Bahagian A

SULIT10SULIT 1449/2

9SULIT 1449/2

PEPERIKSAAN PERCUBAAN

1449/2

SIJIL PELAJARAN MALAYSIA MATHEMATICS

Kertas 22 jam

Dua jam tiga puluh minit

JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU

Untuk Kegunaan Pemeriksa/ Guru

BahagianSoalanMarkah PenuhMarkah Diperoleh

A13

24

34

44

55

64

75

86

96

105

116

B1212

1312

1412

1512

1612

Jumlah

Kertas soalan ini mengandungi 26 halaman bercetak.

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

1

2

3

4A-1 =

EMBED Equation.3 5Distance =

6Midpoint, =

EMBED Equation.3

7Average speed =

8Mean =

9Mean =

10Pythagoras Theorem

11

12

13

14

SHAPES AND SPACE

1Area of trapezium = sum of parallel sides height

2Circumference of circle = (d = 2(r3Area of circle = (r24Curved surface area of cylinder = 2(rh

5Surface area of sphere = 4(r26Volume of right prism = cross sectional area length

7Volume of cylinder = (r2h8Volume of cone = (r2h9Volume of sphere = (r310Volume of right pyramid = base area height

11Sum of interior angles of a polygon =

12

13

14Scale factor, k =

15Area of image =

Section A

[52 marks]

Answer all questions in this section.1The Venn diagram below shows sets P, Q, and R such that the universal set.On the diagrams in the answer space, shade (a) the set P ( Q,(b) the set Q ( (R ( P)(.

[3 marks]

Answer :

(a)

(b)

2Using factorisation, solve the following quadratic equation . [4 marks]Answer :

3 Calculate the value of p and of q that satisfy the following simultaneous linear equations:

[4 marks]

Answer :

4Diagram 1 shows a right prism with a rectangular base EMFGNH which lies on a horizontal plane. Isosceles triangle PEF is the uniform cross section of the prism. M and N are the midpoints of the side EF and GH respectively.

(a) Name the angle between the line PG and the plane EFGH.

(b) Calculate the angle between the line PG and the plane EFGH.[4 marks]

Answer :

(a) (b)

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

[2 marks](b)Write down two implications based on the following compound statement in the answer space.

[2 marks]

(c)Complete the conclusion of the following argument.

Premise 1 : If is an even number, then q is an odd number.

Premise 2 : 8 is an even number.

Conclusion : [1 mark]

Answer :

(a) (b)Implication 1:

.Implication 2:

..(c)Conclusion:.6 Diagram 2 shows a solid right prism. Trapezium ABCD with an area of 40 cm2 is the uniform cross section of the prism and BF = 7 cm. A cone with diameter 6 cm and height 5 cm is taken out of the solid.

Using , calculate the volume, in cm3, of the remaining solid.

[4 marks ]

Answer:

7 Diagram 3 shows a straight line PQ and a straight line RS drawn on a Cartesian plane. Given that PQ is parallel to RS and ST is parallel to y-axis.Find(a)the equation of the straight line ST,(b)the equation of the straight line RS,(c)the intercept of the straight line RS.

[5 marks]

Answer :

(a)

(b)

(c)8(a)Given that , find the value of h and of k. (b)Hence, using matrices, find the value of m and of n which satisfy the simultaneous linear equations below.

[6 marks]

Answer:

(a)

(b)

9Diagram 4 shows a semicircle ORT with centre S. OPQ is a sector of a circle with centre O.

Diagram 4It is given that PT = TS = 6 cm. Use and give your answer correct to two decimal places.

Calculate

(a)the perimeter, in cm, of the whole diagram,

(b)the area, in cm2, of the shaded region.

[7 marks]

Answer : (a) (b)

10Diagram 5 shows the distance-time graph of a bus from Sematan to Kuching passing through Lundu over a period of T minutes.

Graph AB represents the journey from Sematan to Lundu while graph CD represents the journey from Lundu to Kuching.(a)State the length of time the bus stops at Lundu,

[1 mark](b)Calculate the speed, in kmh-1, of the bus from Sematan to Lundu,

[2 marks](c)If the average speed of the whole journey is 90 kmh-1, calculate the value of T in minutes.

[2 marks]

Answer :

(a)

(b)

(c)

11A box contains 3 yellow balls and 2 blue balls. Two balls are picked from the box at random, one after another, without replacement.

(a)List the sample space.

(b)Find the probability that(i) both balls picked are yellow,(ii) the second ball picked is blue.

[5 marks]

Answer:

(a)

(b) (i) (ii) Section B

[48 marks]

Answer any four questions in this section.

12 (a) Complete Table 1 in the answer space for the equation by writing down the values of y when = -2 and =3.

[2 marks]

(b) For this part of the question, use the graph paper provided on page 15. Using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 5 units on the y-axis, draw the graph of for.

[4 marks]

(c) From the graph in 12(b), find

(i) the value of y when x = 2.5,(ii) the values of x when y= -20. [2 marks]

(d) Draw a suitable straight line on the graph in 12(b) to find all the values of x which satisfy the equation for. State the values of x.

[4 marks]

Answer :

(a)

-3-2-101234

-23-1452-16

(b)Refer graph on page 15.(c)

(i)y =

(ii)x =

(d)

x = ,

13Diagram 6 shows four triangles ABC, AFC, FEG and PQG drawn on a Cartesian plane.

Diagram 6

(a) Transformation R is a clockwise rotation of 90 about the origin.

Transformation T is a translation.

Find the coordinates of the image of point Q under each of the following combined transformations:

(i) R,

(ii) RT.

[3 marks]

(b) ACF is the image of ACB under transformation V and EGF is the image of ACF under transformation W.

