SPM Mid Year 2008 Melaka Maths Paper 2

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SULIT 1449/2

1449/2 2008 Hak Cipta JPM [Lihat sebelah

UJIAN PENGESANAN PERTENGAHAN TAHUNSIJIL PELAJARAN MALAYSIA 2008

This question paper consists of 23 printed pages.

MATHEMATICS

Paper 2Two hours and thirty minutes

DO NOT OPEN THIS QUESTION PAPER UNTIL YOU ARETOLD TO DO SO

1. This question paper consist two section: Section A and Section B . Answer all question in Section A and any four questions inSection B.

2. This question paper is bilingual.

3. Write your answers in the spaces provided in the question paper.

4. Working step must be written clearly.

5. Diagram given is not according to scale unless stated.

6. Marks for each question are given in bracket.

7. A list of formulae is given in pages 2 and 3.

8. Non programmable scientific calculator are allowed.

9 This question paper must be hand up at the end of the exam.

Section Question Fullmark

Marksobtained

A

1 3

2 4

3 4

4 4

5 4

6 5

7 5

8 6

9 5

10 5

11 7

B

12 12

13 12

14 12

15 1216 12

Total

1449/2MathematicsPaper 2May2008

JABATAN PELAJARAN MELAKA

NAME :..

FORM:


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MATHEMATICAL FORMULAE

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

RELATIONS1 nmnm aaa

2 nmnm aaa

3mnnm aa )(

4

ac

bd

bcad A

11

5 Sn An

AP)(

)(

6 )(1)'( AP AP

7 2122

12 )()(Distance y y x x

8 Midpoint ,

2,

2),( 2121

y y x x y x

9 Average speed = takentimetravelleddistance

10 Mean = dataof numberdataof sum

11 Mean sfrequencieof sumfrequency)mark of(classsum

12 Pythagoras Theorem222 bac

1312

12

x x y y

m

14 erceptinterceptint

x

ym


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3

SHAPES AND SPACE

1 Area of trapezium = 21

sum of parallel sides height

2 Circumference of circle = r d 2

3 Area of circle = 2r

4 Curved surface area of cylinder = rh 2

5 Surface area of sphere = 24 r

6 Volume of right prism = cross sectional area length

7 Volume of cylinder = h j2

8 Volume of cone = hr 2

31

9 Volume of sphere =3

34

r

10 Volume of right pyramid = 31

base area height

11 Sum of interior angles of a polygon = (n 2) 180

12 o360centeratsubtendedangle

circleof ncecircumferelengtharc

13 o360centreatsubtendedangle

circleof areasectorof area

14 Scale factor, k = PAPA '

15 Area of image = k 2 area of object


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Section A

[52 marks ]

Answer all questions in this section.

1 On the graph in the answer space, shade the region which satisfy the three inequalities y > x , x + y 5 and x 0 [ 3 marks ]

Pada graf yang disediakan , lorekkan rantau yang memuaskan ketiga-tiga ketaksamaan : y > x , x + y 5 dan x 0.

Answer :

y

5

4

3

2

1

0 1 2 3 4 5 x

2 Calculate the value of p and of q that satisfy the following simultaneous linearequations; Hitung nilai p dan nilai q yang memuaskan persamaan linear serentak berikut :

121

q p

3132 q p [ 4 marks ] Answer :

x + y = 5


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3 Using factorization, solve the following quadratic equation: Menggunakan pemfaktoran, selesaikan persamaan kuadratik berikut

2 x 2 + ( x 1 ) 2 = 9[ 4 marks ]

Answer :

4 Diagram 1 shows a cuboid with TUVW as a base Rajah 1 menunjukkan sebuah kuboid dengan tapak TUVW.

Calculate the angle between the plane PRV and the plane QRVU . Hitungkan sudut di antara satah PRV dengan satah QRVU. [4 marks ]

Answer :

R

Q

S

P

T U

V W

5 cm

12 cm

4 cm

Diagram 1


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5 Diagram 2 shows a composite solid consisting of a hemisphere and a cylinder. Rajah 2 menunjukkan sebuah pepejal yang terdiri daripada gabungan sebuah hemisfera dan sebuahsilinder.

Diagram 2

Given that the diameter of the hemisphere is 16 cm. The radius and height of the cylinderare 6 cm . Diberi bahawa diameter hemisphere itu ialah 16 cm. Jejari dan tinggi silinder adalah 6 cm.

Calculate the volume, in cm 3, of the solid. (Use = 3.142). Hitungkan isipadu, dalam cm 3 , pepejal itu. (Gunakan = 3.142). [4 marks ]

Answer :


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6 (a) Complete each of the following statements with the quantifier all or some sothat it will become a true statement.

(i) ..multiples of 5 are odd numbers.

(ii) .regular hexagons have 6 axis of symmetry.

Lengkapkan setiap pernyataan berikut dengan pengkuantiti semua atau sebilangansupaya menjadi suatu pernyataan benar.

