2008 solutions
DESCRIPTION
gully bopTRANSCRIPT
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MathematicsGeneral Proficiency
May2008
1. a) i) 1.053 + 0.82 = 1.81.3
5 4 25-8
ii) L-i= ---12-3 ~4 4
17 4-=-x-10 3
68=-
30
34=-
15
b) i) CAN JA1 : 72.50
250 : x250 x 72.50 = JA$18.125
ii) 30,000 -18,125 = $11,875
$11,875 = CAN$163.79$72.50
2. a) i) 2[(-1) + (3)]=2(-1+3)=2(2)=~
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ii) 4(-1)2- 2(2)(3) 4-12=-2-1+3 4
8= ..-4
=-~
b) i) 4(x +5)
ii) ab+ 16
c) 15 - 4x = 6x + 215 - 2 = 6x +4x
13 = lOx13x=-10
d) i)
ii) 2m2+ 10m - m - 52m(m + 5) -l(m + 5)(2m -1) (m + 5)
3 a) t = 1080- (240 + 189+ 216 + 330)t = 1080 - 975t = lil5.
b) i) Lawyers: 240 x 360 = 8001080 ~
Teachers: 189 x 360 =6301080
Doctors: 105 x 360 = 3501080
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I. a)
ii)
i)
Artists: 216 x 360 = 7201080
Salesperson: 330 x 360 = 11001080
Pie Chart showing career interest of students
Sales Person
15 21 25
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ii) {1S, 21, 2S}
b) i) Parallelogram ABCDwith AB = AD = 7emAngle BAD is 60
- - - -j-A
ii) Length of Diagonal AC= 12em
5. a) i) 8-2=fun
ii) 10 - 6 = 1.m
b) 10 + 5+ 2 + 3 + 8 + 3 + 4 + 5 = 1!lm
c) (10 x 5) + (3 x 8) = 50 + 24=l4...m2
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d)1ml --.JI Area = 0.2 m2
02 m
50m2-- = 25!l boardsO.2m2 -
6. a) i) G
K
ii) a) 12tan 32 = Hi
HJ 12=--0.625HJ = 19.2 m
b) tan 27 12-HK
HK 12= -0.51HK = 23.6 mJK = HK -HJJK =23.6-19.2JK =4.4m
511 p)ge
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b)
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i) A translation of 2 units to the right parallel to the x axis followed by7 units downwards parallel to the axis. => T= (!7)
ii)
,..-s
..... ,:;:-.---..:---:-~
/,1'-l.+- f l,' ,.:-\++-HIi" ,.".J ,.
I_~~_~...: I ,I 1!1
1:+;1>111'1'I'
! j-!;! il
, "!' ,
lH-++-1+f_~H~~::~oNtJ
. I , : ~, .
,. ~~t+t-iit~
',', .8,:; ,
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7. a) i) c=7
ii)7-0 7
M=-=--0-2 2
iii) (0;2 , 7;0) = (1,3.5)
b)7
Y=-'2X+77y= -'2 (-2)+ 7
y=7+7y= 14
=>k=lA
c)7x-2=--x+72
7X+ -x=2+72
2X=92
x = 9(~)x=2
Therefore, y = x - 2y=2-2y=O
Ans=a.JU
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8. a) 6(4) + 6(2.50) + 6(1.20) + 6(1)= 24 + 15 + 7.20 + 6=$522.0
b) i) Ifwe use 6 $4 stamps then the balance of 1.70 cannot purchase any
Therefore she must select: 5 stamps at $4.00 = $20.001 stamp at $2.50 = $2.501 stamp at $1.20 = $1.202 stamps at $1.00 = lllli1
lli.IO
ii) 6 stamps at $1.00 = $6.004 stamps at $4.00 = $16.001 stamp at $2.50 = $2.501 stamp at $1.20 = $1.20
$2.5.IQc) i) 5 stamps at $2.50
6 stamps at $1.206 stamps at $1.0011 stamps
ii) 5 stamps at $2.506 stamps at $1.206 stamps at $1.00
9. a) i) XS
-=xx'
ii) a3/2bs/2 x a1/2b3/2 = a3/2 + y, bS/2+3/2= a2b4
b) i) f(2) = 2(2) -3= 4 - 3=1
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ii) y=2x - 3x = 2y- 3x + 3 = 2y
x+3y=-2
0+3Thereiore f! (0) =2
3=
2
iii) f-lf(x)=~ 22x
2=X
Therefor~f-lf(2) =~
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c)
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i) Temperature - time graph showing how a liquid cools.
