59985092 CXC Mathematics May 2010 Paper 2
Transcript of 59985092 CXC Mathematics May 2010 Paper 2
FORM TP 2Dt00g7
CARIBBEAN EXAMINAT IONS COUNC
SECONDARY EDUCATION CERTIF ICA]-EEXAMINATION
MATHEMATICS
Paper 02 General Proficiency
2 hours 10 minutes
l 9 MAY 2010 (a .m. )
INSTRUC IONS TO CANDIDATES
This paper consis ts of TWO sect ions.
- l ' i rcre u lc [ : lGt l I 'c luest ions in Sect ion I anc i TI iRtr [1 quest ions in Sect iun IL
Answer ALL quest ions in Sect ion I . and any,TWO quest ions f iorn Sect ion I I "
Write your answers in the booklet provided.
. \ l l u o rk i r r r : r r . rus t bc c l cu r l v shou ,n .
A l is t o f lbrntu lae is pror ided o l l pase I o f th is booklet .
TIJST CODE OI234O2A
M A Y i J U N E 2 0 I O
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I i .equired Examination Materials
E,lectron ic calculator( ieornetry set( i raph papcr (prov ided)
DO NOT TURN THIS PAGE UNTII , YOT] ARE TOLD TO DO SO.
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Copyright (t ' , 2008 Caribbean Exarninations Counci [email protected] r ights reserved.
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LIST OF FORMULAE
Volume of a prisrn
Volume of cyl inder
Volunre o1'a right pyramid
Circumference
Area of a circle
Area of trapeziurn
Roots of quadratic equations 17'a.r)
then .r
Trigonometric ratios
Area of t r iangle
V : Ah r,vhere I is the area of a cross-sectionlength.
V: nr:h r,vhere r is the radius of the base and h
I
V : = Ah where I is the area of the base and lt.'J
Page 2
and h is the perpendicular
is the perpendicular height .
is the perpendicular height.
Oppos i te
L-:2Tr where l is the radius of the c i rc lc ' .
A: nrrwhere r is the radius of the c i rc le .
A:+Qr + l t) /r u,here o ancl b are the lengths of the paral lel sides and lr is
the perpendicular distance betrveert the par"al lel siclcs"
+ b - r ' + c - ' 0 .
-b t ,li: q*
s i n 0 =
2ct
opposi te s ide
hvpoterrr-rse
^ a d i a c e n t s i d cc o s H -
t a n O -
I l r 1 - r i r 1 . ' 1 1 1 1 - ;
o1-rposite srde
adjacent side
Areir 01'A-- ] b/, u,hcre /r is the length o1'the base and h is the
pcrpcndicuIar hei -uht
. , \ reu t r1 ' \ . 11 j ( - | , r i , s in ( '
S ine ru le
Cosine n-rle
Area of
where . r
Q :
s in I
. r ) : h2
^ A B C - v J ( i
t t * l ' , r c,)/-
h - : L ' *
sin B s in C
+ cr - 2bc cos ,4
Adjacent
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( a )l . Deten-nine
( i )
( i i )
Mrs. Jack bought
( i ) C ' a l c u l a t c
to 2 s igni f rcant f igures
Page 3
( 3 marks)
( 3 marks)
( I nrark )
SECTION I
Ansrver ALL the questions in this section.
Al l work ing must be c lear ly shown.
the EXACT value of :
I
l - ; - - '
a
')1 : x
)-)J
r < t 1 . 8 91 7
giv ing your answer correct
(b) 150 T-shirts fbr $ I 920 f i 'onr
the cost of ONE T-s l r i r t .
The T-shi r ts are so ld at $19.99 each.
C ' l l c L r la te
( i i 1
( i i i )
( i v )
thc an ' r t r r - ln t o f ' lnonc \ \ l l s . ,T r ick r -ccc i r c r i a t te r '
the TOTAL profit macie
the profit made as a percentagethe nearest rvhole number.
