addmaths revision exercise spm 2015

7/24/2019 AddMaths Revision Exercise SPM 2015

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AddMaths Revision Exercise Paper 2 1

Revision Exercise, AddMaths SPM 2015[cikgubid/AMF5/W46/Fri/KYRHG]

Nov.6, 2015

1) Diagram 1 shows a regionPQRSTUVthat is enclosed by wire fence of length 34 m.

Diagram 1

If the area of the enclosed region is 38 m2, find the integer al!e ofxand ofy.

2) " #!adratic f!nctionfis defined by

3$4)% 22

+++= mmxxxf

.

%a) &'(ressf%x) in the form

qpx ++ 2)%

, wherepand qare constants.

%b) he straight linex* + is the a'is of symmetry of the gra(h of the #!adratic f!nctionf%x).

%i) ind the al!e of m.

%ii) -etch the gra(h of the #!adratic f!nctionf%x) and hence, state the range off%x).

3) %a) ind the ac!te angles!ch that sin, 2cos, and 2 sin are three consec!tie terms

of an arithmetic (rogression.

%b) /ien that

),2%log 81 +k

2

1

and 1 are three consec!tie terms of a geometric (rogression, find

the al!e of k.

4) Diagram 2 shows a circlePQRTwith centre O, of radi!s 1$ cm.

Diagram 2

/ien that OPQRis a rhomb!s, find

%a) the al!e of

, in radians,

cikgubid Tuition,Kuching, SPM 2015


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%b) the length of the ma0or arcPTR,

%c) the area of the shaded region.

) %a) roe that

xxcotcosec21sec

1

1sec

1=

+

+

.

%b) -ole the e#!ation

)3$cos%3)3$cos% oo

xx +=

for

oox 3+$$

.

+) Diagram 3 shows a solid which consists of a cylinder fi'ed on to( of a rectang!lar bloc. he bloc

has a s#!are base of side 2xcm and a height ofxcm. he cylinder has a radi!s ofxcm and a height of

hcm. he total ol!me of the solid is 21+ cm3.

Diagram 3

%a) &'(ress hin terms of

andx.

%b) -how that the total s!rface area,Acm2, of the solid is gien by

xxA

4328

2+=

.

%c) ind the al!e ofxfor whichAis a minim!m. alc!late the minim!m al!e ofA.

) %a) Diagram 4 shows a right (rism with

ABC

as its cross5section. he (er(endic!lar

distance of (ointAto the straight lineBCremains constant at 1$ cm. It is gien that BC*xcm

and C* xcm.

Diagram 4



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Ifxincreases at the rate of $.$2 cm s61, calc!late the rate of increase of the ol!me of the (rism

at the instantx* .



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%b) Diagram shows the c!re

13

+= xy

Diagram 5

ind

%i) the coordinates of (ointA,

%ii) the area of the shaded region.

8) %a) 7r. ham is a golf (layer. he (robability that he s!ccessf!lly hit a ball into a hole is

p.

%i) 7r. ham maes $ hits. ind the al!es ofpif the ariance of the n!mber of s!ccesses is

8.

%ii) 7r. ham maes hits. sing the larger al!e of pin %a), calc!late the (robability that

the n!mber of s!ccesses is at least 3.

%b) he s(eeds of ehicles on a highway are normally distrib!ted with a mean of 1$$ m9ho!r and

a standard deiation of

m9ho!r.

%i) 3$.8: of the ehicles obsered hae s(eeds greater than 1$ m9ho!r. ind the al!e of

.

%ii) sing the al!e of

in %b)%i), calc!late the (robability that a ehicle chosen at random

traels at a s(eed of between ;+ m9ho!r and 1$8 m9ho!r.

;) " ty(e of (erf!me is (rod!ced by mi'ing 3 ty(es of materials,P, QandRin the ratio 2 < 3 < . able 1

shows the (rice inde' of the materials for the year 2$$3 based on 2$$1.

!"#$%&"' P%&($ &)*$x fo% 200+ "-$* o) 2001

P 1$$

Q 11$

R m

a!"e 1

%a) If the com(osite inde' of the raw materials for the year 2$$3 based on the year 2$$1 is 118, find

the al!e of m.

%b) he (ercentage of increase of the com(osite inde' of the materials from the year 2$$3 to the

year 2$$ is e#!al to the (ercentage of increase of the com(osite inde' from the year 2$$1 to

the year 2$$3. alc!late

%i) he com(osite inde' of the materials for the year 2$$ based on the year 2$$1,

%ii) he (rice of a bottle of (erf!me in the year 2$$ if its corres(onding (rice in the year2$$1 was =73$$.

%c) If the (rice inde' of material Qfor the year 2$$2 based on the year 2$$1 is 11, calc!late the

(rice inde' of material Qfor the year 2$$3 based on the year 2$$2.



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AddMaths Revision Exercise Paper 2 #

Ans 2m)26 3m2> 3$

%b)%i) m* 63 %ii)

3)% xf

3) %a)* 3.13o

%b) 1

4) %a)

3

2

rad %b) 41.8; cm %c) 18.12 cm2

) %b) 3.;$o? 23.;$o

+) %a)

2

3421+

x

xh

=

%c)21+

) %a) cm3s61%b)%i) %$, 1) %ii)

4

318

!nits2

8) %a)%i)

19

4

%ii)$.;;3 %b)%i)1$ %ii)$.443;) %a)13$ %b)%i)13;.24 %ii)=741.2 %c)1$4.+


addmaths revision exercise spm 2015

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