38589927 Ramalan Add Maths 2010 Edisi Kristal

8/8/2019 38589927 Ramalan Add Maths 2010 Edisi Kristal

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NO.KAD PENGENALAN/I.C NUMBER

- -

ANGKA GILIRAN/INDEX NUMBER

Examiners CodeQuestion Full Marks

Marks Acquired1 22 43 34 35 46 37 48 49 3

10 311 212 413 314 315 316 417 318 219 320 321 4

22 323 424 325 3

Total 80

JANGAN BUKA KERTAS SOALAN INI

SEHINGGA DIBERITAHU

1. Tuliskan angka giliran dan nombor kad pengenalan anda pada ruang yang disediakan.

Write your index number and I.C. number in thespace provided.

2. Calon dikehendaki membaca arahan di halaman 2dan halaman 3

Candidates are required to read the intructions on page 2 and 3

ADDITIONAL MATHEMATICSPaper 12 hours

KERTAS SOALAN RAMALAN 2010SIJIL PELAJARAN MALAYSIA

3472/1

Form FiveAdditional Mathematics

Paper 1March 2010

2 hours

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INFORMATION FOR CANDIDATES

1. This question paper consists of 25 questions.

2. Answer ALL questions.

3.

Give only ONE

answer for each question.

4. Write your answer 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 diagram 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 4 to 6.

10. You may use a non-programmable scientific calculator.

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


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ALGEBRA

1 a

acbb x

242 = 8 a

bb

c

ca log

loglog =

2 a m x a n = a m + n 9 Tn = a + (n -1)d

3 a m a n = a m n 10 S n = [ ]2 ( 1)2n

a n d +

4 ( a m )n = a m n 11 T n =1nar

5 nmmn aaa logloglog += 12( 1) (1 )

, 11 1

n n

n

a r a r S r

r r

= =

6 nmnm

aaa logloglog = 13 , 11aS r

r =


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STATISTICS

1 N x

x=

8!

( )!n

r n

P n r

=

2 f fx

x =

9!

( )! !n

r n

C n r r

=

3( ) 222 x

N x

N x x ==

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

4( ) 222 x

f fx

f x x f

=

=

11 P(X = r) = , 1n r n r r C p q p q + =

5 C f

F N Lm

m

+= 2

1

12 Mean = np

6 1

0100

Q I

Q=

13 npq =

7i

ii

W I W

I = 14 X Z

=


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GEOMETRY

1 Distance = 2 22 1 2 1( ) ( ) x x y y +

4 Area of a triangle =

12 1 2 2 3 3 1 2 1 3 2 1 3

( ) ( ) x y x y x y x y x y x y+ + + +

2 Midpoint = ++ 2,

22121 y y x x

5. 22~

y xr +=

3 A point dividing a segment of a line

(x , y ) =

++

++

nmmyny

nmmxnx 2121 ,

622

~~

~

^

y x

j yi xr

+

+=


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TRIGONOMETRY

1 Arc length, s =r 8 sin( ) sin cos cos sin A B A B A B =

2 Area of a sector, 212

A r = 9 cos( ) cos cos sin sin A B A B A B = m

3 . 2 2sin cos 1 A A+ = 10

tan tantan( )

1 tan tan B

A B B

=m

4 2 2sec 1 tan A A= +

112

2tantan2

1 tan A

A A

=

5 2 2cos 1 cotec A A= + 12sin sin sin

a b c A B C

= =

6 sin 2A = 2 sin A cos A 13 2 2 2 2 cosa b c bc A= +

7 cos 2A = 2 2cos sin A A

= 22cos 1 A

= 21 2sin A

14 Area of triangle = 1 sin2

ab C


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- -



Marks Acquired1 22 43 34 35 46 37 48 49 3

10 311 212 413 314 315 316 417 318 219 320 321 4

22 323 424 325 3

Total 80


SEHINGGA DIBERITAHU







3472/1


Paper 1March 2010

2 hours

MATHS Catch


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3.

