CSEC Maths January 2006

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rEsr coDE

FORM TP 2006017

01234020

TANUARy 2006

CARIBBEAN EXAMINATIONS COUNCIL SECOIYDARY EDUCATION CERTIFICATE

.

EXAMINATION MATHEMATICS Paper 02 - General Profrciency 2 hoars 40 minutes

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t

04 JANUARY 2006 (a.m.) I

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INSTRUCTIONS TO CANDIDATES

l.

Answer ALL questions in section I, and ANy

2.

Write your answers in the booklet provided.

3-

All working

4.

A list of formulae is provided on page 2 of this booklet.

rwo

in section II.

must be shown clearly.

Examination Materials

I il l-

Electronic calculator (non-programmable) Geometry set Mathematical tables (provided) Graph rLpaper (provided)

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DO NOT TURN THIS PAGE T]NTIL YOU ARB TOLD TO DO SO Copyright @ 2004 Caribbean Examinations Council@. All rights reserved. O 123 40/20I J ANUARY/F 2006

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Page3

CTION

I

Answer ALL the questions in this section.

All working must be clearly shown.

1_ 52

(ii) (b)

I

correct to 3 significant figures, rhe value of 1g.75

A loan of $12 000 was borrowed from

a bank

_ (zJDz.

(

4 marks)

(

3 marks)

2 marks)

at l4vo per annum.

Calculate

(i)

the interest on the loan at the end of the first year

(

(ii)

the total amount owing at the end of the first year.

( lmark)

A repayment of $7 800 was made at the start of the second year. Calculate

(iii)

the amount still outstanding at the start of the second

(iv)

the interest on the outstanding amount at the end of the second year.

year

( I mark ) ( lmark)

Total 12 marks

0 I 23

4020I JANUARY/F 2006

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Page 4

2.

(a)

Given that m = -2 and n = 4, calculate the value of (2m + n)(2m

(b)

Solve the simultaneous equations

-

5x+6y=37

2x-3y(c)

4.

n)

-

(

2 marks)

(

4 marks)

(

2 marks)

(

2 marks)

Factorise comPletelY

(i)

4xz

-

(ii)

6p

-

(iii)

3x2

25

9Ps

+ 4q -

+ 4x -

6qs

( 2 -aSqL-

4.

Total 12 marks

3.

Given the formula t = Lr{" + v)r, express

(a)

r in terms of v' s, and t'

(

3 marks)

t,

on a certain day, 300 customers visited a bakery that

o)

sells bread and cakes'

70 customers bought cakes onlY 80 customers bought neither bread nor cakes 2x customers bought bread onlY r customers bought both bread and cakes

(i)

a

the urepresents the setof customers visiting thebakery on thatday,-Brepresents the set of customers who set of customers who bought bread, *a C represents the information' illustrate to bought cake. Copy anO comptete the Venn diagram

(

3 marks)

(ii)

who Write an expression in x to represent the TOTAL number of customers ( 2 marks) visited the bakery on that day.

(iii)

calculate the number of customers who bought bread

ONLY- ( 3 marks) Total ll marks

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A

TTIT

A

DV/E

\

Page 5

4.

("4

The equation of the line / is

(i)

(ii) (b)

! = 4x + 5.

State the gradient of any line that is parallel to /.

( lmark)

Determine the equation of the line parallel to I that passes rhrough the point (2,4). ( 3 marks)

An answer sheet is provided for this question.

The diagram above shows the positions of three cities, A, B and of Africa. The scale of the map is I : 20 000 000.

C on the north coast

(Jse

your answer sheet when onr*l,"ring the following questions. Show all lines and angles used in your calculations-

(i)

Measure and state, in centimetres, the length of the line segmenl, BC. ( 2 marks)

*\rtiil \

Hence, calculate in kilometres, the actual shortest distance from City B to city c. ( 2 marks)

trBsing

T:=--

a

protractor, determine the bearing of B from A.

(

4 marks)

Total 12 marks

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ANUARY/F 2006

Page 6 5.

The curved surface area of a cylinder = 2nrh, where r is the radius and ft is the height, and the surface area of a sphere is 4n f .

The diagram above, not drawn to scale, shows a solid glass paperweight which consists of a hemisphere mounted on a cylinder. The radius of the hemisphere is 3 cm, the radius of the cylinder is 3 cm and its height is 8 cm.

(a)

Calculate, using n = 3.14,

(D (ii) (iii) (b)

the curved surface area of the the surface area of the the

TOTAL surface

cylinder

hemisphere

area

of the solid

paperweight.

(

2 marks)

(

2 marks)

(

2 marks)

Using a ruler, a pencil, and a pair of compasses, construct the parallelogram KLMN, in which KL = 8cm,KN = 6cm, andZLKN=60?. ( Smarks)

Total 11 marks

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ol23 4020 I JANUARYIF 2006

PageT

An answer sheet is provided for this question.

6.

The diagram below shows quadrilateral PQRS, and its image, quadrilateral p'e'R,y,after it has been rotated.

l,

'i !

I

i

i '

'

(a)

State the coordinates of the points R' and S.

(

2 marks)

(b)

Describe the rotation completely.

(

3 marks)

(c)

on the answer sheet provided, drarv and label quadrilaterql- p'e,RT,,which is-the image of'P'Q'R'S' after it has been?eflebted'in the x-axis. ( 3 marks)

(d)

Describe completely, the single transformation that maps quadrilateral ppR,i onto P'Q'R'S'. ( 2 marks)

Total 10 marks

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123 4O2O I JANUARY/F 2006

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Page 8

The data below are the lengths, to the nearest centimetre, of the right foot of the 25 students in

7.

a class.

t4 15

t6 16

t7 (a)

18 18 18 19 t9

20 20

2t 22 22

22 22 22 23 23

24 2s 25

26 27

Copy and complete the following grouped frequency table for the data above.

Length of Right Foot (cm)

Frequency

t4-16

4

l7-t9 20-22

8

5

26-28

2

(

2 marks)

( lmark)

o)

State the lower boundary of the class interval 14

(c)

State the width of the class intervalz0

(d)

A student's right foot measured 16.8 cm. State the class interval in which this length

-22.

would lie.

-

16.

( lmark)

( lmark)

A student was chosen at random from the group, and the length of his right foot was measured. Calculate the probability that the length was GREATER THAN or EQUAL ( 2 marks) to 20 cm. State the modal.length of a student's right foot.

( lmark)

Calculate an estimate of the mean length of a student's right foot using the midpoints of ( 3 marks) the class intervals in (a) above.

Total

ll

marks

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1

234020IJANUARY/F 2006

Page 9

8.

The path of a ball thrown in the air is given by the equation h = 20t - 5P where ft is the vertical distance above the ground (in metres) and t is the time (in seconds) after the ball was thrown. The table below shows some values of r and the corresponding values of h, correct to 1 decimal place.

t

t

0

0.5

I

1.5

h

0.0

8.8

15

r8.8

2

Copy and complete the table of values.

(b)

Drawthegraph of

-

SPfor

3

r8.8

(a)

h=2ot

2.5

0