Mathematics Examination Question Paper

Topics: Caribbean Examinations Council, Triangle, Trigonometry Pages: 25 (2079 words) Published: January 9, 2013
TEST CODE

OI234O2O

FORM TP 2009092
SECONDARY EDUCATION CERTIF'ICATE

MAY/JUNE2OO9

CARIBBEAN EXAMINATIONS COUNCIL
EXAMINATION MATHEMATICS Paper 02 - General Proficiency
2 hours 40 minutes 20 MAY 2009 (a.m.)

INSTRUCTIONS TO CANDIDATES

1. 2. 3. 4.

Answer ALL questions in Section I, and ANY TWO in Section IL 'Write

All working must be shown clearly.
A list of formulae is provided on page 2 of this booklet.

Examination Materials
N

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

I I

I I I I

DO NOT TURN TIIIS PAGE TINTIL YOU ARE TOLD TO DO SO.
Copyright @ 2OO7 Caribbean Examinations Council@. All riehts reserved.

-

01234020tF 2009

Page2

LIST OF FORMULAE
Volume of a prism

V = Ah where A is the
length.
V

area of a cross-section and å is the perpendicular

Volume of cylinder Volume of a right pyramid Circumference Area of a circle Area of trapezium

=n/hwhere r is fhe radius of the base

ancl l¿ is the perpendicular height.

y = elrwhereA is the area of the base and /¿ is the perpendicular ! C =2nr where r is the radius of the circle.

height'

A

= nf

where r is the radius af the circle.

¡ = ){n

+ b)

lz

where a anú b are the iengtirs of the parailel sides and

l¿

is

the perpendicular distance between the parallel sides.

a* + bx + c -0,
x
=

then

-b!

bz

-

4ac

2a

Trigonometric ratios

opposite side sin 0 = Epotenuse
cos 0

Opposite

=

tan0 =
Area of triangle Area of n =

|øt

where á is the length of the base and

l¿

is

the perpendicular height

Area of

MBC = þø

"inc

c
c)

(-

Area of LABC

= .fs(s - a)(s - b)(s c

whete
a sin A

s=

a+b+

Sine rule

.ittB = únC

bc

Cosine rule

a2=b2+c2-ZbccosA
GO ON TO THE NEXT PAGE

0t234020tF 2009

Page 3

SECTION I
Answer ALL the questions in this section.

All working must be clearly shown.
1.

(a)

Using a calculator, or otherwise, calculate the EXACT value of

(i)

21 2- + i-6\

( 3 marks)

(iÐ

,5)

( 3 marks)

(b)

The basic wage earned by a truck driver for a 40-hour week is \$560.00.

(i) (iÐ (iiÐ

Calculate his hourly

rate. overtime.

(

1

mark )

For overtime work, the driver is paid one and a half times the basic hourly rate. Calculate his overtime wage for 10 hours of

( 2 marks)

Calculate the TOTAL wages earned by the truck driver for a 55-hour week, ( 3 marks)

Total L2 marks
2.

(a)

Factorise completely:

2ax+3ay

(iÐ s* - 20
(b)

-

2bx

-

3by

(iii) 3f + 4x- t5
One packet of biscuits costs \$x and one cup of ice cream costs \$y.

( 2 marks) ( 2 marks) ( 2 marks)

One packet of biscuits and two cups of ice cream cost \$8.00, while three packets of biscuits and one cup of ice cream cost \$9.00.

(i) (iÐ

Write a pair of simultaneous equations in

informationabove.

x

and

y to represent the given ( 2marks)

Solve the equations obtained in (b) (i) above to find the cost of one packet ( 4 marks) of biscuits and the cost of one cup of ice cream.

Total 12 marks
GO ON TO THE NEXT PAGE
o1234020/F 2009

1
Page 4

3.

(a)

In a survey of 50 students,
23 owned cellular phones 18 owned digital cameras ,r owned cellular phones and digital cameras 2x owned neither.

Let C represent the set of students in the survey who owned cellular phones, and D the set of students who owned digital cameras.

Copy and complete the Venn diagram below to represent the information obtained from the survev. U

( 2 marks)

(iÐ (iiÐ
(b)

Write an expression in x for the TOTAL number of students in the survey. Calculate the value of

"v.

( lmark) ( 2...