Add Maths F4 Year End Exam 2007 SBP P1 Ques & Ans

8/3/2019 Add Maths F4 Year End Exam 2007 SBP P1 Ques & Ans

1/19

SULIT 3472/1

SEKTOR SEKOLAH BERASRAMA PENUHKEMENTERIAN PELAJARAN MALAYSIA

PEPERIKSAAN AKHIR TAHUN TINGKATAN 4 2007

This question paper consists of 13 printed pages

Kod Pemeriksa

QuestionFull

Marks

Marks

Obtained

1 2

2 3

3 44 2

5 3

6 3

7 2

8 3

9 4

10 3

11 3

12 4

13 4

14 4

15 3

16 4

17 3

18 4

19 3

20 3

21 4

22 2

23 3

24 3

25 4

TOTAL 80

Name : ..

Form : ..

3472/1

Additional Mathematics

Paper 1

Oct 2007

2 hours

ADDITIONAL MATHEMATICS

Paper 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 scientificcalculator.

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

the examination .


2/19

SULIT 3472/22

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

commonly used.

ALGEBRA

12

42

b b acxa

2 am an = a m + n

3 am an = a m n

4 (am

)n

= anm

5 loga mn = log am + loga n

6 loga n

m

= log am loga n

7 log a mn

= n log a m

8 logab =a

b

c

c

loglog

9 Tn = a + (n 1)d

10 Sn = ])1(2[2

dnan

11 Tn = arn 1

12 Sn =r

ra

r

rann

1

)1(

1

)1(, (r 1)

13r

aS

1

, r


3/19

SULIT 3472/1

STATISTICS

1 Arc length, s = r

2 Area of sector , L =21

2r

3 sin2A + cos

2A = 1

4 sec2A = 1 + tan

2A

5 cosec2

A = 1 + cot2

A

6 sin 2A = 2 sinA cosA

7 cos 2A = cos2A sin

2A

= 2 cos2A 1

= 1 2 sin2A

8 tan 2A =A

A2

tan1

tan2

TRIGONOMETRY

9 sin (A B) = sinA cosB cosA sinB

10 cos (A B) = cosA cosB sinA sinB

11 tan (A B) =BtanAtan

BtanAtan

1

12C

c

B

b

A

a

sinsinsin

13 a2

= b2

+ c2

2bc cos A

14 Area of triangle = Cab sin2

1

1 x =N

x

2 x = f

fx

3 =N

xx 2)(= 2

2

xN

x

4 =

f

xxf2

)(= 2

2

xf

fx

5 m = Cf

FN

Lm

2

1

6 1

0

100Q

IQ

71

11

w

IwI

8

)!(

!

rn

nPr

n

9!)!(

!

rrn

nC

r

n

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

11 p (X=r) = rnrrn qpC

, p + q = 1

12 Mean = np

13 npq

14 z =

x

3


4/19

SULIT 4 3472/1

Answer all questions.

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 13 xx:f and 59 xx:gf . Find

(a) )(1 xf ,

(b) g (x)

[ 3 marks]

Answer: (a) ..

(b) ...

3

2

2

1

1

3

5

9

8

7

DIAGRAM 1

For

xaminers

use only


5/19

SULIT 5 3472/1

3 Diagram 2 shows the function kx,x

baxx:h where a , b and kare constants.

Find

(a) the value of k

(b) the values ofa and of b

[ 4 marks ]

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

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

4 Form the quadratic equation which has the roots 2 and41 . 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)x2

= 3x 4 has two equal roots.Find the value of p.

[3 marks]

Answer: ..

5

3

4

x

9

62

1

h (x)

DIAGRAM 2

Fo

examin

use o


6/19

SULIT 6 3472/1

6 Given the roots of 3x2

4x + 5 = 0 are and . Form a quadratic equation with roots

13 and 3 +1.

[3 marks]

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

7 Find the range of values ofx for which 2x2

+ 5x 12 < 0.

[2 marks]

Answer: ...

8

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

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

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

For

xaminers

use only

3

6

2

7

y

x

DIAGRAM 3

4 ( 6, 4 )

Diagram 3 shows the graph of the

function y = (x p)2 -5, where p isa constant.

Find

(a) the value ofp,

(b) the equation of the axis of

symmetry,

(c) the coordinates of the

minimum point.

[ 3 marks]

3

8

O


7/19

SULIT 7 3472/1

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 ofm.

[4 marks]

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

10 Express 12 n 3 ( 2n ) + 7( 12 n ) in the simplest form.[3 marks]

Answer: ........

11 Solve the equation 24 x =x8

2.

[3 marks]

Answer: ........

For

examin

use on

10

9

11


8/19


9/19

SULIT 9 3472/1

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

3

2that passes through the midpoint ofPQ.