: c i l i ng , . \LL o f the T -sh i r t s( I m a r k )
( I m a r k )
of the cost price, giving your answer correct to( 2 marks)
Total I I rnarks
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*
( a )) Ci iven tha t r l - 1 . b :2 anc l
( i ) a t - b + c
( i i ) b1 ( '1
Wri tc the lb l lowing phrases
( i ) seven t i rnes the surn
( i i ) the product of l -WO
c' : --3. f ind the r, 'alue of-:
as a lgebr-a ic express ions:
o1- . r anc l . r '
consc'cutir e nurnbers rvhen the
Pagc 4
( l m a r k )
( I m a r k )
( l m a r k )
s r n u l l c r t t u r t t h c r i s . r '
( l m a r k )
( - t r r n l r r k . r
r I r r r r u ' k )
I I r r t r t t ' k r )
( 2 r n a r k s )
Total l2 marks
t l ie given in 1i : t 'n l t1 iot t
t
(b)
(cl)
( c ) So lve the pa i r o f s in rLr l taneous equat ions :
f-\ ' t .t '-: 7
.r f.t ' - I
Factori se conr 1'l I ete l rv :
( i ) 4,r ' r : l
( i i ) ?a .v 2ay - b r + l r r
( i i i t 3 , r r + l 0 - r 8
3 . (a) A survey u,as conducted among 40 tourists. f-hc rcsrr l ts u cr ' . . ' :
l f i r is i tcc i . \n t igua l . \ t30 v is i tcd Barbados ( B )3x visi ted both Antigua and Barbados.r visi ted neither Antigua nor Barbaclos
(i) Copy'and complete the Venn diagrerm below to representabor e.
-.-=-\- - - 1 - - -__ ._
I >I)
( i i )
( i i i )
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Write an expression, in -rr,survey.
Calculate the value o{ ' .r .
( 2 marks)
to represent tl-re 1-OTAL number of tourists in thc( 2 marks)
( 2 marks)
GO ON TO T I IE NE,XT 'PAGF,
(b) The diagram below, not drawnwith cross section ABCDE. tr is
to scale, shows a wooden toy inthe midpoint of EC, and IBAE
Page 5
the shape of a prism,: ZCBA : 90o.
-1.
Calculate
(i) the length of EF
( i i ) the l c -ng th o f DF
rr i i r the area of the face ABCDE.
5 c m
( I m a r k )
( 2 marks)
( 3 marks)
Total 12 marks
( 2 marks)
Total I I marks
\ \ i r . ' r r ' . r r r ic : J i rect l r :> the : t lLr r r r - ' r r i r . . thc r ar ia t ion eqr- rat ion is wr i t ten ! : kx2,u 'hereA r s ir c rrit: ti.tn t.
( i) Given that 1' : 50 when -r : 10, f ind the value of k. ( 2 marks)
( i i ) calculate the value ofy when x : 30. ( 2 marks)
(i) Using a ruler, a pencil and a pair of compasses, construct triangle EFG withE G : 6 c mlFEG: 60"and IEGF: 90o. ( 5 marks)
( i i ) Measure and state
(b)
the length of EF
the size of /-EtrG.
a)
b)
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L
(a ) The functions / 'and g are defined as /(x):2t - 5 and g(.r) : xr + 3.
( i ) Calcu late the value of
/(4)
s/(4)
( i i ) F ind l ' r ( r ) .
The diagram below shows the graph of-y : x2 + 2x - 3 for the dornain - 4
graph above to deternr ine
the scale used on the -r-axis
the value ofy fbr which,r - - 1 .5
the values of r tor which y: 0
the range of values of-t,, giving your answerb are real numbers.
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(
(
I mark )
2 marks)
marks)
< 2 .
( I m a r k )
( 2 marks )
( 2 marks )
in the fbrm a = t- < b, where a and( 2 marks )
Total l2 marks
GO ON TO THE NE,XT PAGE
a)
b )
(b )
( 2
< J
Use the
( i )
( i i )
( i i i )
( iv )
J , 1
I- t + 2.r
: t '
3
\ I I\ ' , ' Ii,\ )
I\i
! l
',1/,\
\
I N 2 \
\ f,\ .,
..:N\
-f
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6.
Page 7
An answer sheet is provided for this question.
(a) The diagram below, not drawn to scale, shows two straight lines, PQ andRS, intersectinga pair of parallel lines, TU and VW.
R P
Determine, giving a reason for E,ACH of your answers, the value of
( i ) r
( i i ) y .
( 2 marks)
( 2 marks)
(b) The diagram below shows triangle LMl,{,and its image, triangle L' M hr ,afterundergoinga rotat ion.
(i) Describe the rotation FULLY by stating
a ) the centre
b) the angle
c ) the direct ion. ( 3 marks)
( i i )
( i i i )
L,MN.