Give only ONE





answer.







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ALGEBRA

1 a

acbb x

242 = 8 a

bb

c

ca log

loglog =

2 a m x a n = a m + n 9 Tn = a + (n -1)d

3 a m a n = a m n 10 S n = [ ]2 ( 1)2n

a n d +

4 ( a m )n = a m n 11 T n =1nar


, 11 1

n n

n

a r a r S r

r r

= =

6 nmnm


r =


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4

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STATISTICS

1 N x

x=

8!

( )!n

r n

P n r

=

2 f fx

x =

9!

( )! !n

r n

C n r r

=

3( ) 222 x

N x

N x x ==

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

4( ) 222 x

f fx

f x x f

=

=

11 P(X = r) = , 1n r n r r C p q p q + =

5 C f

F N Lm

m

+= 2

1

12 Mean = np

6 1

0100

Q I

Q=

13 npq =

7i

ii

W I W

I = 14 X Z

=


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GEOMETRY

1 Distance = 2 22 1 2 1( ) ( ) x x y y +


12 1 2 2 3 3 1 2 1 3 2 1 3

( ) ( ) x y x y x y x y x y x y+ + + +

2 Midpoint = ++ 2,

22121 y y x x

5. 22~

y xr +=


(x , y ) =

++

++

nmmyny

nmmxnx 2121 ,

622

~~

~

^

y x

j yi xr

+

+=


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TRIGONOMETRY




3 . 2 2sin cos 1 A A+ = 10

tan tantan( )

1 tan tan B

A B B

=m

4 2 2sec 1 tan A A= +

112

2tantan2

1 tan A

A A

=


a b c A B C

= =



= 22cos 1 A

= 21 2sin A


ab C


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1

TIPS

FOKUS A+

e-DISI Kristal

Answer all questions .

1.

2.

3.

4.

2

1

[2 marks]

Answer:

2

1

[2 marks]

Answer:

2

1

[2 marks]

Answer:

2

1

[2 marks]

Answer:

Functions

Functions

Functions

Quadratic Equation


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5.

6.

7.

2

1

[2 marks]

Answer:

2

1

[2 marks]

Answer:

2

1

[2 marks]

Answer:

Quadratic Function

Quadratic Functions

Indices and Logarithms


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8.

9.

10.

11.

2

1

[2 marks]

Answer:

2

1

[2 marks]

Answer:

2

1

[2 marks]

Answer:

2

1

[2 marks]

Answer:

Indices and Logarithms

Progression

Progressions

Progression


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12.

13. 2

1

[2 marks]

Answer:

2

1

[2 marks]

Answer:

Linear law

Coordinate Geometry


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14.

15.

16.

2

1

[2 marks]

Answer:

2

1

[2 marks]

Answer:

2

1

[2 marks]

Answer:

Coordinate Geometry

Vector

Vector


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17.

18.

19. 2

1

[2 marks]

Answer:

2

1

[2 marks]

Answer:

2

1

[2 marks]

Answer:

Trigonometric Functions

Circular Measures

Differentiation


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20.

21.

22.

23.

2

1

[2 marks]

Answer:

2

1

[2 marks]

Answer:

2

1

[2 marks]

Answer:

2

1

[2 marks]

Answer:

Differentiations

Statistics

Permutations andCombinations

Integrations


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24.

25.

2

1

[2 marks]

Answer:

2

1

[2 marks]

Answer:

Probability

Probability Distributions


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e-DISI KRISTAL

FORECAST PAPER

SIJIL PELAJARAN MALAYSIA (SPM)

MARKING SCHEME

ADDITIONAL MATHEMATICS

PAPER 1

2010

NOTE

This marking scheme serves as a guide only. Other method which are equivalent and

Suitable may also be adapted and used in the awarding of marks.

