Set 1_K2

SULIT

PEPERIKSAAN PERCUBAAN 1449/2 SIJIL PELAJARAN MALAYSIA

MATHEMATICS

Kertas 2

2 jam Dua jam tiga puluh minit

JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU

Untuk Kegunaan Pemeriksa/ Guru

Bahagian Soalan Markah

Penuh

Markah

Diperoleh

A

1 3

2 4

3 4

4 4

5 5

6 4

7 5

8 6

9 6

10 5

11 6

B

12 12

13 12

14 12

15 12

16 12

Jumlah

Kertas soalan ini mengandungi 26 halaman bercetak.

NAMA :

TINGKATAN :

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.

SULIT 1449/2

1449/2 2010 Hak Cipta Zon A Kuching SULIT

2

For

Examiners

Only

MATHEMATICAL FORMULAE

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

commonly used.

RELATIONS

1 m n m na a a

2 m n m na a a

3 n

m mna a

4 A-1

= bcad

1

ac

bd

5 Distance = 2 2

2 1 2 1x x y y

6 Midpoint, ,x y = 2

,2

2121 yyxx

7 Average speed =

8 Mean =

9 Mean =

10 Pythagoras Theorem

2 2 2c a b

11 ( )

( )( )

n AP A

n S

12 ( ') 1 ( )P A P A

13 2 1

2 1

y ym

x x

1449/2 [Lihat sebelah

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sum of data

number of data

sum of (classmark frequency)

sum of frequencies

distance travelled

time taken

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1449/2 2010 Hak Cipta Zon A Kuching [Lihat halaman sebelah

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3

14 intercept

intercept

ym

x

SHAPES AND SPACE

1 Area of trapezium = 2

1 sum of parallel sides height

2 Circumference of circle = d = 2 r

3 Area of circle = r2

4 Curved surface area of cylinder = 2 rh

5 Surface area of sphere = 4 r2

6 Volume of right prism = cross sectional area length

7 Volume of cylinder = r2h

8 Volume of cone = 3

1r

2h

9 Volume of sphere = 3

4r

3

10 Volume of right pyramid = 3

1 base area height

11 Sum of interior angles of a polygon = o2 180n

12 arc length angle subtended at centre

circumference of circle 360

13 360

centreat subtended angle

circle of area

sector of area

14 Scale factor, k = PA

PA'

15 Area of image = 2 area of objectk

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Section A

[52 marks]

Answer all questions in this section.

1 The Venn diagram below shows sets P, Q, and R such that the universal set P Q R .

On the diagrams in the answer space, shade

(a) the set P Q,

(b) the set Q (R P) .

[3 marks]

Answer :

(a)

(b)

R

Q

P

R

Q

P

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5

2 Using factorisation, solve the following quadratic equation 2 6

2 5

y y.

[4 marks]

Answer :

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

12 1

3

3 6

p q

p q

[4 marks]

Answer :

For

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4 Diagram 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)

Diagram 1

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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 5q 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:

.

7 is a factor of 40

x y if and only if 3 3x y

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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 22

7, calculate the volume, in cm

3, of the remaining solid.

[4 marks ]

Answer:

Diagram 2

C

G H

A B

D

E F

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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 x intercept of the straight line RS.

[5 marks]

Answer :

(a)

(b)

(c)

x

y

T

S (6, 8)

R

4

P(2, 9)

Q

Diagram 3

0

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8 (a) Given that 9 3 1 3 1 01

1 6 9 0 1hk , 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.

3 5

6 9 6

m n

m n

[6 marks]

Answer:

(a)

(b)

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

Diagram 4

It is given that PT = TS = 6 cm.

Use 7

22 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)

For

Examiners

only

45o

S O T P

R

Q

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10 Diagram 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)

T 0 30

120

Distance (km)

Time

(minutes)

Diagram 5

55

90

A

B C

D

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11 A 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)

For

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14

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Section B

[48 marks]

Answer any four questions in this section.

12 (a) Complete Table 1 in the answer space for the equation 432 2 xxy by writing

down the values of y when x = -2 and x =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 432 2 xxy for 43 x .

[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 0582 2 xx for 43 x . State the values of x.

[4 marks]

Answer :

(a)

x -3 -2 -1 0 1 2 3 4

y -23 -1 4 5 2 -16

(b) Refer graph on page 15.

(c)

(i) y =

(ii) x =

(d)

x = ,

Table 1

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Graph for Question 12

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For

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13 Diagram 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 translation4

2.

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]

y

8

-4

6

2

-6

4

0 -2 2 x 4 10 6 8

E

Q

P

A

B C

G A

F 6

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Answer :

(a) (i)

(ii)

(b) (i) ..

..

(ii)

(c) (i) Scale factor = .

(ii)

For

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18

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14. The data in Table 2 shows the frequency distribution of the mass, in kg, of a group of 32

students in a particular class.

Mass (kg) Frequency

35 39 4

40 44 6

45 49 10

50 54 7

55 59 3

60 64 2

Table 2

(a) Based on the data in Table 2,

(i) state the midpoint of the modal class,

(ii) calculate the estimated mean of the mass of the students.

[4 marks]

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

[2 marks]

(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 the horizontal axis and 2 cm to 5 students on

the vertical axis, draw an ogive for the data.

[4 marks]

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

than 57 kg.

[2 marks]

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Answer:

(a) (i)

(ii)

(b)

Mass (kg) Frequency Upper Boundary Cumulative frequency

35 39 4

40 44 6

45 49 10

50 54 7

55 59 3

60 64 2

Table 3

(c) Refer graph on page 20.

(d)

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Graph for Question 14

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15 You 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)

P

S

N

T

M

Q

U R

3 cm

3 cm

5 cm

6 cm

Diagram 7(i)

For

Examiners

only

X

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(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]

3 cm

P

S

N

T

M

Q

U R

3 cm

D

E

F

G

5 cm

6 cm

7 cm

4 cm

L

K

Diagram 7 (ii)

Y

W

V

J

Y

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Answer :

(b) (i)

(ii)

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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]

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Answer:

(a) (i)

(ii) .

(b)

(c)

(d)

END OF QUESTION PAPER

For

Examiners

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INFORMATION FOR CANDIDATES

1. 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.

Set 1_K2

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Transcript of Set 1_K2