ADDITIONAL MATHEMATICS 0606/11

*3081135600*

Cambridge IGCSETM

ADDITIONAL MATHEMATICS Paper 1

You must answer on the question paper. No additional materials are needed.

0606/11 October/November 2020

2 hours

INSTRUCTIONS Answer all questions. Use a black or dark blue pen. You may use an HB pencil for any diagrams or graphs. Write your name, centre number and candidate number in the boxes at the top of the page. Write your answer to each question in the space provided. Do not use an erasable pen or correction fluid. Do not write on any bar codes. You should use a calculator where appropriate. You must show all necessary working clearly; no marks will be given for unsupported answers from a

calculator. Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in

degrees, unless a different level of accuracy is specified in the question.

INFORMATION The total mark for this paper is 80. The number of marks for each question or part question is shown in brackets [ ].

DC (PQ/FC) 187997/3 ? UCLES 2020

This document has 16 pages. Blank pages are indicated.

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2 Mathematical Formulae

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

1. ALGEBRA

x = -b!

b2 - 4ac 2a

Binomial Theorem

(a + b) n = an + en1oan-1b + en2oan-2b2 + f + enroan-rbr + f + bn

where

n

is

a

positive

integer

and

eno r

=

(n

n! - r)

!r!

Arithmetic series

un = a + (n - 1) d

Sn

=

1 2

n (a

+

l)

=

1 2

n {2a

+

(n

-

1) d}

Geometric series

un = arn-1

Sn

=

a (1 - rn) 1-r

(r ! 1)

S3

=

a 1-r

(r

1 1)

Identities

2. TRIGONOMETRY sin2A + cos2A = 1 sec2A = 1 + tan2A cosec2A = 1 + cot2A

Formulae for ABC

a sin A

=

b sin B

=

c sin C

a2 = b2 + c2 - 2bc cos A

T

=

1 2

bc sin A

? UCLES 2020

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3 1

y

24

- 2

- 1

0

4

x

The diagram shows the graph of y = p (x) , where p (x) is a cubic function. Find the two possible

expressions for p (x).

[3]

2 (a) Write down the amplitude of 1 + 4 cosb3xl.

[1]

(b) Write down the period of 1 + 4 cosb3xl.

[1]

(c) On the axes below, sketch the graph of y = 1 + 4 cosb3xl for -180? G x? G 180?. y 6 5 4 3 2 1

- 180

- 120

- 60

0

60

120

180 x

[3]

? UCLES 2020

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4

1

3

(a)

Write

p`qr2j3 `q3pj-1r3

in the form paqbrc, where a, b and c are constants.

[3]

2

1

(b) Solve 6x3 - 5x3 + 1 = 0.

[3]

? UCLES 2020

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5

4

It is given that

y

=

tan 3x sin x

.

(a)

Find

the

exact

value

of

d y dx

when

x

=

r 3

.

[4]

(b)

Hence

find

the

approximate

change

in

y

as

x

increases

from

r 3

to

r 3

+ h,

where

h

is

small.

[1]

(c) Given that x is increasing at the rate of 3 units per second, find the corresponding rate of change in

y

when

x

=

r 3

,

giving

your

answer

in

its

simplest

surd

form.

[2]

? UCLES 2020

0606/11/O/N/20

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