SULIT 3472/1

SEKTOR SEKOLAH BERASRAMA PENUHKEMENTERIAN PELAJARAN MALAYSIA

PEPERIKSAAN AKHIR TAHUN TINGKATAN 4 2010

This question paper consists of 13 printed pages

[ Lihat sebelah3472/1 SULIT

Kod Pemeriksa

QuestionFull

MarksMarks

Obtained1 22 33 44 25 36 37 28 39 410 311 312 413 414 415 316 417 318 419 320 321 422 223 324 325 4

TOTAL 80

Name : ………………..……………

Form : ………………………..……

3472/1Additional MathematicsPaper 1Oct 20102 hours

ADDITIONAL MATHEMATICSPaper 1

Two hours

DO NOT OPEN THIS QUESTION PAPER UNTIL INSTRUCTED TO DO SO

1 This question paper consists of 25 questions.

2. Answer all questions. 3. Give only one answer for each question.

4. Write your answers clearly in the spaces provided in the question paper.

5. Show your working. It may help you to get marks.

6. If you wish to change your answer, cross out the work that you have done. Then write down the new answer.

7. The diagrams in the questions provided are not drawn to scale unless stated.

8. The marks allocated for each question and sub-part of a question are shown in brackets.

9. A list of formulae is provided on pages 2 to 3.

10. A booklet of four-figure mathematical tables is provided..11 You may use a non-programmable scientific calculator.

12 This question paper must be handed in at the end of the examination .

SULIT 3472/2

The following formulae may be helpful in answering the questions. The symbols given are the ones commonly used.

ALGEBRA

1

2 am an = a m + n

3 am an = a m n

4 (am) n = a nm

5 loga mn = log am + loga n

6 loga = log am loga n

7 log a mn = n log a m

8 logab =

9 Tn = a + (n 1)d

10 Sn =

11 Tn = ar n 1

12 Sn = , (r 1)

13 , <1

CALCULUS

1 y = uv ,

2 , ,

3

4 Area under a curve

= dx or

= dy

5 Volume generated

= dx or

= dy

3472/2 SULIT

2

5 A point dividing a segment of a line

( x,y) =

6 Area of triangle =

1 Distance =

2 Midpoint

(x , y) = ,

3

4

GEOMETRY

SULIT 3472/1

STATISTICS

[ Lihat sebelah3472/1 SULIT

1 Arc length, s = r

2 Area of sector , L =

3 sin 2A + cos 2A = 1

4 sec2A = 1 + tan2A

5 cosec2 A = 1 + cot2 A

6 sin 2A = 2 sinA cosA

7 cos 2A = cos2A – sin2 A = 2 cos2A – 1 = 1 – 2 sin2A

8 tan 2A =

TRIGONOMETRY

9 sin (A B) = sinA cosB cosA sinB

10 cos (A B) = cosA cosB sinA sinB

11 tan (A B) =

12

13 a2 = b2 + c2 – 2bc cos A

14 Area of triangle =

3

SULIT 3472/1

Answer all questions.

3472/1 SULIT

1 =

2 =

3 = =

4 = =

5 m =

6

7

8

9

10 P(A B)=P(A)+P(B)-P(A B)

11 p (X=r) = , p + q = 1

12 Mean µ = np

13

14 z =

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SULIT 5 3472/1

1 Diagram 1 shows the relations between two sets of number.

(a) State the object of 9,

(b) Represent the relation by a set of ordered pairs.

[ 2 marks ]

Answer : (a) ……………………..

(b) ……………………...

2 Given the function and . Find (a) ,

(b) g (x) [ 3 marks]

Answer : (a) ……………………..

(b) ……………………...

3 Diagram 2 shows the function where a , b and k are constants.

Lihat Sebelah3472/1 SULIT

34

2

23

1

1

3

5

9

8

7

DIAGRAM 1

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SULIT 6 3472/1

Find (a) the value of k

(b) the values of a and of b [ 4 marks ]

Answer : (a) ...………………………......

(b)..............................................

4 Form the quadratic equation which has the roots 2 and . Give your answer in

the form ax2 + bx + c = 0, where a, b and c are constants.[2 marks]

Answer : .........…………………

5 Given that the quadratic equation (p + 1)x 2 = 3x 4 has two equal roots. Find the value of p.

[3 marks]

Answer : ……………………..

