Tampines Prelim 2009 Am 1

8/14/2019 Tampines Prelim 2009 Am 1

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TAMPINES SECONDARY SCHOOL

PRELIMINARY EXAMINATION 2009

SECONDARY FOUR EXPRESS

ADDITIONAL MATHEMATICS 4038 / 1

PAPER 1

3 Sept 2008

2 hours

Additional Materials: Writing Paper

READ THESE INSTRUCTIONS FIRST

Write your name, class and register number 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.

Write your calculator model on the top right hand corner of your answer script.

Answer all questions.Write your answers on the separate writing papers provided.

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

question.The use of a scientific 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 partquestion.

The total number of marks for this paper is 80.

Setter: Ms CNFThis document consists of 6 printed pages and 0 blank pages.

Name:_________________________________( ) Class : Sec 4_____


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Mathematical Formulae

1. ALGEBRA

Quadratic Equation

For the equation 02 cbxax ,

a

acbbx

2

42

Binomial Theorem

nrrnnnnn bbar

nba

nba

naba

......

21

221 ,

where n is a positive integer and!)!(

!

rrn

n

r

n

2. TRIGONOMETRY

Identities

AAec

AA

AA

22

22

22

cot1cos

tan1sec

1cossin

BA

BABA

BABABA

BABABA

tantan1

tantan)tan(

sinsincoscos)cos(

sincoscossin)sin(

AAA cossin22sin

AAAAA2222 sin211cos2sincos2cos

A

AA 2

tan1

tan22tan

)(2

1sin)(

2

1sin2coscos

)(2

1cos)(

2

1cos2coscos

)(2

1sin)(

2

1cos2sinsin

)(2

1cos)(

2

1sin2sinsin

BABABA

BABABA

BABABA

BABABA

Formulae for ABC

Cc

Bb

Aa

sinsinsin

Abccba cos2222

Cab sin2

1


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1 Show that the exactvalue of cos120 + sin135 =2

1

2

1 [3]

2 Solve, for xand y, the simultaneous equations [5]

6448 23

y

x

273

181

12

y

x

3 Given that M =

32

41, find M-1 and hence, solve the simultaneous equations [5]

2p 8r+ 16 = 02p 3r= - 1

4 (i) Find )3ln(2 xxx

dx

d . [2]

(ii) Hence, find 4

1

ln dxxx . [4]

5 (i) Express)31(

67

xx

x

in partial fractions. [3]

(ii) Hence, or otherwise, find the gradient of the curve)31(

67xx

xy at the point [3]

where x= 2.


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6 A particle starts from a point Oand moves in a straight line with a velocity, vm/s,

given by 2322 ttv , where tseconds is the time after leaving O. Calculate

(i) the acceleration of the particle at the end of 3.5 seconds, [2]

(ii) the values of twhen the particle is instantaneously at rest, [3]

(iii) the total distance travelled by the particle after 3.5 seconds. [4]

7 The equation of a curve isx

xy

sin1

cos3

. Find the x coordinate, where 0 x , [5]

of the point at which the tangent to the curve is parallel to the line y= 9.

8 (a) Given that5

4sin A ,

13

12cos B and that A and Bare in the same [5]

quadrants, find each of the following without the use of calculators:

(i) Atan (ii) )sin( BA (iii) B2

1sec

(b) Solve the equation 03cos2sin4sin xxx for 0 < x< 2. [4]

9 The line 3x 2y 1 = 0 intersects the curve 9x2 + y= 7 at points A and B. Find

(i) the coordinates of A and B, [3]

(ii) the distance AB. [2]

10 (a) Find the range of values of cfor which cxx 93 2 > 2. [3]

(b) Find the range of values of kfor which the equation kxkxx 32 will have [3]real roots.


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11 (a) Find the first three terms in the expansion of

62

xx . Hence, find the [4]

coefficient of x4 in the expansion of

6

2 2)32(

xxx .

(b) Find the term independent of x, in the expansion of

8

5

3

4

12

xx . [4]

12 [4]

Variables xand yare related by the equation xyqypx 32 . When a graph of

y

1against

x

1is drawn, the resulting line has a gradient of 2.5, and passes

through (0, 4). Calculate the value of pand of q.

(0, 4)


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A diagram above shows a piece of grassland, made up of a rectangle and a quadrant.

The length and breadth of the rectangle is 4xm and ym respectively.The centre of the quadrant, Ois the midpoint of the length of the rectangle.Given that the perimeter of the grassland is 8 m,

(i) show that the area of the grassland is given by the formula [4]221616 xxxA .

Given that xcan vary,

(ii) find the stationary value of A, [4]

(iii) determine whether this stationary value is a maximum or minimum. [1]

End of paper

y

4x

O

Tampines Prelim 2009 Am 1

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