add maths paper 1

21
PROGRAM DIDIK CEMERLANG AKADEMIK SPM MODEL SPM QUESTIONS ( PAPER 1 ) ORGANISED BY: JABATAN PELAJARAN NEGERI PULAU PINANG ADDITIONAL MATHEMATICS MODULE 19 http://mathsmozac.blogspot.com http://sahatmozac.blogspot.com

Upload: johncarl

Post on 08-Sep-2015

28 views

Category:

Documents


9 download

DESCRIPTION

Feel free with my lesson

TRANSCRIPT

  • PROGRAM DIDIK CEMERLANG AKADEMIK

    SPM

    MODEL SPM QUE 1 )

    ORGA

    JABATAN PELAJARA

    ADDITIONALMATHEMATICS

    MODU

    http://maths

    http://sahatmozac.blogspot.comSTIONS ( PAPER

    NISED BY:

    LE 19N NEGERI PULAU PINANG

    mozac.blogspot.com

  • Additional Mathematics ( Paper 1) SPM

    Jabatan Pelajaran Pulau Pinang 2

    3472/1 NO. KAD PENGENALANAdditionalMathematicsPaper 1 ANGKA GILIRAN

    2 Hours

    JABATAN PELAJARAN NEGERI PULAU PINANG

    ADDITIONAL MATHEMATICS

    Paper 1

    Two Hours

    JANGAN BUKA KERTAS SOALAN INISEHINGGA DIBERITAHU

    1. Tuliskan angka giliran dan nombor kadpengenalan anda pada ruang yangdisediakan.

    2. Calon dikehendaki membaca arahandi halaman 2.

    Kod PemeriksaQuestions Marks Actual Marks

    1 22 33 34 35 36 37 38 39 310 211 412 413 414 215 216 317 418 419 420 421 322 423 324 325 4

    Total

    http://mathsmozac.blogspot.com

    http://sahatmozac.blogspot.com

  • Additional Mathematics ( Paper 1) SPM

    Jabatan Pelajaran Pulau Pinang 3

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

    8. The marks allocated for each question and sub-figure mathematical tables is provided .

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

    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 examination.

    http://mathsmozac.blogspot.com

    http://sahatmozac.blogspot.com

  • Additional Mathematics ( Paper 1) SPM

    Jabatan Pelajaran Pulau Pinang 4

    Answer all questions

    1 . Diagram 1, the function h maps x to y and the function k maps y to z.

    DIAGRAM 1

    Determine

    (a) hk 1 ( 4),

    (b) kh 1 ( 2). [2 marks]

    Answer : (a) ___________

    (b) ___________

    2. The function p1 is defined as p1 (x) =x

    x43 , x 4.

    Find

    (a) p(x),

    (b) p(5). [3 marks]

    Answer : (a) ___________

    (b) ___________

    x y z

    4

    3

    2

    hk

    http://mathsmozac.blogspot.com

    http://sahatmozac.blogspot.com

  • Additional Mathematics ( Paper 1) SPM

    Jabatan Pelajaran Pulau Pina

    3. The following information refers to the functions h and g.

    Find f (x). [3 marks]

    Answer : ___________

    4. The straight line y = t intercept with the curve y = 3 + 5x 4x2 at the two points A and B .

    Find the range of values of t . [3 marks]

    Jawapan : ___________

    5. Solve the quadratic equation5

    23

    12 2

    xx Give your answer correct to three decimal

    places . [3 marks]

    g (x) = 4 3 x

    fg (x) = 2 x + 5

    http://sahatmozac.blogspot.comng 5

    Answer : x = ___________

    http://mathsmozac.blogspot.com

  • Additional Mathematics ( Paper 1) SPM

    Jabatan Pelajaran Pulau Pinang 6

    6. Diagram 2 shows the graph of a quadratic functions g(x) = 4 2(x + h)2 where h is constant.

    DIAGRAM 2

    The curve y = g(x) has maximum point (3, k) , where k is a constant .State

    (a) the value of h,

    (b) the value of k,.

    (c) the equation of the axis of symmetry .[3 marks]

    Answer : (a) h = ___________

    (b) k = ___________

    (c) ___________

    7. Solve the equation .)4)(8(

    164 13

    xx

    x [3 marks]

    Answer : x = ___________

    y = g(x)

    (3,k)

    x

    y

    O

    http://mathsmozac.blogspot.com

    http://sahatmozac.blogspot.com

  • Additional Mathematics ( Paper 1) SPM

    Jabatan Pelajaran Pulau Pinang 7

    8. Solve the equation log2 (x 1) + 2 = 2 log2 x [3 marks]

    Answer : x = ___________

    9. Given that log2 x = p and log2 y = r, express

    2

    3

    232log

    yx in term p and r.

    [3 marks]

    Answer : ___________

    10. The sum of the first n term of an arithmetric progression is given by Sn= 5n 3. Find the

    fifth term . [2 marks]

    Answer : ___________http://mathsmozac.blogspot.com

    http://sahatmozac.blogspot.com

  • Additional Mathematics ( Paper 1) SPM

    Jabatan Pelajaran Pulau Pinang 8

    11. The first three terms of an arithmetic progression are 21 , 1, 2 ,

    Find

    (a) the common ratio ,

    (b) the sum of the first 10 terms after the 5th term .

    [ 4 marks]

    Answer : (a) ___________

    (b) ___________

    12. The sum of the first n terms of an arithmetric progression 47, 44, 41, is 1325. Find

    (a) the common difference of the progression ,

    (b) the value of n. [4 marks]

    Answer : (a) ______________

    (b) n = ___________

    http://mathsmozac.blogspot.com

    http://sahatmozac.blogspot.com

  • Additional Mathematics ( Paper 1) SPM

    Jabatan Pelajara

    13. Diagram 3 shows a straight line graph of log10 y againts log10 x.

    The variables x and y are related by equation y = p x q, where p and q are contants .