THANK YOU


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ANSWER 1 FUNCTIONS ANSWER 5 QUADRATIC FUNCTIONS

ANSWER 2 FUNCTIONS

ANSWER 3 FUNCTIONS

ANSWER 4QUADRATIC EQUATIONS

ANSWER 6 QUADRATIC FUNCTIONS

ANSWER 7 INDICES AND LOGARITHMS

ANSWER 8 INDICES AND LOGARITHMS


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ANSWER 9 PROGRESSION ANSWER 12 LINEAR LAW

ANSWER 13 COORDINATE GEOMETRYANSWER 10 PROGRESSIONS

ANSWER 11 PROGRESSIONSANSWER 14 COORDINATE GEOMETRY


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ANSWER 15 VECTOR

ANSWER 16VECTOR

ANSWER 17 TRIGONOMETRIC FUNCTIONS

ANSWER 18 CIRCULAR MEASURES

ANSWER 19 DIFFERENTATIONS

ANSWER 20 DIFFERENTATIONS


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ANSWER 21 INTEGRATIONS ANSWER 24 PROBABILITY

ANSWER 22 STATISTICS ANSWER 25 PROBABILITY DISTRIBUTIONS

ANSWER 23 PERMUATATION & COMBINATIONS


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- -



Marks Acquired123456789

101112131415

Total 100


SEHINGGA DIBERITAHU







3472/1


Paper 2March 2010

2 hours

MATHS Catch


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3.

Give only ONE





answer.







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e-DISI Kristal

3

FOKUS A+

Sulit

MATHS Catch

ALGEBRA

1 a

acbb x

242 = 8 a

bb

c

ca log

loglog =

2 a m x a n = a m + n 9 Tn = a + (n -1)d

3 a m a n = a m n 10 S n = [ ]2 ( 1)2n

a n d +

4 ( a m )n = a m n 11 T n =1nar


, 11 1

n n

n

a r a r S r

r r

= =

6 nmnm


r =


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e-DISI Kristal

4

FOKUS A+

Sulit

MATHS Catch

STATISTICS

1 N x

x=

8!

( )!n

r n

P n r

=

2 f fx

x =

9!

( )! !n

r n

C n r r

=

3( ) 222 x

N x

N x x ==

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

4( ) 222 x

f fx

f x x f

=

=

11 P(X = r) = , 1n r n r r C p q p q + =

5 C f

F N Lm

m

+= 2

1

12 Mean = np

6 1

0100

Q I

Q=

13 npq =

7i

ii

W I W

I = 14 X Z

=


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FOKUS A+

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MATHS Catch

GEOMETRY

1 Distance = 2 22 1 2 1( ) ( ) x x y y +


12 1 2 2 3 3 1 2 1 3 2 1 3

( ) ( ) x y x y x y x y x y x y+ + + +

2 Midpoint = ++ 2,

22121 y y x x

5. 22~

y xr +=


(x , y ) =

++

++

nmmyny

nmmxnx 2121 ,

622

~~

~

^

y x

j yi xr

+

+=


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6

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MATHS Catch

TRIGONOMETRY




3 . 2 2sin cos 1 A A+ = 10

tan tantan( )

1 tan tan B

A B B

=m

4 2 2sec 1 tan A A= +

112

2tantan2

1 tan A

A A

=


a b c A B C

= =



= 22cos 1 A

= 21 2sin A


ab C


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MAT HS Catch Catch Catch Catch

KERTAS SOALAN RAMALAN ADD MATHS SPM 2010

Section A

[40 marks ]

Answer All Question

**PERHATIAN:Analysis soalan dibekalkan sebagai rujukan untuk membantu pelajar melihat trend soalan dengan lebihbaik.Diharapkan pelajar dapat mengenal pasti apakah soalan yang pernah keluar,biasa keluar dan akan keluar.Janganabaikan Analisis yang kami berikan ini**

SPM06 SPM07 SPM08 SPM09

12 =+ y x and52 22 =++ xy y x

032 = y x and

09102 2 =++ y x x 043 =+ y x and

0402 = xy x

13 = pk and

02 =+ k pk p


Tidak keluar Tidak keluar Bahagian A (Q2-7 marks) Tidak keluar

Solve the simultaneous equation 0832 =+ y x and 012 2 =++ x xy .Give your answer correct to foursignificant figures.

