kertas model peperiksaan sebenar (spm)

JABATAN PELAJARAN NEGERI PERAK KERTAS MODEL PEPERIKSAAN SEBENAR SPM

MATEMATIK

Kertas 2

Dua jam tiga puluh minit

Kod Pemeriksa

Bahagian SoalanMarkah Penuh

Markah Diperoleh

A

1 3

2 4

JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU

1.Kertas soalan ini mengandungi dua bahagian : Bahagian A dan Bahagian B. Jawab semua soalan daripada Bahagian A dan empat soalan dalam Bahagian B.

2.Jawapan hendaklah ditulis dengan jelas dalam ruang yang disediakan dalam kertas soalan. Tunjukkan langkah-langkah penting. Ini boleh membantu anda untuk mendapatkan markah.

3.Rajah yang mengiringi soalan tidak dilukis mengikut skala kecuali dinyatakan.

4.Satu senarai rumus disediakan di halaman 2 & 3

5.Anda dibenarkan menggunakan kalkulator saintifik yang tidak boleh diprogram.

3 4

4 4

5 4

6 5

7 5

8 6

9 6

10 5

11 6

B 12 12

13 12

14 12

15 12

16 12

SULIT1449/2MatematikKertas 22009

jam

1449/2

NAMA :

TINGKATAN :

Untuk Kegunaan Pemeriksa

SULIT 1449/2

Jumlah

Kertas soalan ini mengandungi 15 halaman bercetak.

MATHEMATICAL FORMULAE

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

RELATIONS

1. .

2.

3.

4.

5.

6.

7.

8. Midpoint

9. Average speed =

12. Pythagoras Theorem

13

14.

1449/2 2009 Hak Cipta JPN Perak [Lihat sebelahSULIT

76 se


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10. Mean =

11. Mean =

SHAPE AND SPACE

1. Area of trapezium = sum of parallel sides height

2. Circumference of circle= d = 2r

3. Area of circle = r2

4. Curved surface area of cylinder = 2rh

5. Surface area of sphere = 4r2

6. Volume of right prism = cross sectional area length

7. Volume of cylinder = r2h

8. Volume of cone = r2h

9. Volume of sphere = r3

10. Volume of right pyramid = base area height

11. Sum of interior angles of a polygon = ( n 2 ) 180 0

12.

13.

14. Scale factor, k =

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15. Area of image= k 2 area of object

SECTION A[ 52 marks]

Answer all question in this section.

1. On the graph provided, shade the region which satisfies the three inequalities y ≤ x + 5, x + y ≤ 5 and y > 1. [3 marks]

Answer:

2. Calculate the values of e and f that satisfy the simultaneous linear equations.

[4 marks]

Answer:

x

y

y = x + 5

x + y = 5

O

1 -

78


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3. Diagram 1 below shows a right prism with PST is the uniform cross section of the prism.

Diagram 1

A solid cylinder of diameter 6 cm is taken out from the solid prism. Using ,

calculate the volume in cm3 of the remaining solid.[4 marks]

Answer:

4. Solve the quadratic equation

Answer: [4 marks]

80


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5. Diagram 2 shows a right prism with an isosceles triangle base, STU. The isosceles triangle STU is the uniform cross-section of the prism.

ST = SU and W is the midpoint of TU. Calculate the angle between the line PW and the base STU. [4 marks]

Answer:

6. (a) State whether the following sentence is a statement or a non-statement. Give a reason for your answer.

(b) State whether each of the following statements is true or false.(i) { 0 } is an empty set or is an empty set.(ii){ } is and empty set and is also an empty set.

(c ) Complete the following argument.

Premise 1 : If a > 3, then 5 a > 15.Premise 2 : 5 a < 15.Conclusion :________________________________________________

[5 marks]Answer:(a) _____________________________________

13 cm

P

W10 cm

12 cm

Q

R

S T

U

DIAGRAM 2

2 + 7 = 1 + 6


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(b) i.___________________ ii. _________________(c) Conclusion: ____________________________________

7. Bottle A contains three red marbles and two yellow marbles. Bottle B contains four red marbles and three yellow marbles. A marble is chosen at random from each bottle.

Find the probability that(a) both marbles are in yellow,(b) both marbles are in different color. [5 marks]

Answer:

8.

.

T

Diagram 6

O S

Q

R

P

150

Diagram 3 shows two sectors OPQ and ORS with centre O. OP = 8 cm, QR = 6 cm andOS = 2 OT. POTS is a straight line.

Using , calculate

a) the perimeter, in cm, of the whole diagram b) the area, in cm2, of the shaded region. [6 marks]

Answer :

82

3


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9. The following diagram shows the distance-time graph of the journeys of two particles S and T.

Graph ABCD represents the journey of the particle S from station X to Y. The graph EF represents the journey of the particle T from station Y to X. Both particles leave station X and station Y respectively at the same time along the same road.(a) State the length of time, in minute, during which the particle S is stationary.(b) If the journey starts at 1500, at what time do the particles meet?(c) Given that the distance travelled by particle S over the 60 minutes period is 186km.