(i) .. gandaan 5 adalah nombor ganjil

(ii) . heksagon sekata mempunyai 6 paksi simetri

(b) State the converse of the following statement and hence determine whether itsconverse is true or false. Nyatakan akas bagi pernyataan berikut dan seterusnya nyatakan samada akas itu benar atau palsu

( c ) Complete the premise in the following argument:

Premise 1 : .Premise 2 : KLMN is a rectangle

Conclusion : The sum of interior angle of KLMN is 360.

Lengkapkan premis dalam hujah berikut

Premise 1 : .Premis 2 : KLMN adalah segiempat tepat

Kesimpulan : Jumlah sudut pedalaman bagi KLMN ialah 360.[5 marks ]

Answer :

(a) (i) ..multiples of 5 are odd numbers.

(ii) .regular hexagons have 6 axis of symmetry.

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

......................................................................................................................................................

(c) Premis 1 : ............................................................................................................

.............................................................................................................................

If x > 7, then x > 4. Jika x > 7, maka x > 4.


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7 Diagram 3 shows eight labeled cards in a box. Rajah 3 menunjukkan lapan kad yang berlabel di dalam sebuah kotak. .

Diagram 3

(a) List the sample space for the cards above.Senaraikan ruang sampel bagi kad kad di atas.

(b) A card is picked at random from the box.Sekeping kad di pilih secara rawak daripada kotak itu.

By listing outcomes, find the probability that Dengan menyenaraikan kesudahan, cari kebarangkalian bahawa

(i) the cards labeled with even numbers

kad yang berlabel nombor genap

(ii) the cards labeled with prime numberskad berlabel nombor perdana [5 marks ]

Answer :

(a)

(b) (i)

(ii)


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8 Diagram 4 shows a sector PQR with centre O and a semicircle RSO with OR as thediameter. Rajah 4 menunjukkan sebuah sektor bulatan PQR berpusat O dan sebuah semibulatan RSO dengan ORsebagai diameter

.

OR = 14 cm. Using =7

22, calculate

OR = 14 cm . Dengan menggunakan =722 , hitungkan

(a) perimeter, in cm , of the whole diagram . perimeter , dalam cm, seluruh rajah .

(b) area, in cm 2, of the shaded region.

luas , dalam cm2

, rantau berlorek .

[ 6 marks ]

Answer :

(a)

(b)

120

OQ

Diagram 4

R


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9 (a) Diagram 5 shows a graph of function

Diagram 5

Find the value of n and of k Hitungkan nilai n dan nilai k [2 marks ]

(b) On the graph provided, shaded the region which satisfies the threeinequalities

Pada graf yang disediakan, lorekkan rantau yang memuaskan ketiga-tiga ketaksamaan

x y 2 , 4y x and 4 y [3 marks ]

Answer :

(a) (i) n :.

(ii) k :..

(b)

y = 2 x

y

x + y = 4O x

y= xn + k y

xO

4


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10 Diagram 6 shows a straight line PQ and a straight line RS drawn on a Cartesian plane.PQ is parallel to RS. QR is parallel to the x-axis.

Rajah 6 menunjukkan garis lurus PQ dan garis lurus RS dilukis pada satah Cartesan. Garis lurus PQadalah selari dengan garis lurus RS dan garis lurus QR adalah selari dengan paksi-x .

(a) State the equation of a straight line QR . Nyatakan persamaan garis lurus QR.

(b) Find the equation of a straight line RS . Hence state the y-intercept of RSCari persamaan garis lurus RS. Seterusnya nyatakan pintasan-y bagi garis lurus itu.

[5 marks ]

Answer :

(a)

(b)

y

xO

Q R(6, 4)

S

P (3, 0)

Diagram 6


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11 Given that the inverse matrix of

31

12is

21

31 n

m.

Diberi bahawa matriks songsang bagi

31

12

ialah

21

31 n

m

(a ) Find the values of m and of n.Carikan nilai m dan nilai n . [3 marks ]

(b) Hence , using matrices , calculate the value of p and of q.Seterusnya ,dengan menggunakan kaedah matrik , hitungkan nilai p dan nilai q yang memuaskan persamaan linear serentak berikut:

72 q p73q p

[4 marks ] Answer :

(a)

(b)


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(c) Given that region JKLMN represents an area of 18 unit 2. Calculate the area,in unit 2, represented by the pentagon UPTSRZYX .

Diberi bahawa JKLMN mewakili luas 18 unit 2. Hitungkan luas, dalam unit 2 , luas pentagonUPTSRZYX.

[3 marks ]

Answer :

(a) (i)

(ii)

(iii)

(b) (i) G :...

..

(ii) H : .

..

(c)


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13. For this question, use the graph paper provided on page 16 . You may use flexible curve.(a) Complete the Table 1 for the equation 2326 x x y .