[5 marks ]

The diagram shows the graph of a quadratic function 42)( 2 = kx x x g .The graph has a maximum

point at P(-1,h) and intersects the g(x)-axis at point Q

(a) State the coordinates of Q (b) By using the method of completing the square, find the value of h and of k.

Find the range of values of x if 4)( > x g .

[6 marks ]

QUESTION 1 SIMULTANEOUS EQUATION Form 4

Analysis Simultaneous Equation

QUESTION 2 QUADRATIC FUNCTION Form 4

Q2-Analysis Quadratic Function


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Keluar Bahagian A Keluar Bahagian A Keluar Bahagian A Keluar Bahagian A


x y cos2= for 20 x

x y 2cos3= for 20 x

Prove x x

x2tan

sec2tan2

2=

x y 2cos

23

= for 23

0 x

The diagram shows the first three of a series of cylinders

The radius and height of each cylinder differ by 1 cm respectively from the radius and height of the prvious

cylinder.Find

(a) The volume of the 8th cylinder(b) Which cylinder has a curved surface area of 66 cm 2

[7 marks ]

(a) Prove that x x

2sintan1tan2

2=

+

(b) (i) Sketch the graph of x y 2sin= 20 x (ii)Hence, using the same axes, draw a suitable straight line to find the

number of solutions for the equation 1tan1tan2

2=

+

x xfor 20 x .State the number of solutions.

[8 marks ]

QUESTION 3 PROGRESSION Form 5

Q3-Analysis Progression

QUESTION 4 TRIGONOMETRIC FUNCTION Form 5

Q4-Analysis Trigonometric Function


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Bahagian A [8 marks] Bahagian A [6 marks] Bahagian A [6 marks] Tidak keluar


Bahagian A [7 marks] Bahagian B [10 marks] Bahagian A [7 marks] Bahagian A [8 marks]

A set of data consists of 12 numbers.The sum of the numbers is 96 and the sum of the squares of the numbers is 1200.

(a) Find the mean and variance of the 12 numbers(b) Another number is added to the set of data and the mean is increased by 1.Find

(i) The value of the number(ii) The standart deviation of the set of 13 numbers.

[6 marks ]

The diagram shows a triangle POQ.The point R lies on OP and the point T lies on PQ.The straight line QRintersects the straight line OT at point

(a) Given that 2:1: = RP OR , 1:2: = PT PQ and xOP 9= , yOQ 8= Express each of the following

vectors in terms of x and/or y

(i) QR

(ii) OT

(b) Given that OT hOS = and QRk QS = ,hence ,find the values of h and k. (c) Given that units x 2= , units y 3= and o POQ 90= , find PQ .

[8marks ]

QUESTION 5 STATISTICS Form 4

Q5-Analysis Statistics

QUESTION 6 VECTOR Form 5

Q6-Analysis Vector


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Keluar bahagian B Keluar bahagian A dan B Keluar bahagian B Keluar bahagian A dan B

SPM06 SPM07 SPM08 SPM091+= x pk y

Plot Graph againts x

k p

kx y += 22

Plot Graph againts x

xhk y 2=

Plot Graph againts x 1+=

x p

yk

Plot Graph againts

The diagram shows the curve 27 x y = and the straight line 12 = x y .

