IGCSE AMaths y13 Sp 1

8/10/2019 IGCSE AMaths y13 Sp 1

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UCLES 2012 [Turn over

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONSInternational General Certificate of Secondary Education

ADDITIONAL MATHEMATICS 0606/01

Paper 1 For Examination from 2013

SPECIMEN PAPER

2 hoursCandidates answer on the Question Paper.

Additional Materials: Electronic calculator

READ THESE INSTRUCTIONS FIRST

Write your Centre number, candidate number and name on all the work you hand in.

Write in dark blue or black pen.

You may use a pencil for any diagrams or graphs.

Do not use staples, paper clips, highlighters, glue or correction fluid.

Answer allthe questions.

Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles indegrees, unless a different level of accuracy is specified in the question.

The use of an electronic calculator is expected, where appropriate.

You are reminded of the need for clear presentation in your answers.

At the end of the examination, fasten all your work securely together.

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 80.

www.Xtrem

ePapers.com


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UCLES 2012 0606/01/SP/13

Mathematical Formulae

1.

ALGEBRA

Quadratic Equation

For the equation ax2+ bx+ c= 0,

a

acbbx

2

42

= .

Binomial Theorem

(a+ b)n= an+

1

n an1b+

2

n an2b2+ +

r

n anrbr+ + bn,

where nis a positive integer and

r

n

=!)!(

!

rrn

n

.

2.

TRIGONOMETRY

Identities

sin2A+ cos2A= 1.

sec2A= 1 + tan

2A.

cosec2A= 1 + cot2A.

Formulae for ABC

C

c

B

b

A

a

sinsinsin== .

a2= b2+ c

2 2bccosA.

=2

1 bcsinA.


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UCLES 2012 0606/01/SP/13 [Turn over

For

Examiner's

Use

1 Shade the region corresponding to the set given below each Venn diagram.

BA

C

BA

C

)( CBA )( CBA

BA

C

)'( CBA [3]

2 Find the set of values ofxfor which (2x+ 1)2> 8x+ 9. [4]


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For

Examiner's

Use

3 Prove thatA

A

A

A

sin

cos1

cos1

sin ++

+

2cosecA. [4]


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For

Examiner's

Use

4 A function f is such that f(x) = ax3+ bx

2+ 3x+ 4. When f(x) is divided by x 1, the remainder

is 3. When f(x) is divided by 2x+ 1, the remainder is 6. Find the value of aand of b. [5]

5 (i) Solve the equation 2t= 9 +t

5. [3]

(ii) Hence, or otherwise, solve the equation 2x 21

= 9 + 5x 21

. [3]


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For

Examiner's

Use

6 Given that a= 5i 12jand that b=pi+j, find

(i) the unit vector in the direction of a, [2]

(ii) the values of the constantspand qsuch that qa+ b= 19i 23j. [3]


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For

Examiner's

Use

7 (i) Express 4x2 12x+ 3 in the form (ax+ b)

2+ c, where a, band care constants and a> 0.

[3]

(ii) Hence, or otherwise, find the coordinates of the stationary point of the curve y= 4x2 12x+ 3.[2]

(iii) Given that f(x) = 4x2 12x+ 3, write down the range of f. [1]


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For

Examiner's

Use

8 A curve is such that2

2

d

d

x

y= 4e2x. Given that

x

y

d

d= 3 whenx= 0 and that the curve passes through

the point (2, e4

), find the equation of the curve. [6]


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For

Examiner's

Use

9 (i) Find, in ascending powers ofx, the first 3 terms in the expansion of (2 3x)5. [3]

The first 3 terms in the expansion of (a + bx)(2 3x)5 in ascending powers of x are64 192x+ cx

2.

(ii) Find the value of a, of band of c. [5]


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For

Examiner's

Use

10 (a) Functions f and g are defined, forxo, by

f(x) = 3 x,

g(x) =2+x

x

, wherex 2.

(i) Find fg(x). [2]

(ii) Hence find the value ofxfor which fg(x) = 10. [2]

(b) A function h is defined, forxo, by h(x) = 4 + lnx, where x> 1.

(i) Find the range of h. [1]

(ii) Find the value of h1(9). [2]


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For

Examiner's

Use

(iii) On the same axes, sketch the graphs ofy= h(x) andy= h1

(x). [3]


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For

Examiner's

Use

11 Solve the following equations.

(i) tan2x 3cot2x, for 0


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For

Examiner's

Use

(iii) sec(z+2

) = 2, for 0


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For

Examiner's

Use

12 A curve has equation y=1

2

+x

x

.

(i) Find the coordinates of the stationary points of the curve. [5]


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For

Examiner's

Use

The normal to the curve at the point where x= 1 meets thex-axis at M. The tangent to the curve atthe point wherex= 2 meets they-axis atN.

(ii) Find the area of the triangle MNO, where Ois the origin. [6]


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University of Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University ofCambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.

UCLES 2012 0606/01/SP/13

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