Describe in full

(i) Transformations V, (ii) A single transformation which is equivalent to the combined transformation WV. [5 marks]

(c) QGP is the image of EGF under an Enlargement.

(i) State the scale factor,

(ii) Given that the area of the shaded region EQPF is 56 cm2. Calculate the area, in cm2, of triangle EGF.

[4 marks]

Answer :

(a)(i)

(ii)

(b) (i) ..

..

(ii)

(c) (i)Scale factor = .

(ii)

14. The data in Table 2 shows thefrequency distributionof the mass, in kg, of a group of 32 students in a particular class.

Mass (kg)Frequency

35 394

40 446

45 4910

50 547

55 593

60 642

Table 2

(a) Based on the data in Table 2,

(i) state the midpoint of the modal class,(ii) calculate the estimated mean of themass of the students. [4marks]

(b) Using data in Table 2,complete Table 3 in the answer space.[2marks]

(c) For this part of the question, use the graph paper provided on page 20.

Using the scale of 2 cm to 5 kg on thehorizontalaxis and 2 cm to 5 students on theverticalaxis, draw an ogive for the data.

[4marks]

(d) Based on the ogive in 14(c), find the percentage of the students with weight more than 57 kg.

[2marks]

Answer:

(a) (i)

(ii)

(b)

Mass (kg)FrequencyUpper BoundaryCumulative frequency

35 394

40 446

45 4910

50 547

55 593

60 642

Table 3

(c) Refer graphon page 20.

(d)

15You are not allowed to use graph paper to answer this question.(a)Diagram 7(i) shows a solid right prism with rectangular base PQMN on a horizontal table. The surface PSTN is its uniform cross-section. The rectangle RSTU is an inclined plane. The edges UM, TN, SP and RQ are vertical edges.

Draw to full scale, the elevation of the solid on a vertical plane parallel to MN as viewed from X.

[4 marks]

Answer :

(a)

(b)Another solid right prism is joined to the solid in the Diagram 7 (i) at the vertical plane MNWVU to form a combined solid as shown in Diagram 7 (ii).

The surface DEFGJ is its uniform cross-section and GFNW is an inclined plane.

The rectangle DJKL is a horizontal plane and the base EFNPQM is on a horizontal plane. DE and JG are vertical. JG = KW = 5 cm.

Draw to full scale,

(i) the elevation of the combined solid on a vertical plane parallel to FP as viewed from Y,

[4 marks]

(ii)the plan of the combined solid.

[4 marks]

Answer :

(b)(i)

(ii)

16. Diagram 8 shows the locations of three points, P, Q and R on the surface of the earth. N is the North Pole, S is the South Pole and O is the centre of the earth.PR is a diameter of the earth. The longitude of R is 65E and the latitude of P is 48S.

Diagram 8

(a)(i) State the latitude of R.(ii) State the location of P.

[4 marks]

(b)V lies 5 820 nautical miles due North of P.Calculate the latitude of V.

[3 marks]

(c)Calculate the distance, in nautical miles, from P to Q measured along the common parallel of latitude.

[3 marks]

(d)An aeroplane took off from P and flew due south to Q passing through South Pole. If the average speed of the aeroplane is 500 knots, calculate the time taken for the whole journey.

[2 marks]

Answer:(a)(i)

(ii).

(b)

(c)

(d)

INFORMATION FOR CANDIDATES1.This question paper consists of two sections: Section A and Section B.2.Answer all questions in Section A and four questions from Section B.3.Write your answers in the spaces provided in the question paper.

4.Show your working. It may help you to get marks.

5.If you wish to change your answer, cross out the answer that you have done. Then write down the new answer.

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

7.The marks allocated for each question and sub-part of a question are shown in brackets.

8.A list of formulae is provided on page 2 to 3.

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

10.Hand in this question paper to the invigilator at the end of the examination.

S (6, 8)

SULIT

sum of (classmark frequency)

sum of frequencies

sum of data

number of data

distance travelled

time taken

TINGKATAN :

NAMA :

Q

P(2, 9)

EMBED Equation.DSMT4

R

Diagram 2

A

B

F

6

F

Y

X

For

Examiners only

J

V

W

Y

Diagram 7 (ii)

K

L

4 cm

7 cm

6 cm

5 cm

G

F

E

D

3 cm

R

U

Q

T

y

E

C

S

D

G

1.Tulis Nama dan Tingkatan anda dalam petak yang disediakan.

2. Kertas soalan ini adalah dalam bahasa Inggeris sahaja.

3. Calon dibenarkan menjawab keseluruhan atau sebahagian soalan sama ada dalam bahasa Inggeris atau bahasa Melayu.

4. Calon dikehendaki membaca maklumat di halaman belakang kertas soalan ini.

H

Diagram 5

For

Examiners only

T

Time (minutes)

M

30

0

120

Distance (km)

S

O

B

x

C

R

A

P

N

For

Examiners only

S

T

For

Examiners only

Q

For

Examiners only

For

Examiners only

For

Examiners only

P

For

Examiners only

Diagram 7(i)

6 cm

5 cm

3 cm

3 cm

R

U

Q

M

T

N

Q

G

C

55

[Lihat sebelah

SULIT

1449/2

D

P

Q

R

P

Q

END OF QUESTION PAPER

For

Examiners only

B

A

90

45o

R

P

T

Diagram 3

EMBED Equation.DSMT4 if and only if EMBED Equation.DSMT4

7 is a factor of 40

Diagram 1

E

Graph for Question 14

8

6

0

10

4

x

2

-2

0

4

-6

2

6

-4

8

y

Table 1

Graph for Question 12

For

Examiners only

3 cm

P

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