Calculate the value of v.(d) Find the distance, in kilometres, from station Y when the particles meet.(e) Calculate the average speed in m/s of particle S for the whole journey.

[ 6 marks ]

Answer:

A

D

F

C B

60 0

v

145 E

Speed (ms-1)

Time (minute) 20 40 100

80

Station X

Station Y


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10. In Diagram 4, KL, LN and MN are straight lines. L is on y-axis. LN is parallel to x-axis and KL is parallel to MN.

Diagram 4

The equation of straight line KL is 2x + y + 4 = 0, find(a) The equation of straight line LN, (b) The equation of straight line MN hence state its x-intercept.

[ 5 marks ]Answer :

11. It is given matrix U = and matrix V = such that UV =

a) find the values of u and v. b) using the matrix method, calculate the values of x and y that satisfy the following simultaneous equations [6 marks]

Answer :

84

NL

M(1,6)

KO x

y


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SECTION B[ 48 marks]

Answer any four questions from this section.

12. (a) Table 1 shows values of x and y for equation .

Find the values of v and w.[ 2 marks ]

(b) For this part of the question, use graph paper. You may use a flexible curve ruler.

By using a scale of 2 cm to 1 unit on the x-axis and 2 cm to10 unit on the y-axis,

Draw the graph of for .[ 4 marks ]

(c) From your graph, find(i) the value of y when x = 15,(ii) the value of x when y = 20.

[ 2 marks](a) Draw a suitable straight line on your graph to find the values of x that satisfy the

equation for .State the values of x.

[ 4 marks] Answer :

x 3 2 1 0 1 2 3 4

y 29 v 7 8 9 4 w 48

TABLE 1


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13. Diagram 5 shows four quadrilateral ABCD, ADEF, GHJK and LPNM drawn on Cartesian plane.

Diagram 5

(a) Transformation M is a reflection about the line x = 3.

Transformation N is the translation

State the coordinates of the image of point (2,4) under the following transformations:

i) MN ii) NM

(b) ADEF is the image of ABCD under transformation V and GHJK is the image of ADEF

under transformation W.

Describe in fulli) Transformation Vii) A single transformation which is equivalent to transformation WV.

(c) LPNM is the image of ABCD under an enlargement.i) State the coordinates of the centre of the enlargement.ii) Given that the area LPNM is 72.8 unit2, calculate the area of ABCD.

86


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[12 marks]

Answer:

a. i) ____________________________________________________

ii) ____________________________________________________

b. i) _____________________________________________________

ii) ____________________________________________________

c. i) _____________________________________________________

ii) ________________________________


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14. The data in Diagram 6 shows the mass in kg of 50 students in a class.

40 52 47 64 52 35 54 43 39 5443 39 54 57 53 39 55 38 46 4245 53 60 38 54 62 47 45 52 5338 55 62 54 45 54 36 58 44 4252 48 49 46 49 48 45 54 41 46

Diagram 6

(a) Based on the data in Diagram 7 and using a class interval of 5 kg, complete Table 2 in the answer space. [4 marks]

(b) From the table in a),(i) state the modal class,(ii) calculate the mean mass of the students and give your answer correct to 2

significant figures. [4 marks] (c) By using a scale of 2 cm to 5 kg on the x-axis and 2 cm to 1 student on the y-axis,

draw a histogram based on the data. [4 marks]

Answer:(a)

Mass Frequency Midpoint

35-39

40-44

Table 2(b)

(c)

88


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15. Diagram 8 shows a right prism with a horizontal rectangular base ABCD. BCHGF is the uniform cross -section of the prism. GHIJ is a horizontal plane. ABFE and DCHI are vertical planes.

(a) Draw to full scale, the elevation of the solid on a vertical plane parallel to BC as seen from X [3 marks]

Answer:

D

B

G

E

A

J

1 cm

C

I

F

H

X4 cm3 cm

3 cm

2 cm

DIAGRAM 8(i)


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(b) A solid right prism with uniform cross-section KLM is removed from the solid. The remaining solid is shown in diagram 8(ii).

Draw at full scale

(i) the plan of the remaining solid . [4 marks] (ii) the elevation of the remaining solid on a vertical plane parallel to AB as

seen from Y. [5 marks] Answer:

90

NL

K M

1 cm

Y

D

B

G

E

A

J

1 cm

C

I

H

4 cm3 cm

3 cm

2 cm

DIAGRAM 8(ii)


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16. P(650 S, 400 E), Q(650 S, 600 W), R and S are four points on the surface of the earth. PR is the diameter of the parallel of latitude 650 S.(a) (i) State the longitude of R. (ii) Calculate the shortest distance, in nautical mile, from P to R measured along the

surface of the earth. [4 marks](b) S lies north of Q and the distance of SQ measured along the surface of the earth is 5100 nautical mile. Calculate the latitude of S. [3 marks](c) An aero plane took off from P and flew due west to Q and then flew due north to S. The average speed for the whole flight was 560 knots. Calculate

(i) the distance, in nautical mile, taken by the aero plane from P to Q measured along the common parallel of latitude,

(ii) the total time, in hours, taken for the whole flight. [5 marks]

Answer:

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kertas model peperiksaan sebenar (spm)

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