6 Given the roots of 3x2 – 4x + 5 = 0 are and . Form a quadratic equation with roots and 3 +1.

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3

5

4

3

2

4

x

9

62

1

h (x)

DIAGRAM 2

SULIT 7 3472/1

[3 marks]

Answer : …….............................

7 Find the range of values of x for which 2x2 + 5x – 12 < 0.[2 marks]

Answer : ………………………...

8

Answer : (a) …….............................

(b) ....................................

(c) ....................................

9 The graph of the quadratic function f(x) = x2 – 4mx +2 – 7m touches the x – axis at two points. Find the range of values of m.

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3

6

243

7

y

x

DIAGRAM 3

4 ( 6, 4 )

Diagram 3 shows the graph of the function y = (x p)2 -5, where p is a constant. Find

(a) the value of p, (b) the equation of the axis of

symmetry,(c) the coordinates of the

minimum point. [ 3 marks]

3

86

O

SULIT 8 3472/1

[4 marks]

Answer : ……..……...……….....

10 Express 3 ( 2n ) + 7( ) in the simplest form. [3 marks]

Answer : ……………...……….....

11 Solve the equation = .

[3 marks]

Answer : …...…………..………...

12 Solve the equation .[4 marks]

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3

10

43

9

3

11

Straight line JK : y = (4+p)x+ k

Straight line RS :

where p and k are constants.

SULIT 9 3472/1

Answer : ……………...……….....

13 Given log 2 m = x , and log 5 m = y, express log m 80 in terms of x and y. [4 marks]

Answer : …………...……….....

14 The following information refers to the equation of two straight lines, JK and RS which are perpendicular to each other.

Express k in terms of p. [4 marks]

Answer : ………..………..........

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4

14

4

13

4

12

SULIT 10 3472/1

15 Given that P ( 3 , 6 ) and Q ( 9 , 8 ). Find the equation of a straight line with gradient

that passes through the midpoint of PQ.

[3 marks]

Answer : ........................................

16 A point P moves such that its distance from two fixed points, A(3 ,2) and B ( 1, 4), are in the ratio of PA : PB = 4 : 3. Find the equation of locus P.

.

[4 marks]

Answer : .....................................

17 A set of data consists of four numbers. The sum of the numbers, 12k and the sum

of the squares of the numbers, = 100. Express the variance in terms of k.

[3 marks]

Answer : …...…………..……..…...

18 A set of positive integers 1, m – 1, 6 and 8 is in ascending order. Find the value of m if

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3

17

43

16

3

15

SULIT 11 3472/1

(a) the mode is 1, (b) the mean is 4, (c) the median is 5.

[4 marks]

Answer : (a) .…………..……..…...

(b) ....................................

(c) ....................................

19 Diagram 4 shows a semicircle OPQR with centre O.

Given that the radius is 3 cm and the perimeter of sector QOR is 7.55 cm . Find the value of .

[3 marks]

Answer : …...…………..……..…...

Lihat Sebelah3472/1 SULIT

Q

P RO

DIAGRAM 4

34

19

43

18

3 cm

rad

SULIT 12 3472/1

20 Diagram 5 shows a sector OPQ with centre O.

Given that the area of the sector OPQ is 64 cm2 and OPQ = 2 rad. Find the length of the arc PQ. (Use = 3.142)

[3 marks]

Answer : …...…………..……..…...

21 Diagram 6 shows a sector MTKR with centre T.

Given that the radius of the sector is 5 cm and R is the midpoint of MK . Find the perimeter of the shaded region.

[Use ] [4 marks]

Answer : …...…………..……..…...

3472/1 SULIT

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OP

2 rad

DIAGRAM 5

4

21

3

20

T

M K

5 cm74°

DIAGRAM 6

R

4 cm

Q

SULIT 13 3472/1

22 Given that , find (x).

[ 2 marks]

Answer : …...…………..……..…...

23 The curve y = 2x2 – 5x + 1 has a gradient 3 at the point Q . Find the coordinates of the point Q.

[3 marks]

Answer : …...…………..……..…...

24 Find the equation of the tangent to the curve y = x2 ( x – 4) at the point ( 3, 9 ).[3 marks]

Answer : …...…………..……..…...

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3

24

23

22

3

23

SULIT 14 3472/1

25 It is given that y = u – u 2 and x = 2u 3. Find in terms of x.

[4 marks]

Answer : …...…………..……..…...

END OF THE QUESTION PAPER

3472/1 SULIT

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