Mid Year - n.sembilan

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UNIT PEPERIKSAAN & PENILAIAN

SMK TUNKU BESAR BURHANUDDIN

71550 SERI MENANTI, N. SEMBILAN

PEPERIKSAAN PERTENGAHAN TAHUN

TINGKATAN 5 2010

MATHEMATICS

Kertas 2

Dua jam tiga puluh minit

Pemeriksa

Bahagian Soalan MarkahPenuh

MarkahDiperoleh

A

1 4

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 soalandalam 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 dilukismengikut skala kecuali dinyatakan.

4.Satu senarai rumus disediakan di halaman 2 & 3

5.Anda dibenarkan menggunakan kalkulator

saintifik yang tidak boleh diprogram.

3 3

4 3

5 5

6 67 5

8 5

9 6

10 6

11 5

B

12 12

13 12

14 12

15 12

Jumlah

Kertas soalan ini mengandungi 14 halaman bercetak

Di Sediakan Oleh Di Semak Oleh

______________________

(Sunita binti Mukhtar )

Panatia Matematik SMKTBB

SULIT

1449/2

Mathematics

Kertas 2

Mei 2010

212 jam

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Rumus-rumus berikut boleh membantu anda menjawab soalan. Simbol-simbol yang diberi adalah yang

biasa digunakan.

PERKAITAN

1. nmnm aaa +

=× .

2. nmnm aaa −

=÷

3. ( ) mnnm aa =

4.

−

−−

=−

ac

bd

bcad A

11

5.)(

)()(

S n

An A P =

6. )(1)'( A P A P −=

7.2 2

1 2 1 2( ) ( ) Jarak x x y y= − + −

8. Titik Tengah

( )

++

=2

,2

, 2121 y y x x y x

9. Purata laju = diambil yang masa

dilalui yang jarak

10. Min =databilangan

datanilaitambahhasil

11. Min =apanker ketambahhasil

)apanker ketengahtitik nilai( tambahhasil ×

12. Teorem Pithagoras222 bac +=

13.12

12

x x

y ym

−−

=

14. xasanint p

yasanint pm

−−−=

BENTUK DAN RUANG

1. Luas trapezium = ×

2

1hasil tambah dua sisi selari × tinggi

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2. Lilitan bulatan = π d = 2π j

3. Luas bulatan = π j2

4. Luas permukaan melengkung silinder = 2π jt

5. Luas permukaan sfera = 4π j2

6. Isipadu prisma tegak = luas keratan rentas × panjang

7. Isipadu silinder = π j2t

8. Isipadu kon =3

1π j2t

9. Isipadu sfera =34 π j3

10. Isipadu piramid tegak = ×

3

1luas tapak × tinggi

11. Hasil tambah sudut pedalaman poligon = ( n − 2 ) × 180 0

12. 0360

pusat sudut

tanbulatanlili

lengkok panjang =

13. 0360

pusat sudut

tanbulaluas

sektor luas=

14. Faktor skala, k = PA

PA '

15. Luas imej = k 2 × luas objek

Section A

[52 marks]

Answer all questions in this section

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1 Using factorisation, solve the following quadratic equation :

h2 = 9( h – 1)

2

[4 marks]

Answer :

2 Calculate the value of v dan w taht satisfy the following simultaneous linear equations :

2 1v w+ = and 4 3 18v w− = −[4 marks]

Answer :

3 Venn Diagram in diagram 1(a) and 1(b) shows set ξ , P , Q dan R . In diagram provided in the

answer spances. shade

(a) )( ′∪∩ RQ P (b) )( RQ P ∩∩′ Jawapan :

(a) (b)

[3 marks]

4 The diagram shows a solid formed by joining a cone with hemisfere

The height of the con is 7cm, Diameter of the cone and the hemisfere is 6 cm

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ξ P

R

Q P

ξ P

R

Q P

Diagram 1(a) Diagram 1(b)



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Diagram 2

Using7

22=π , Calculate the volume, in cm3 , of the solid

Answer :

5.

M( -3, 7)

In Diagram 2, O is the origin. Straight line KL is parallel to straight line MN. The equation of

straight line KL is 2x + y = 4

The points L and N lie on the y- axis

Find(a) The equation of straight line MN

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x

y

K

L

N



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(b) The x –intercept of the straight line MN

[5 marks]

Jawapan : (a)

(b)

(c)

6

(a) M is a 2 X 2 matrix where M3 4 1 0

2 5 0 1

=

, find the matrix of M

(b) Write the following simultaneous linear equations as matrix equation :

3 4 5

2 5 8

p q

p q

+ =

+ =

Hence, using matrix method, calculate the value of p and q

[6 marks]

Answer :(a)

(b)

.

7. Diagram 4 shows the speed-time graph of a particle for a period of 18 seconds

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a) State the the length time, in seconds, the particle moves with uniform speed

b) Calculate the rate of change, in ms-2, in the first 6 seconds

c) Calculate the value of u, if the average speed of the particle in the last 12 seconds

[5marks]Answer :

a)

b)

c)

8 Diagram 5 shows the distance – time of the journey of a car from Pulau Pinang to Johor Bahru over a

period of t hours. Distance (km)

800

300

Time (hour)

0 4 2 t

(a) State the length of time, that car is stationary

(b) State the distance in km, from Johor Bahru when the car is stationary

(c) Calculate the car average speed, in km h-1, during the 6 first hours

(d) If the average speed of the car for the whole journey is 80km/h

Calculate the value of t

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Time(s)

Speed(ms/s)

u

4

1018

22

Diagram 4

6

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[5 marks] Answer :

(a)

(b)

(c

d)

9.

