C A R I B B E A N E X A M I N A T I O N S C ... - CSEC Math Tutor

CARIBBEAN

E XAM I NAT I O N S

COUNCIL

CARIBBEAN SECONDARY EDUCATION CERTIFICATE?

EXAMINATION

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05 JANUARY 2021 (a.m.)

FILL IN ALL THE INFORMATION REQUESTED CLEARLY IN CAPITAL LETTERS.

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SUBJECT

PROFICIENCY

1

2

3

4

0

2

0

MATHEMATICS ¨C Paper 02

GENERAL

REGISTRATION NUMBER

SCHOOL/CENTRE NUMBER

NAME OF SCHOOL/CENTRE

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Current Bar Code

CANDIDATE¡¯S FULL NAME (FIRST, MIDDLE, LAST)

DATE OF BIRTH

D

D

M

M

Y

Y

Y

SIGNATURE __________________________________________________

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IS

TH

W

NO

T

ON

E

PA

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TE

RI

DO

TEST CODE

FORM TP 2021019

01234020

JANUARY 2021

CAR I B B EAN E XAM I NAT I O N S C O U N C I L

CARIBBEAN SECONDARY EDUCATION CERTIFICATE?

EXAMINATION

MATHEMATICS

Paper 02 ¨C General Proficiency

2 hours 40 minutes

READ THE FOLLOWING INSTRUCTIONS CAREFULLY.

1.

This paper consists of TWO sections: I and II.

2.

Section I has SEVEN questions and Section II has THREE questions.

3.

Answer ALL questions.

4.

Write your answers in the spaces provided in this booklet.

5.

Do NOT write in the margins.

6.

All working MUST be clearly shown.

7.

A list of formulae is provided on page 4 of this booklet.

8.

If you need to rewrite any answer and there is not enough space to do so on the

original page, you must use the extra page(s) provided at the back of this booklet.

Remember to draw a line through your original answer.

9.

If you use the extra page(s) you MUST write the question number clearly in the

box provided at the top of the extra page(s) and, where relevant, include the

question part beside the answer.

10.

ALL diagrams in this booklet are NOT drawn to scale, unless otherwise stated.

Required Examination Materials

Electronic calculator

Geometry set

DO NOT TURN THIS PAGE UNTIL YOU ARE TOLD TO DO SO.

Copyright ? 2019 Caribbean Examinations Council

All rights reserved.

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Page 4

Volume of a prism

V = Ah where A is the area of a cross-section and h is the perpendicular

length.

Volume of a cylinder

V = ¦Ðr2h where r is the radius of the base and h is the perpendicular height.

Volume of a right pyramid

V = ¡ª Ah where A is the area of the base and h is the perpendicular height.

Circumference

C = 2¦Ðr where r is the radius of the circle.

Arc length

¦È

S = ¡ª¡ª

¡Á 2¦Ðr where ¦È is the angle subtended by the arc, measured in

1

3

360

degrees.

Area of a circle

A = ¦Ðr2 where r is the radius of the circle.

Area of a sector

A = ¡ª¡ª ¡Á ¦Ðr2 where ¦È is the angle of the sector, measured in degrees.

Area of a trapezium

1

A=¡ª

(a + b) h where a and b are the lengths of the parallel sides and h

2

If ax2 + bx + c = 0,

¨Cb + ¡Ì b2 ¨C 4ac

2a

then x = ¡ª¡ª¡ª¡ª¡ª¡ª

Trigonometric ratios

length of opposite side

sin ¦È = ¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª

length of hypotenuse

length of adjacent side

cos ¦È = ¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª

length of hypotenuse

DO NOT WRITE IN THIS AREA

¦È

360

is the perpendicular distance between the parallel sides.

Roots of quadratic equations

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LIST OF FORMULAE

Area of a triangle

1

Area of ¦¤ = ¡ª bh where b is the length of the base and h is the perpendicular

2

height.

1

2

Area of ¦¤ ABC = ¡ª ab sin C

Area of ¦¤ ABC = ¡Ì s (s ¨C a) (s ¨C b) (s ¨C c)

a+b+c

where s = ¡ª¡ª¡ª¡ª

2

b

¡ª¡ª =

sin B

Sine rule

a

¡ª¡ª

sin A

Cosine rule

a2 = b2 + c2 ¨C 2bc cos A

=

c

sin C

¡ª¡ª

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GO ON TO THE NEXT PAGE

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length of opposite side

tan ¦È = ¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª

length of adjacent side

DO NOT WRITE IN THIS AREA

DO NOT WRITE IN THIS AREA

DO NOT WRITE IN THIS AREA

Page 5

SECTION I

Answer ALL questions.

All working must be clearly shown.

1.

(a)

(i)

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

4 +¡ª

2 ¨C 1 ¡ª.

5

1¡ª

7

3

6

.................................................................................................................................

(2 marks)

(ii)

3

27 as a fraction in its LOWEST terms.

Write the value of ¡Ì

¡ª¡ª

92

.................................................................................................................................

(2 marks)

GO ON TO THE NEXT PAGE

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