I I I !. I I I!A
i ! ! 1 ! iI ,! i ! i
I ! IjI ! .!
~' \ i iI ! 1! , I! , ! I i,
\ i'j , Ii I j 1
1\ I I I .I , i ,.. \ I,
1\ 1I, \ I I
..... '
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ii) a)
b) 33-27 .rate = -- = 0.66C/mm35-26
10. a) y + 4x = 27y = 27 - 4x
into (2) x(27 - 4x) + x = 4027x - 4X2 + X = 40_4X2 + 28x - 40 = 0- X2 + 7x - 10 = 0_X2 + 5x + 2x - 10 = 0-x(x - 5) + 2 (x - 5) = 0( -x + 2)(x - 5) = 0
either -x + 2 = 0 Y = 27 - 4(2)x=L => y =19.
or x-s=O y = 27 -4(5)x=~ y=Z
b) No,as (10,5) lies outside the shaded region.i) a)
b) Yes,as (6,6) lies within the shaded region.
ii) Y ~ 2y~2xY< -4 X + 12- 5
iii) a) P = 3x + sy
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11. a)
b)
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b) Minimum Profit OccursAt point (1,2)
P = 3(1) + 5(2)= 3+ 10=lli
i)
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Hi) Area of minor sector :=: nr2~360= n(8.52) (117)
360= 73.7 ern-
Area of shaded region= 73.7 - 32.2:=: 41.5 em?
iv) Length of major arc AB:=: 2n(8.S)(243)
360:=: 3.6- em (ld.p)
12. a) XI't---------- \""15 ".ft\.~ --
~ '""I
b) i) RST:=: 33 + (180 -112)= 330 + 68=101
ii) Rfs = 1:8(alternate angles)
Hi) 2600
c) i) - see diagram -
ii) (approx.) 11:km
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13. a)
b)
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i)
ii)
N
B t- -*-M~ A
a
_see diagram above -
~=~+~AB AD DB
= -a+ b=b.-a
1~=-~PA 30A
1=3"2
-+=~+-+PM PA AM
1 ~= "3a+ 1hAB
1= 3"a+ 1h (b. - a)1= -a + 1hb - 1har
1= 1hb --a- 6-1= -(3b - a)6 - -
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c) ~=~+~MN MB BN
= l(h -g) +h= lh -lhf! + h
3= - b -lha2- -
= lh (3h - g)
MN = 3PM => P, M and N are collineard) AN = AB +Bfii
=Q-~+Q= 2Q-~=2G) + C~)= (!) + C~)= (-24)
Therefore, IANI = ~( _4)2 + (2)2= .fjJj= 4.47
14. a) X2 = (~2 ~) (~2 ~)
(4 + 0 0 + 0)-10+5 0+1
X2 + Y = (~5 ~) + (j - ~)= (8 -1)
-2 8
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b) 1 (3 - 2)3-2 -1 1
~(3 - 2)1 -1 1
(3 - 2)-1 1
c) i) a).J,ff3 3-=-.J..22 2k=1..5
b) E' (3, 10.5) F' (12,6)
ii) a) R (0, -900) =(CO~90 Sin90)-sm90 cos90
= (~1 ~)
(~1 e' E' F) Coo E" ~")b) ~) 7.5 3 12 = 18 10.518 10.5 6 -75 -3 -12D" (18, -7.5) E" (10.5, -3) F" (6, -12)
c) 3 (0~)= (~~ ~)2 -1
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