marks]

Answer :

$a%

$&%

$c

d%

D'

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#iagram -,shows 3@> with the centre O and a circle 9E> with centre /'9 is the mid)oint of > and 3 8 2!

Using,

22=π , calculate

$a% *he )erimeter in cm of the whole diagram$&% *he area cm of the shaded region

[- marks]

.nswer

a%

&%

1< #iagram shows three num&ered cards in &o6 ? and four num&ered in &o6 F

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#iagram -



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5 15 1D - 15 1

Ao6 ? Ao6 F

. card is )iced at random from each of the &o6es

Ay isting the )ossi&le outcomes, find the )ro&a&ility that

a% a card with a num&er which is a multi)le of 2 or a multi)le of 5 are )iced

&% a card with a num&er which is a multi)le of 2 and a multi)le of 5 are )iced

[ 5 mars ]

.nswer :

a%

&%

11 $a% $ ( % Com)lete the following mathematical sentence in the answer s)ace &y

1< 5

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$ ii % Com)lete the following statement the quantifier GallH or G someH to mae it a true

statement '

000000000000000000000000000 multi)les of are divisi&le &y 2

[2 marks ]$&% Com)lete the conclusion in the following argument

?remise 1 : (f 6 is a factor of 12, then x is a factor of 24

?rermise 2 : 6 is not a factor of 24

Conclution : IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII

[1 marks]

$c% =rite down two im)lications &ased on the following sentence :

m J 15 if and only if m J 5

[2 marks]

Answer :

$a% $ ( %IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII

$ ii % IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII

$&%Conclusion:IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII

$c%(m)lication 1 : IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII

(m)lication 2 :IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII

Section B

[4! marks]

Answer fo! questions from this section.

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12 $a% Com)lete *a&le 1 in the answer s)ace fo the equation

4

x= −

x −4 −2'5 −1 0<'5 <'5 1 2 '2 4

1 1'- ! 0! 04 01'25 01

*a&le 1

[2 marks]

!or this part of the question" use the graph paper provi#e# on page $%. &ou ma use a

f'exi('e curve ru'e

$&% Ay using a scale of 2 cm to 1 unit on the 60a6is and 2 cm e)ada 2 unit on the0ya6is, draw the

gra)h4

x

= − for 4 4 x− ≤ ≤ '

[5 mars]

$ c % 9rom your gra)h, find

$ i% the value of when x 8 1'!

$ii% the value of x when 8 '4

[2 marks]

$a% #raw a suita&le straight line on your gra)h to find all the value of 6 which satisfy the

equation4

x

= − for 4 4 x− ≤ ≤

tate these values of x [ marks] Answer :

$a%

x −4 −2'5 −1 0<'5 <'5 1 2 '2 4

1 1'- ! 0! 04 01'25 01

*a&le 1

$c% $ i % y 8 IIIIIIIIIIIIIIIIIIII

$ ii% x 8 IIIIIIIIIIIIIIIIIIIII

$d% 6 8 IIIIIIIIIIIIIIIIIIIIIII, IIIIIIIIIIIIIIIIIIIIIII

13 #iagram shows rectangle )" *" ! dan +'

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$a% *ransformation " is a reflection a&out line x 8 and transformation # is clocwise rotation

of D<< a&out the )oint $4, 4%' tate the coordinate of image of )oint K under

,i- *ransformation "

,ii- *ransformation "#

[ marks]

$(% Kectangle ) is the image of rectangle of 9 under transformation $ and rectangle * is the

image of rectangle # under transformation ='

#escri&e in full

$i% *ransformation $

$ii% . single transformation which equavalent to transformation %$&

[5 marks]

$c% Kectangle + is the image of rectangle 9 under an enlargement

$i% tate the centre coordinate of the centre of the enlargement

$ii% Eiven the area of rectangle ! is unit2, calculate the area of rectangle of +&

[4 marks]

Answer :

$a% $i%

$ii%

$(% $i%

$ii%

$c% $i%

$ii

14 *he #ata in diagram ! shows the donations, in K/, of families to their childrenLs school welfared

fund'

4< 24 1 < 22 2- 5 1D

2 2! D 4 D 2!

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02 01 O 1 2 4 5 - ! x

)

*

!

+

K

K.@.>

5

2

1

-

4

•



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2 5 45 21 ! 22 2 5

< 4 1 4< 2 14 2!

2< 2 2D 2- 2 22 ! 44

$a% Using data in diagram ! and a class interval of K/ 5 , com)lete the ta&le 2 in the answer s)ace

[4 marks]

Answer :

#onations $K/% frequency Cumulative frequency

11 0 15

1- 2<

*a&le 2

$&% !or this part of the questions" use the graph paper provi#e#

Ay using a scale of 2 cm to K/ 5 on the x0 a6is and 2 cm to 5 families on the 0a6is, draw

an ogive &ased on the data

[- marks]

$ c % 9rom your ogive in $&%

$ i % 9ind the third quartile

$ii % hence, e6)lain &riefly the meaning of the third quartile

Answer :

$ c %

$i%

$ii%

1' $a% Com)lete *a&le 1 in the answer s)ace fo the equation- x= −

x − −2'5 −2 01 < 1 2 2'5

21'- 14 - 5 0D'-

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*a&le 1

[2 marks]

!or this part of the question" use the graph paper provi#e# on page $%. &ou ma use a

f'exi('e curve ru'e$c% Ay using a scale of 2 cm to 1 unit on the 60a6is and 2 cm e)ada 5 unit on the0ya6is, draw the

gra)h- x= − &agi nilai x dalam +ulat 2'5 x− ≤ ≤ '

[4 mars]

$ c % 9rom your gra)h, find

$ i% the value of when x 8 1'5

$ii% the value of x when 8 1<

[2 marks]

$&% #raw a suita&le straight line on your gra)h to find all the value of 6 which satisfy the

equation ! - < x x− − = for 2'5 x− ≤ ≤ '

tate these values of x [4 marks]

Answer :

$a%

x − −2'5 −2 01 < 1 2 2'5

21'- 14 - 5 0D'-

*a&le 1

$c% $ i % y 8 IIIIIIIIIIIIIIIIIIII

$ ii% x 8 IIIIIIIIIIIIIIIIIIIII

$d% 6 8 IIIIIIIIIIIIIIIIIIIIIIIII ,IIIIIIIIIIIIIIIIIIIIIIIII

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FORM 5 MATH PAPER 2