Lengkapkan Jadual1 yang memuaskan persamaan 2326 x x y . [3 marks ]

x 3 2 1 0 1 2 2.5 3 4 y 27 10 6 5 15 30

Table 1

(b) Using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 5 units on the y-axis, draw thegraph of 2326 x x y for 43 x . Dengan menggunakan skala 2 cm kepada 1 unit pada paksi x dan 2 cm kepada 5 unit pada

paksi-y ,lukis graf bagi fungsi 2326 x x y untuk 43 x .[4 marks ]

(c) From your graph, find Dari graf anda , carikan

(i) the values of x when y = 18nilai-nilai x apabila y = 18

(ii) the value of y when x = 1.5nilai y apabila x = 1.5 [2 marks ]

(d) Draw a suitable straight line on your graph to find all the values of x which satisfy

the equation 023214 x x for 43 x . State the values of x

Pada graf , lukiskan satu garis lurus yang memuaskan persamaan 023214 x x bagi

43 x . Nyatakan nilai-nilai x tersebut . [3 marks ]

Answer :(a) x 3 2 1 0 1 2 2.5 3 4

y 27 10 6 5 15 30Table 1

(b) Refer graph on page 16.

(c) (i) x = .

x = .

(ii) y = ..

(d)

x = .

x = .


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GRAPH FOR QUESTION 13


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14 Table 2 shows the distribution of the weight of 40 students in a school. Jadual 2 menunjukkan taburan kekerapan bagi berat 40 orang pelajar di sebuah

sekolahWeight (g) Frequency

35 39 2

40 44 545 49 850 54 1055 59 760 64 465 69 370 74 1

Table 2(a) (i) State the modal class for the data in the Table 2

Nyatakan kelas mod bagi data yang diberi dalan Jadual 2

(ii) Complete Table 3 in the answer space . Lengkapkan Jadual 3 di ruang jawapan yang disediakan . [4 marks ]

(b) Using the scale of 2cm to 5 kg on the x-axis and 2cm to 5 students to y-axis, draw an ogive for the data.

Dengan menggunakan skala 2cm kepada 5 kg pada paksi x dan 2cm kepada 5 orang pelajar pada paksi-y, lukiskan satu ogif bagi data di atas.

[5 marks ](c) From the graph, find

Daripada graf itu, carikan(i) median

(ii) interquartile range julat antara kuartil [3 marks ]

Answer :(a) (i)

(ii)Weight (g) Frequency Upper

boundariesCumulativefrequency

35 39 240 44 5

45 49 850 54 1055 59 760 64 465 69 370 74 1

Table 3(b) Refer graph on page 18

(c) (i)

(ii)


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GRAPH FOR QUESTION 14


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15 (a) Given that p varies directly as n 2 and p = 36 when n = 3, express p interm of n . Hence, find the positive value of n when p = 100

Diberi bahawa p berubah secara langsung dengan n 2 dan p = 36 apabila n = 3, ungkapkan p dalam sebutan n. Seterusnya carikan nilai n apabila p = 100 [3 marks ]

(b) Given that x

y1

and y = 3 when x = 36.

Diberi bahawa x y

1

dan y = 3 when x = 36.

Calculate ; Hitungkan

(i) the value of y when x = 4nilai y apabila x = 4

(ii) the value of x when y =49

nilai x apabila y =49

[4 marks ]

(c) Table 2 shows the relation between three variables, p , m and r . Jadual 2 menunjukkan hubungan antara tiga pembolehubah p, m dan r.

p m r

4 9 610 25 y6 w 2

Table 2

Given thatr m

p , calculate the values of w and y.

Diberi bahawar m

p , hitungkan nilai-nilai w dan y. [5 marks]

Answer :(a)


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(b) (i)

(ii)

(c)


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16 You are not allowed to use graph paper to answer this question. Anda tidak dibenarkan menggunakan kertas graf untuk menjawab soalan ini.

(a) Diagram 8(i) shows a right prism with uniform cross section NRW is removed from the solid . Rajah 8(i) menunjukkan sebuah pepejal berbentuk prisma dengan keratan rentas seragam NRW telahdikeluarkan daripada pepejal tersebut

The base JKLM is a rectangle on a horizontal plane.The rectangle RSZW is an inclined plane. The rectangle PQRST is a horizontal plane.

.Tapak JKLM ialah segiempat tepat terletak pada satah mengufuk.Segiempat tepat RSZW ialah satah condong . Segiempat PQRST ialah satah mengufuk .

NU = VW = 3 cm

Draw to full scale, the plan of the solid. Lukis dengan skala penuh, pelan pepejal itu. [ 3 marks ]

Answer :(a)

K

L M

P Q

R

ST

U V

W

Z

N

J 5 cm

2 cm

5 cm2 cm

6 cm

Diagram 8(i)


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Answer :

(b) (i)

(b) (ii)

END OF QUESTION PAPER

SPM Mid Year 2008 Melaka Maths Paper 2

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