Triangle LMl,lis translated by the vecto , ( t l
t - ) 1\ "./
State TWO geometric relat ior-rships betrveen tr iangle Lh4l ' /and i ts image, tr iangle( 2 marks)
Determine the coordinates of the image of the point I under this transformation.( 2 marks)
Total 1l marks
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\.1. . I
:X4 ' \
\
I \II
--1
IJ
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L
7.
Page [3
A class of 24 students threw the cricket ball at sports. The distance thrown by each student wasmeasured to the nearest metre. The results are shown below.
22
48
5 5
3 6
50
34
29
63
3 5
45
46
54
52.,)Z J
5 6,) ,\J Z
i n t c . n a l l r l l . )
represent 5histogram to
47
43
43
19
30
10
59
60
(
(
metres, and a scale of Iillustrate the data.
(
(a) Copy and complete the fiequency table for the data shown above.
Distance (m) Frequency
20 29 aJ
30 39 5
(b )
(c)
State the lou'er bor-rndan t i-rr the class
Using a scale of I cm on the r -ax is to
-)'-aris to represent I student. drar.v a
3 marks)
I rna rk )
cm on the
5 marks)
(d) Deternt ine
( i ) thc nunrber of st l ldents r i ho threw' the bal l a distance recorded as 50 rnetres orn r o r e ( l m a r k )
( i i ) the probabi l i ty that a stLldel t t . choscn i i t ratrdor-n. threuas 50 metres or more.
the bal l a distance recorded( I m a r k )
Total 11 marks
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8.
Page 9
An answer sheet is provided for this question.
The diagrar-n bclou,shows the first three figures in a sequence of figures. Each figure is made
up of squares of s ide I cm.
Fig. I Fig. 2
On your answer sheet, draw the FOURTH figure (Fig. 4) in the sequence.( 2 marks)
StLrcir rhc 1-rx11..1-n: in the table shown below, and on the answer sheet pror ided. cotttplr- ' tc
l l r c r i , r i : n r n r l - c l c . l r r t . t i i ) . ( i i i ) a n c J ( i r ) .
( a )
( b )
( i )
( i i )
( i i i )
( i v )
I Area ofFigure ,
t-J,T
Perimeterof Figure
(cm)
l x 6 2 : 1
2 4 2 x 6 - 2 : 1 0
aJ 9 3 x 6 - 2 : 1 6
4
5
l 5
l t
( 2 marks)
( 2 marks)
( 2 marks)
( 2 marks)
Tota l l0 marks
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Page 10
SECTTON II
Answer TWO questions in this section.
ALGEBRAAND RELATIONS, FUNCTTONS AND GRAPHS
g. (a) The diagram below shows the speed-time graph of the motion of an athlete durin-e a
race.
Speedin m/s
t 4
l 2
l 0
8
6
4
2
0 r 2 3 1 5 6 7 8 9 1 0 1 1 1 2 1 3Time in seconds
( i ) Using the graPh, determine
a) the MAXIMUM sPeed
b) t |e purnber of seconds fbr u,hich the speed vr 'as constant
c) the TOTAL distance col 'ered b1, the athlete durin,e the race.( 4 marks)
(ii) During which time-period of the race r'vas
a) the speed of the athlete increastng
b) the speed of the athlete decreasing
c) the acceleration of the athlete zero? ( 3 marks)
/ \
/ \
/ \
/ \
/ \
/ \
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\
(b)
Page I I
A farmer supplies his neighbours with r pumpkins andy melons daily, using the follow-ing conditions:
First condition '. ),> 3
Secondcond i t i on : y<xThird condition : the total number of pumpkins and melons must not exceed 12.
( l m a r k )(i) Write an inequality to represent the THIRD condition.
( i i ) LJsing a scale of 1 cm to represent one pumpkin onto represent one melon on the r-axis, draw the graphs
the x-axis and I cmof the THREE lines
associated u. i th the THREE inequali t ies. ( 4 marks)
(iii) Identify, by shading, the region which satisfies the THREE inequalities.( l m a r k )
(iv) Determine, from your graph, the minimum values of x and y which satisfy the
conditions. ( 2 marks)
Total 15 marks
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(a )10.
MEASUREMENT, GEOMETRY AND TRIGONOMETRY
not drawn to scal e" PO is a tansent to the circle PTSR, so that
Page 12
marks)
marks)
marks)
its foot"f lagpole6 m a n d
In the diagram below,/.RPQ: 46"IRQP:32 "and TRQ is a straightl ine.