    (a) Calc

    (b) Find

    14. The follow

    parallel to e

    Express p

    log10 y

    log10 x

    2

    4 O

    http://sahatmozac.blogspot.comDIAGRAM 3

    ulate the value of p and q,n Pulau Pinang 9

    the value of y if x = 10. [4 marks]

    Answer : (a) p = ___________

    q = ___________

    (b) y =___________

    ing information refers to the equations of two straight lines , AB and CD , which

    ach other.

    in terms q. [2 marks]

    Answer : p =___________

    AB : 2y = p x + q

    CD : 3y = (q + 1) x + 2

    Where p and q are constants

    http://mathsmozac.blogspot.com

  • Additional Mathematics ( Paper 1) SPM

    Jabatan Pelajaran Pulau Pinang 10

    15. Given that B point is (8, 5) and O is origin.

    (a) ExpressOB in terms of

    ~i and

    ~j .

    (b) Find the unit vector in the direction ofOB . [2 marks]

    Answer : (a) ___________

    (b) ___________

    16. Given thatOA = 2

    ~i + 3

    ~j ,

    OB = 10

    ~i + 6

    ~j and R is a point on AB such that AR :

    AB = 2 : 3. Find

    (a)AB ,

    (b)OR . [3 marks]

    Answer : (a) ___________

    (b) ___________

    17. Solved the equation 3cot

    1 22 xsekx

    for 0 x 360.

    [4 marks]

    Answer : x = ___________http://mathsmozac.blogspot.com

    http://sahatmozac.blogspot.com

  • Additional Mathematics ( Paper 1) SPM

    Jabatan Pelajaran P

    18. Diagram 4 shows the sector OPQ, centre O with a radius of 5 cm . Line PR is perpendicular tothe line OQ and QR = 1 cm.

    [4 marks]

    Find ( a ) POR in radians ,

    ( b ) the perimeter of the shaded region .

    Answer : ( a ) .

    ( b ) .

    19. Given that 2)25(4)( xxxf , find )(" xf [4 marks]

    RAJAH 4

    Q

    P O

    R

    http://sahatmozac.blogspot.comulau Pinang 11

    Answer : ___________

    http://mathsmozac.blogspot.com

  • Additional Mathematics ( Paper 1) SPM

    Jabatan Pelajaran Pulau Pinang 12

    20. Given that x = t + 3t 2 and y = 2t 1

    (a) finddydx in term of t.

    (b) If y decreases from 4.0 to 3.98, Find the corresponding small change in t .

    [4 marks]

    Answer : (a) ___________

    (b) ___________

    21. Given that 2321

    xxy and )(4 xf

    dxdy

    with )(xf is a function in x .

    Calculate the value of dxxf )(32

    2 . [3 marks]

    Answer : ___________

    http://mathsmozac.blogspot.com

    http://sahatmozac.blogspot.com

  • Additional Mathematics ( Paper 1) SPM

    Jabatan Pelajaran Pulau Pinang 13

    22. A chess team consists that of 5 students . The team will be chosen from a group of 6 boys

    and 4 girls . Calculate the number of teams that can be formed such that each team consists

    of

    (a) 4 boys,

    (b) Not more than 2 girls.[4 marks]

    Answer : (a) ___________

    (b) ___________

    23. The mean of five numbers is m. The sum of the squares of the numbers is 720 and the

    standard deviation is 9h2. Express m in term of h.

    [3 marks]

    Answer: m = ___________

    http://mathsmozac.blogspot.com

    http://sahatmozac.blogspot.com

  • Additional Mathematics ( Paper 1) SPM

    Jabatan Pelajaran Pulau Pinang 14

    24. Ali has 6 accessories of the item which consists of P, Q, R, S, T and U. He wants to arrange

    4 of the items in a row . Find the probability that

    (a) the arrangment is TUPS ,

    (b) the arrangment does not incule P item

    [3 marks]

    Answer : (a) ___________

    (b) ___________

    25. X is a random variable of normal distribution with a mean of 10 and a variance 9 , find the

    value of r such that P ( X < r ) = 0 . 9 7 5.

    [4 marks]

    Answer : ___________

    END OF QUESTION PAPER

    http://mathsmozac.blogspot.com

    http://sahatmozac.blogspot.com

  • Additional Mathematics ( Paper 1) SPM

    Jabatan Pelajaran Pulau Pinang 15

    Answers

    1. ( a ) h k 1 ( 4) = 2

    ( b ) k h 1 ( 2) = 4

    2 . ( a ) p 1 ( x ) =x

    x43

    p 1 ( y ) = yy43

    x =y

    y43

    x ( 4 y ) = 3 y

    4 x x y = 3 y

    y ( x + 3 ) = 4 x

    y =3

    4xx

    p ( x ) =3

    4xx , x 3,

    ( b ) 35)5(4)5(

    p

    =25

    3 . g ( x ) = 4 3 x

    y = 4 3 x

    3 x = 4 y

    x =3

    4 y

    g 1(x) =3

    4 x

    f ( x ) = f g g 1 ( x ) = f g

    34 x

    = 2 53

    4

    x

    =3

    223 x

    4 . y = t , y = 3 + 5 x 4 x 2

    3 + 5 x 4 x 2 = t

    http://mathsmozac.blogspot.com

    http://sahatmozac.blogspot.com

  • Additional Mathematics ( Paper 1) SPM

    Jabatan Pelajaran Pulau Pinang 16

    4 x 2 5 x + t 3 = 0

    Intercept at two points , use b 2 4 a c > 0

    ( 5 ) 2 4 ( 4 ) ( t 3 ) > 0

    1 6 t < 7 3

    t