Find

(a) The coordinates of points A and B(b) the volume generated, in terms of ,when the shaded region is revolved through 360 0 about the y -axis

[10 marks ]

SECTION B[40 marks]

Answer four questions only

Table 1 shows experiment values of two variables x and y . Variables x and y are related by the equation

xhk

hx y += 22 where h and k are constants.

x 1 2 3.5 4 5

y 17.4 28 60 75.8 125

TABLE 1

a) Plot x y

against x by using a scale of 2 cm to 1 unit on the both axis. Hence, draw the line of best fit.

b) Use your graph from (a) to find the values of (i) h , (ii) k , (iii) y when x =2.5[10 marks ]

QUESTION 7 INTEGRATION Form5

Q7-Analysis Integration

QUESTION 8 LINEAR LAW Form 5

Q8-Analysis Linear Law

TIPS EXAMSoalan Ini Biasa akan Tan a 3 Perkara 1-Coordinate 2-Area shade Re ion 3-Volume Shade Re ion

y1

x1 y10log

x y y )1( + x


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Bahagian B (10 marks) Keluar Bahgian A -

(6 Markah)

Bahagian B (10 marks) Bahagian B (10 marks)


Keluar bahagian B sahaja Keluar bahagian B sahaja Keluar bahagian B sahaja Keluar bahagian B sahaja

9.The diagram shows a staright line PQR and KLM

Q is the midpoint of line PR and the equation of line PQR is 1232 = x y .(a) Find

(i)the coordinates of point Q (ii) the area of quadrrilateral OPQL

A point A moves in such a way that its distance from point P is equal to its distance from the y axis.Find theequation of the locus of A [10 marks ]

The diagram shows a circles AGEF with centre O and radius 10 cm.BGD is a tangent to the circle at G.Thestraight lines BO and DO intersect the circle at A and E respectively.OAGE is a rhombus.BCD is an arc of a circlewith centre O

Calculate

(a) The angle ,in terms of (b) The length in cm, of arc BCD (c) The area of the shade region .

[10 marks ]

QUESTION 9 COORDINATE GEOMETRY Form 4

Q9-Analysis Coordinate Geometry

QUESTION 10 CIRCULAR MEASURE Form 4

Q10-Analysis Circular Measure


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Bahagian B sahaja [10 marks] Bahagian B sahaja [10 marks] Bahagian B sahaja [10 marks] Bahagian B sahaja [10 marks]

[20 marks] Answer TWO questions

SPM06 SPM07 SPM08 SPM09Bahagian C sahaja [10 marks] Bahagian C sahaja [10 marks] Bahagian C sahaja [10 marks] Bahagian C sahaja [10 marks]

(a) In a survey carried out in a school, it is found that 18 out of 30 students like to read during their free time.If 10 students from that school are choosen at random,calculate the probability that

(i) Exactly 4 students like to read during their free time,(ii) At least 2 of the selected students like to read during their free

time

(b)The masses of fish from a pond follow a normal distribution with a mean of 600 g and a standard deviation of 20 g.

(i) A fish is chosen at random from the pond.Find the probability

that the fish is more than 625 g.

(ii) If 200 fish have masses between 575 g and 625 g, estimate the total number of fish in the pond.[10 marks ]

SECTION C

A particle moves in a straight line and passes through a fixed point, O, with a velocity of 20 m s -1 .Its

accelaration, a m s -2,t s after passing through O is given by t a 28 = .the particle stops after k s.

(a)Find

(i) the maximum velocity of the particle,(ii) the value of k.

(b) Sketch a velocity time graph of the motion of the particle for k t 0 .Hence, or otherwise, calculatethe total distance travelled during that period.

