ADDITIONAL MATHEMATICS 4049/02 - SEAB

*0123456789*

MINISTRY OF EDUCATION, SINGAPORE in collaboration with CAMBRIDGE ASSESSMENT INTERNATIONAL EDUCATION General Certificate of Education Ordinary Level

S

ADDITIONAL MATHEMATICS

Paper 2 SPECIMEN PAPER

Candidates answer on the Question Paper. No Additional Materials are required.

4049/02

For examination from 2021

2 hours 15 minutes

READ THESE INSTRUCTIONS FIRST

Write your centre number, index number and name in the spaces at the top of this page. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. DO NOT WRITE ON ANY BARCODES.

Answer all the questions. Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question. The use of an approved scientific calculator is expected, where appropriate. You are reminded of the need for clear presentation in your answers.

The number of marks is given in brackets [ ] at the end of each question or part question.

The total number of marks for this paper is 90.

This document consists of 19 printed pages and 1 blank page.

? UCLES & MOE 2019

[Turn over

Quadratic Equation For the equation ax2 + bx + c = 0,

2 1. ALGEBRA

x = -b !

b2 - 4ac 2a

Binomial expansion

JN

JN

JN

(a + b)n = an + LKK1nPOOan-1b + LKK2nPOOan-2b2 + ... + LKKnrPOOan-rbr + ... + bn ,

where

n

is

a

positive

integer

and

JLKKnrNPOO

=

r!

n! (n -

r) !

=

n (n

-

1) ... (n r!

-

r

+

1)

Identities Formulae for ABC

2. TRIGONOMETRY

sin2 A + cos2 A = 1 sec2 A = 1 + tan2 A cosec2 A = 1 + cot2 A sin(A ? B) = sin A cos B ? cos A sin B cos(A ? B) = cos A cos B sin A sin B

tan(A

?

B)

=

tan A ! tan B 1 " tan A tan B

sin 2A = 2 sin A cos A

cos 2A = cos2 A ? sin2 A = 2 cos2 A ? 1 = 1 ? 2 sin2 A

tan

2A

=

2 tan A 1 - tan2A

a sin A

=

b sin B

=

c sin C

a2 = b2 + c2 ? 2bc cos A

=

1 2

bc sin A

? UCLES & MOE 2019

4049/02/SP/21

3

1

Express

2x3 - 8 x3 + 4x

in partial fractions.

[6]

? UCLES & MOE 2019

4049/02/SP/21

[Turn over

4

2 (a) Variables x and y are related by the equation yx n = k , where n and k are constants. Explain clearly how

n and k can be calculated when a graph of lg y against lg x is drawn.

[3]

(b) The time for a complete oscillation, t seconds, of a pendulum of length l m is proportional to l . In an experiment with pendulums of different lengths, the following table was obtained.

Length of pendulum, l m

0.2

0.4

0.6

1.0

Time of one oscillation, t sec

0.90

1.27

1.55

2.02

(i) On the grid on page 5, draw a straight line graph to illustrate this data.

[2]

(ii) Use your graph to estimate the time of one oscillation for a pendulum of length 0.8 m.

[2]

It is known that the correct formula connecting t and l is t = 2

l g

, where

g is the acceleration due

to gravity.

(iii) Use your graph to estimate the value for g.

[3]

? UCLES & MOE 2019

4049/02/SP/21

5

? UCLES & MOE 2019

4049/02/SP/21

[Turn over

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

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download