[3 marks]

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

16 A point P moves such that its distance from two fixed points, A(3 ,2) and B ( 1, 4), arein 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, x 12kand the sum

of the squares of the numbers, 2x = 100. Express the variance in terms ofk.[3 marks]

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

For

examin

use on

17

16

15


10/19

SULIT 10 3472/1

18 A set of positive integers 1, m 1, 6 and 8 is in ascending order.

Find the value ofm if

(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: ..........

For

xaminers

use only

Q

P RO

DIAGRAM 4

3

19

4

18

3 cm

rad


11/19

SULIT 11 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 lengthof 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 3.142 ][4 marks]

Fo

examin

use o

OP

2 rad

DIAGRAM 5

2

20

T

M K

5 cm74

DIAGRAM 6

R

4 cm

Q


12/19

SULIT 12 3472/1

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

22 Given that2

31

1

)x()x(f

, find f (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: ..........

For

aminers

se only

3

24

2

22

3

23


13/19

SULIT 13 3472/1

25 It is given that y = u u2

and x = 2u 3. Finddx

dyin terms ofx.

[4 marks]

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

END OF THE QUESTION PAPER

Fo

exami

use o

25


14/19

3472/1 2007 Copyright SBP Sector, Ministry of Education, Malaysia

SULIT

SULIT

3472/1

Additional

Mathematics

Paper 1

Okt

2007

SEKOLAH BERASRAMA PENUH

KEMENTERIAN PELAJARAN MALAYSIA

PEPERIKSAAN AKHIR TAHUN

TINGKATAN 4

2007

ADDITIONAL MATHEMATICS

Paper 1

MARKING SCHEME

This marking scheme consists of 6 printed pages


15/19


16/19

3

Number Solution and marking schemeSub

MarksFull

Marks

72

34 x

(2x 3)(x + 4 ) < 0 or2

B1

2

8 (a) p = 3

(b) x = 3

(c) ( 3 , - 5 )

1

1

1

3

92m ,

4

1m

(4m 1 )( m + 2 ) > 0 or

4m2

+ 7m 2 > 0

(-4m)2

4 (1)(2 7m) > 0

4

B3

B2

B1

4

10 5 ( 2n 1

)

2n

2

732

2n

21

3 ( 2n

) + 7 ( 2n

2- 1

)

3

B2

B1

3

11x =

5

3

2x + 4 = 1 3x

22(x+2)

3

B2

B1

3

-423

2

4

1


17/19

4


MarksFull

Marks

12 x = 8

6

3

x

x

4

log x3

log x = 64 or logx3

log x = 6 log 2

82

2

log

xlogor 2 log22 or 2 log88

4

B3

B2

B1

4

13

yx

14

4 logm 2 + logm 5

logm 24 + logm 5

22

m

m

log

mlogmlog or

55

m

m

log

mlogmlog or

mlog

log

2

2 80 or

mlog

log

5

8 80 or log m( 24

x 5)

4

B3

B2

B1

4

14p

pk 4

14

p

kp

p

k and 4 + p

p

k or 4 + p

4

B3

B2

B1

4

15 3y = 2x + 15

y 7 =3

2( x 3 )

Mid point PQ = ( 3 , 7 )

3

B2

B1

3


18/19

5


MarksFull

Marks

16 5x2

+ 5y2

+ 62x 68y + 49 = 0

9 [ x2

+ 6x + 9 + y2

4y + 4 ] = 4 [ x2

2x + 1 + y2

+ 8y + 16 ]

3 22 23 )y()x( = 4 22 41 )y()x(

3PA = 4PB

4

B3

B2

B1

4

17 25 9k 2

2100 12

4 4

k

n = 4

3

B2

B1

3

18 (a) 2

(b) 2

44

8611

)m(

(c) 5

1

2

B1

1

4

19 = 0.5167

5513 .

QR = 1.55

3

B2

B1

3

20 16

r = 8

642

1 2 r

3B2

B1

3

21 Perimeter = 12.4586

Perimeter = 6.4586 + 6

Arc MK = 5 ( 1. 2917)

1.2917 rad

4

B3

B2

B1

4


19/19

6


MarksFull

Marks

22331

6

)x()x(f

)()x(f 3312 3

2

B1

2

23 Q ( 2, - 1)

4x 5 = 3

3dx

dyor 54 x

dx

dy

3

B2

B1

3

24 y = 3x 18

y + 9 = 3 ( x 3)

xxdx

dy83

2

3

B2

B1

3

25

2

2 x

dx

dy

dx

dy

2

2321

x

))(u(dx

dy

2

121

udx

dy21 or 2

du

dxor u =

2

3x

4

B3

B2

B1

4

Add Maths F4 Year End Exam 2007 SBP P1 Ques & Ans

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