Diagram 6,shows OKJH with the centre O and a circle FGH with centre M.

F is the midpoint of OH and OK = 28

Using7

22=π , calculate

(a) The perimeter in cm of the whole diagram

(b) The area cm of the shaded region

[6 marks]Answer

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Diagram 6



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a)

b)

10 Diagram 7 shows three numbered cards in box P and four numbered in box Q

5 15 19 3 6 15 17

Box P Box Q

A card is picked at random from each of the boxes

By Listing the possible outcomes, find the probability that

a) a card with a number which is a multiple of 2 or a multiple of 5 are picked

b) a card with a number which is a multiple of 2 and a multiple of 5 are picked

[ 5 marks ]

Answer :

a)

b)

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11 (a) ( I ) Complete the following mathematical sentence in the answer space by

10 5

( ii ) Complete the following statement the quantifier “all” or “ some” to make it a true

statement .

--------------------------- multiples of 3 are divisible by 2

[2 marks ]

(b) Complete the conclusion in the following argument

Premise 1 : If x is a factor of 12, then x is a factor of 24

Prermise 2 : x is not a factor of 24

Conclution : _____________________________________

[1 marks]

(c) Write down two implications based on the following sentence :

3m > 15 if and only if m > 5

[2 marks]

Answer :

(a) ( I )_____________________________________________________________________

( ii ) ____________________________________________________________________

(b)Conclusion:____________________________________________________________________

(c)Implication 1 : ______________________________________________________________

Implication 2 :______________________________________________________________

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Section B

[48 marks]

Answer four questions from this section.

12 (a) Complete Table 1 in the answer space fo the equation4

y x

= −

x −4 −2.5 −1 -0.5 0.5 1 2 3.2 4

y 1 1.6 8 -8 -4 -1.25 -1

Table 1

[2 marks]

For this part of the question, use the graph paper provided on page 31. You may use aflexible curve rule

(b) By using a scale of 2 cm to 1 unit on the x-axis and 2 cm kepada 2 unit on the-yaxis, draw the

graph4

y x

= − for 4 4 x− ≤ ≤ .

[5 marks]

( c ) From your graph, find

( i) the value of y when x = 1.8

(ii) the value of x when y = 3.4

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

equation

4

y x= − for 4 4 x− ≤ ≤

State these values of x [3 marks] Answer :

(a)

x −4 −2.5 −1 -0.5 0.5 1 2 3.2 4

y 1 1.6 8 -8 -4 -1.25 -1

Table 1

(c) ( i ) y = ____________________

( ii) x = _____________________

(d) x = _______________________, _______________________

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13 Diagram 7 shows rectangle D, E, F dan G.

(a) Transformation P is a reflection about line x = 3and transformation R is clockwise rotation

of 900 about the point (4, 4). State the coordinate of image of point K under

(i) Transformation P

) Transformation PR

[3 marks]

(b) Rectangle D is the image of rectangle of F under transformation V and rectangle E is theimage of rectangle D under transformation W.

Describe in full

(i) Transformation V

(ii) A single transformation which equavalent to transformation WV.

[5 marks]

(c) Rectangle G is the image of rectangle F under an enlargement

(i) State the centre coordinate of the centre of the enlargement

(ii) Given the area of rectangle F is 7 unit2, calculate the area of rectangle of G.

[4 marks]

Answer :(a) (i)

(ii)

(b) (i)

(ii)

(c) (i)

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-2 -1 O 1 2 3 4 5 6 7 8

y

x

D

E

F

G

K

RAJAH 7

5

2

3

1

7

6

4

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(ii)

14 The Data in diagram 8 shows the donations, in RM, of families to their children’s school welfared

fund.

40 24 17 30 22 26 35 19

2

3

28 33 33 39 34 39 28

2

7

35 45 21 38 22 27 35

3

0

34 31 37 40 32 14 28

2

0

32 29 26 32 22 38 44

(a) Using data in diagram 8 and a class interval of RM 5 , complete the table 2 in the answer space

[4 marks] Answer :

Donations (RM) frequency Cumulative frequency

11 - 15

16 – 20

Table 2

(b) For this part of the questions, use the graph paper provided

By using a scale of 2 cm to RM 5 on the x- axis and 2 cm to 5 families on the y-axis, drawan ogive based on the data

[6 marks]

( c ) From your ogive in (b)

( i ) Find the third quartile

(ii ) hence, explain briefly the meaning of the third quartile

Answer :( c )

(i)

(ii)

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Diagram 8



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15 (a) Complete Table 1 in the answer space fo the equation36 y x= −

x −3 −2.5 −2 -1 0 1 2 2.5

y 33 21.63 14 6 5 -9.63

Table 1

[2 marks]

For this part of the question, use the graph paper provided on page 31. You may use aflexible curve rule

(c) By using a scale of 2 cm to 1 unit on the x-axis and 2 cm kepada 5 unit on the-yaxis, draw the

graph36 y x= − bagi nilai x dalam julat 3 2.5 x− ≤ ≤ .

[4 marks]

( c ) From your graph, find( i) the value of y when x = 1.5

(ii) the value of x when y = 10

[2 marks](b) Draw a suitable straight line on your graph to find all the value of x which satisfy the

equation 3 8 6 0 x x− − = for 3 2.5 x− ≤ ≤ .

State these values of x [4 marks] Answer :

(a)

x −3 −2.5 −2 -1 0 1 2 2.5

y 33 21.63 14 6 5 -9.63

Table 1

(c) ( i ) y = ____________________

( ii) x = _____________________

(d) x = _________________________ ,_________________________

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Mid Year - n.sembilan