[10 marks ]

QUESTION 11 PROBABILITY Form 5

Q11-Analysis Probability

QUESTION 12 MOTION ALONG A STRAIGHT LINE Form 5

Q12-Analysis Motion along a Straight Line


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Bahagian C sahaja [10 marks] Bahagian C sahaja [10marks]

Bahagian C sahaja [10 marks] Bahagian C sahaja [10marks]


Bahagian C sahaja [10 marks] Bahagian C sahaja [10 marks] Bahagian C sahaja [10 marks] Bahagian C sahaja [10 marks]

The diagram shows a quadrilateral PQRS such that PQR is an acute angle.(a) Calculate

(i) PQR (ii) , PSR (iii) The area of quadrilateral PQRS

(b) A triangle PQR has the same measurements as those given for trianle PQR,that is, RQ = 8.4 cm ando PRQ 42' = ,but which is different in shape to triangle PQR.

(i) Sketch the triangle PQR(ii) State the size of R PQ ' [10 marks ]

QUESTION 14 LINEAR PROGRAMMING Form 5A private college offers two diploma courses,product design and Business Studies.the monthly fees for Product designand business studies courses are RM50 and RM70 per month.the enrolment of students is based on the followingconstraints:

I. : The total number of students is not more than 170II. : The number of students enrolled for product Design is not more than three times the number of students

enrolled for Business studies.III. : The number of students enrolled for Business studies exceeds twice the number of students enrolled for

Product Design at most by 20.

Given that there are x students enrolled for Product Design Course and y students enrolled for Bussiness Studies course(a) Write down three inequalities,other than 0 x and 0 y ,that satisfy all of the above conditions.(b) Hence, using scale of 2 cm to 20 students for both axes, construct and shade region R that satisfies all the above

conditions.(c) Based on your graph from (b), find

(i) The range of the number of students enrolled for Business Studies if the number of students enrolledfor Product Design is 60.

(ii) The maximum total monthly fees collected per month [10 marks ]

QUESTION 13 SOLUTION OF TRIANGLE Form 4

Q13-Analysis Solution of Triangle

Q14-Analysis Linear Programming


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Bahagian C sahaja [10 marks] Bahagian C sahaja [10 marks] Bahagian C sahaja [10 marks] Bahagian C sahaja [10 marks]

QUESTION 15 INDEX NUMBER Form 4

The table shows the prices and the price indices for 4 ingredients, A,B,C and D,used in making biscuits of aparticular kind.the diagram shows a pie chart which represents the relative amount of the ingredients A,B,C andD used in making these biscuuits

(a) Find the values of x,y,z(b)

(i) Calculate the composite index for the cost of making these biscuits in the year 2004 based onthe year 2000.

(ii) Hence,calculate the corespondng cost of making these biscuits in the year 2000 if the cost in theyear 2004 was RM30.50

(c) The cost of making these biscuits is expected to increased by 40% from the year 20074 to the year2010.Find the expected cpmposite index for the year 2010 based on the year 2000

[10 marks ]

Q15-Analysis Index Number


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FORECAST PAPER

SIJIL PELAJARAN MALAYSIA (SPM)

MARKING SCHEME

ADDITIONAL MATHEMATICS

PAPER 2

2010NOTE

This marking scheme serves as a guide only. Other method which are equivalent and

Suitable may also be adapted and used in the awarding of marks.

THANK YOU


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ANSWER 1 SIMULATANEOUS EQUATION ANSWER 2 QUADRATIC FUNCTIONS


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ANSWER 3 PROGRESSION ANSWER 4 TRIGONOMETRIC FUNCTION


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ANSWER 5 STATISTIC ANSWER 6 VECTOR


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ANSWER 8 LINEAR LAWANSWER 7 INTEGRATION


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ANSWER 9 COORDINATE GEOMETRY ANSWER 10 CIRCULAR MEASURE


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ANSWER 11 PROBABILITY ANSWER 12 MOTION STRAIGHT LINE


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ANSWER 13 SOLUTION OF TRIANGLE ANSWER 14 LINEAR PROGRAMMING


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ANSWER 15 INDEX NUMBER

38589927 Ramalan Add Maths 2010 Edisi Kristal

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Transcript of 38589927 Ramalan Add Maths 2010 Edisi Kristal