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

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,:; ,

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

..... '

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)

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 - -

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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