2005 Solutions

Suggested Solutions to Past CXC Examination Papers

2005-2010

Compiled By Experienced CXC Instructors

Page

Solution Paper 2 - 2005

1

Paper 2 - 2006

15

Paper 2 - 2007

31

Paper 2 - 2008

47

Paper 2 - 2009

63

Paper 2 - 2010

80

Questions? Comments? Email [email protected]

Mathematics General Proficiency May 2005

1.

a) = =

21

10

5

3

63-50 15

-- 13/15

b)

i)

ii)

A:

12.50 x 3 = $37.50 'v

B:

$33.90 --

c:

--

D:

15 X 100

=$li.25

2

$31.00 $6.20

=5 108.28 = $16.24

6 x 0.75 = $4.50 6 x 0.40 = $2.40 Total made = $6.90 Total spent = $5.88

*NB:The exact profit was not necessary

(Difference: $6.90 - $5.88

in this case.

= $1.02)

Amanda made a Rmfit

IIPage

a)

2

ab(5a

ii) iii)

(3k-l) (3k+ 1) 2yL4y-y+ 2 2y(y - 2) -l(y - 2) (2y -1) (y - 2)

b)

6xz - 8x + lSx -20 6xz + 7x - 20

c)

i)

2(x - 3) = 2x-6

ii)

x + x - 3 + 2x - 6 = 39 4 x - 9 = 39 4x =48 x = 12

i)

3x

l

3.

+ b)

i)

a)

+

x = 24 4x=24 x=6

~ students

b)

·Solving the equation was not necessary in this case.

take both Music and Drama.

=

ii)

Student who take drama only 7 + x :. 7 + 6 = 1.3. students take only Drama.

i)

y- 5 2

2 = -(x + 3) 3

y='3x+2+S 2

y='3x+7

y=mx+c or

2

5=-(-3)+c 3

5

= -2 + c

c=7 ii) 21Page

2 x - 3y = 0

2

Y = -x 3

+7

-3y = -2x y=Y m

=

-2x -3 2 -X 3

=!.3 .:for the line 2x - 3y = 0 therefore it is parallel to y = !. x +7 3

(Parallel lines have the same gradient)

4.

a)

Area of small pizza

= rr(7.5)2 = 176.79 em-

Area of medium pizza = rr(152) = 707.14em2 707.14 176.79

=4

The medium pizza is more than twice as large as the small pizza. It is four times as large.

b)

· SIzeo

f1-0

3

f me diIUmplzza=--= . 707.14 3

23571 . em 2

ratio of area to cost of medium pizza =

ratio of area to cost of small pizza

235.71 15.95

= 14.78 em2/$

= 176.79 = 13.65 12.95

em2/$

Therefore, it is better to buy a slice of medium pizza, rather than a small pizza.

31Page

5.

The graph below shows the answer for 5(a), 5(b) (i) 5(b) (ii) - lern: 1 unit on both axis. _J __

c.

..

,

1; ;

. ,

~,

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;\

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..

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..

.

...., .

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;',

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:

..

.,.. ..

.1.· ..

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.

:

! ; ..~. ; ,

'

.'

.'F';'

"

....

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I' .: ' I·

~

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./

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.

..

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s :

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.

. "r:,

F, '.

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.i

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I'

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':

,:.. ',',y-,

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:ii

,n

.., "Et','

':~. ·c.

,

,

.

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1

~. ,l

I: .;

J'

:" ';', I,

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....

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,,>

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:,';'i, i,':'

.

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.

",: ....

'., 4\Page

'

"., cT, ',:

..

, ;t.

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:'

"

Hi) Composite transformation c)

1.8

tan a =2

a = tan"! 0.9 a = 42°

6.

a)

i)

EAD

= 57°

Reason: Alternate angles of parallel lines

Then x = 180 - (57 + 80) = 43°

b)

ii)

DAB=108-57 = 51° Since angle of a quadrilateral add up to 360°. Then y = 360 - (51 + 57 + 90) = 360 -198 = 162°

i)

32 + (-3)2 = 9 + 9

=18 ii)

=

Ifx Yzy + 5 x-5=Yzy y=2(x-5) r1(x) = 2x -10 rl(6) = 2(6) -10 12 -10 =~

=

iii)

fg(x) = 1fzX2 + 5 f g(2) = 1fz(22) + 5 =Yz(4)+5 =2+5

=Z SIPage

7.

a)

Cumulative Frequency Table showing the height of applicants Height/ern

Cumulative Frequency

$155

10

$160

65

$165

170

$170

280

$175

360

$180

390

$185

400

Cumulative Frequency Curve of Heights of Applicants y

400

3!lO

300

J

250

~ Q

200

',.~"

150

100

50

!SS

16S

110 H.ipt

61Page

(cmj

,17,S;

1&0

lSS

x

b)

8.

a)

i)

275 applicants

ii)

167 em

iii)

162.5 em

iv)

95 400

i) (4

ii)

I

103

X

72)

+ (3

x 6)

+2

216

(8 X 112) + (3 x 10) + 2

1000

~------~------------------------

iii)

b)

1,--_n_3 --l.1_C(_n _-2_)x_C_n_+1_)2_+_(3_X_n~_2_1,--

(a - b) (a - b) (a + b) + ab(a + b) = (a - b) (a- - b2) + a-b + ab= a3 - ab- - a-b + b3 + a2b + ab= a3 - ab- + ab- - a-b + a2b + b3 = a3 + b3

__

n3__

Difference

of squares

• (a - b)(a

+ b) = aL

71Page

b'

9.

a)

5xz + 2x-7 5(xZ + ~x) - 7 5

5 [Xl + ~X + (!)Z ~ - 7 - 5(!)2 5

5

1 Sex +_)25

b)

c)

5

7-1 5

1

i)

- 7-

ii)

When X + 5 = 0, then x = - '5

5

1

1

S(x + !)2 = 36 5

5

(x + !)2 = 36 5

X

25

+ ~ = ../36/25 1

6

x=--+5

-

-5

E"Ith er

x = - -1 + -6 5

5

1

6

5 7

5

x=----

or

-

=1

5

d) v

x

81Page

10.

a)

i)

40-0_'J£.77/2 £".,J,LL m 15-0 --

s

== gradient

Acceleration of first portion

Distance travelled = ii)

0

22

of graph

(40 + 50)

= 10(90)

= 9.illlm

20

b)

c)

= 6km/h

i)

12km 2h

ii)

He took a rest or stopped.

iii)

~=8km/h

i)

x=6

ii)

x~6

1.5

5

y>-x +5 - 8

"evaluate ::-point in the region for each line.

1

y