P
Calculate, giving a reason for EACH step of 1,'otrr ans\\er.
( i ) Z.PTR
( i i ) zrPR
( i i i ) tTSR.
( 2
(3
(2
(b) The diagram below, not drawn to scale. shows a vertical flagpolc. lrT. u'itlr
F. or"r thc horizontal plane LI '-G. LT and Of are *tt ' , - ' : r ihich 5Ll l lport thc
in i ts posit ion. The angle of eler at iott of f t iot l G is 5 5' . EF : 8 m, FG :
/_EFG : 120".
Calculate, giving your answer correct to
(i) the height, FT, of the flagpole
(ii) the length of trG
3 significant figures
(iii) the angle of elevation of T from E.
( 2 marks)
( 3 marks)
( 3 marks)
Total l5 marks
GO ON TO THE NEXT PAGE
01234020/F 2010
:
Pagc l 3
VECTORS AND MATRICt rS
t l . (a ) A and B nr -c tuo I r ? rna i r i ces such tha t
( l 1 ( s - r \A: I a r rd B : i
- " li l 5 l - 2 I i
( 2 marks)
( l m a r k )
/ r - \
write i I or the product of TWO matrices.\ 1 ) l
( 2 marks)
( iv) Hence, ca lcu late the values of r and_r , . ( 2 marks)
(b) -fhe diagrant bc' low. not drawn to scale" shows tr ianele . lKl, .
'''.-|--- ' ' / l
J . _
i\ ,
\ / r incl \ l r i 'c ntr ints on ,, /K ttncl JL re spectively. such t lrat
. / \ l = . . / A a n c l J , \ : ! . 1 1 . .
( i) C'opr thc dia-erarn in your answer booklet ancl shor,v the pcl ints Mand,V.
_ _ ) _ ) ( 2 m a r k s )
( i i ) Givcn thar . /A,1 : uarrd. t r l , , / :v ,rvr i te. irr terrns of z and y, alt crpression fbr
-)a) .IK
->b) i I \
--)c ) L L .
( i i i ) Us ing yoL l l ' f i r t c l ings in (b ) t i i ) . c iec lL rcc TWO geornet r i ca l re la t ionsh ips be twee lKL and ,ll,\'. ( 2 marks)
Total l5 marks
( i ) I ' i n c i . \ 8 .
l i i t I ) c t c r n i i r r e B r . t h e i l r v e r s e o f B .
t i t i r ( i i r e n t l l r t
5 - : \ i ' 2 \
: I r . ; =
l , j
K
( 4 marks)
END OF TEST
01234020/F 20 I 0
Answer Sheet for Question 6
( a ) R
TEST CODE OI234O2O
MAY/JUNE 201O
NCIL
Candidate Number .. . . . . . .
P
FORM TP 2010087CARIBBEAN EXAMINAT IONS COU
SECONDARY EDUCATION CERTIFICATEEXAMINATION
MATHEMATICS
Paper 02 General Proficiency
( l )
( i i )
Y :
I
( b ) v
tI
X.'i',} I '
1\
//
\
:L :;z 1, \
I
N:
N' :
i -
1\l. i . . . i
: ' , - 4r r l
: i -3, . ' . [ .
,|
II
.v
I
( i ) a )
b )
c )
centre of rotation
angle of rotation
di rcct ion of ' ro tat ion
( i i )
( i i i )
LMIV and L' M N are and
lmase of L under the translation is (
ATTACH THIS ANSWER SHEET TO YOUR ANSWER BOOKLET
FORM TP 2010087TEST CODE OI234O2O
MAY/JUNE 20 1O
CARIBBEAN EXAMINAT IONS COUNCIL
SECONDARY EDUCATION CERTIFICATEEXAMINATION
MATHEMATICS
Paper 02 General Proficiency
Answer Sheet for Question 8 Candidate Number ........
( a )
( i i i )
( iv )
( b )
( i )
( i i )
FigureArea ofFigure(cm')
Perimeterof Figure
(cm)
l x 6 2 - 4
2 ,1- 2 x 6 - 2 : l 0
1J
c1 3 x 6 - 2 : 1 6
4
5
l 5
n
ATTACH THIS ANSWER SHEET TO YOUR ANSWtrR BOOKLET