22 soalan cuti terancang add maths ting 4

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SULIT 3472

3472

Matematik

Tambahan

May

2010

2 jam

SEKOLAH MENENGAH KEBANGSAAN SS17, SUBANG JAYA

PEPERIKSAAN SEMESTER 1 2010

TINGKATAN 4

MATEMATIK TAMBAHAN

JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU

INFORMATION FOR CANDIDATES

1. This question paper consists of two sections : Section A and Section B.

2. Answerall questions in Section A and Section B.

3. Answer questions from Section A in the question paper and Section B

in the test-pad.

4. Give only one answer / solution to each question.

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

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. You may use a non-programmable scientific calculator.

Kertas soalan ini mengandungi 11 halaman bercetak dan 1 halaman tidak bercetak.

Dua jam tiga puluh minit


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ADDITIONAL MATHS FORM FOUR (26 MAY 2012 TO 10 JUNE 2012)

1 Solve the simultaneous equations 2x + 3y = 5 and x2

-2xy + 3y2

= 2.

Give your answer correct to three significant figures. ( 5 marks )

2 ( a ) It is given that log 73 = k. If 73l -1

= 21, find l interms of k. ( 3 marks )

( b ) Given that 2 log 9 y - 3 log 27 x = 2, find y in terms of x. ( 5 marks )

( c ) Given that log xa = 2.32 and log xb = 2.81, find the value

of log abx . ( 2 marks )

3 The function f ( x) = x2

-6hx + 8h2

+ 1 has a minimum value of t + 2h2,

where t and h are constants.

( a ) By completing the square, show that t = 1 - 3h

2

. ( 4 marks ) ( b ) Hence, find the value of h and t if the graph of the function is

symmetrical about x = h - 1 . ( 4 marks )

4 The quadratic equation 3x2

- 2px + 9q = 0 has the roots of -5 and 2.

Find

( a ) the value of p and q . ( 4 marks )

( b ) the range of k such that 3x2

- 2px + 9q = k has no real roots. ( 4 marks )

5 The function f and its inverse function f-1

are defined by f( x) = hx ,

x - 3

x = 3, f-1

( x) = kx , x = 2 respectively, where h and k are constants.

x - 2

Another function g is defined by g( x) = 1 , x = 0.

x

( a ) Find the value of h and k . ( 3 marks )

( b ) If gf-1

( x)= -5x, find the values of x. ( 4 marks )

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Prepared by, Checked by

LIANG WAI MIN CHONG KIM LIAN

LEONG YEE PING ( Head of Mths & Science Dept. )

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D

6.

E F

A ( 7 - x ) cm

B C

6x cm

DIAGRAM 5

Diagram 5 shows a prism with a uniform triangular cross-section of ABC.

Given that BC = 6x cm, CF = ( 7 - x ) cm and the height of the prism is 4 cm,

( a ) ( i ) show that the volume of the prism, V cm3, is given by

V = 84x - 12x2

, ( 2 marks )

( ii ) determine the maximum value of V. ( 4 marks )

( b ) A length of 40 cm wire is bent into a square. When the wire is

heated, the length expanded at a rate of 0.2 cm s -1. Find the

rate of change of the area of the square. ( p = 3.142 ) ( 4 marks )

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1. V

C 77o

A 48o

B

DIAGRAM 6

Diagram 6 shows a tent VABC in the shape of a pyramid with right-angled

triangle ABC as the horizontal base. V is the vertex of the tent. The

angle between line VB and the horizontal plane is 35o

and VBA = 77o

.Given that VC = 3.6 m, calculate

( a ) the length of VB, ( 3 marks )

( b ) the length of AB if the area of the triangle ABC is 5.6 cm2

, ( 4 marks )

( c ) the area of triangle VAB. ( 3 marks )

2.

Item Weightage

A 24B

16C 28D 12E 20

TABLE 3

Table 3 shows the prices, price indices and the respective weightages of

five items.

( a ) Find the values of x, y and z . ( 3 marks )

( b ) Calculate the composite index of the items for the year 2006

based on the year 2003. ( 2 marks )

( c ) The price of item B increases by 20% from the year 2006 tothe year 2007. Find the price index of item B for the

year 2007 based on the year 2003. ( 3 marks )

( d ) The monthly expenses for the five items for the year 2006

is RM567. Find the corresponding monthly expenses

for the year 2003 ( 2 marks )

END OF QUESTION PAPER

15.00

y

14.0020.00

Answer one question from this section.

Section C

( 10 marks )

Price index for

year 2006 based

on the year 2003

20.50 x

Price in the year

2003 ( RM )

Price in the year

2006 ( RM )

z

120

110

125

130

16.50

16.50

18.2029.00

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12 ( a ) Lengkapkan Jadual 1 pada ruang jawapan untuk nilai bagi y = 8 .

x

x -5 -4 -2 -1 -0.8 0.8 1 2.5 5

y -1.6 -4 -8 10 3.2 1.6

( 3 markah )

Jadual 1

( b ) Untuk ceraian soalan ini, gunakan kertas graf pada halaman 13. Anda bibenarkan

menggunakan pembaris fleksibel.

Dengan menggunakan skala 2 cm kepada 1 unit pada paksi-x dan 1 cm kepada 1 unit

pada paksi-y, lukis graf bagi y = 8 untuk nilai x dalam julat -5 < x < 5.

x ( 4 markah )

( c ) Daripada graf itu, cari

( i ) nilai y apabila x = 4.

( ii ) nilai x apabila y = 5.4. ( 2 markah )

( d ) Dengan melukis satu garis lurus yang sesuai pada graf, cari nilai-nilai x dalam julat -5 < x < 5

yang memuaskan persamaan 8 - x2

= 0. ( 3 markah )

Jawapan :

( a )

x - 4 -0.8 1

y

( b ) Rujuk graf di halaman 13.

( c ) ( i ) y =

( ii ) x = .

( d ) x = ..

Bahagian B

( 48 Markah )

Jawab empat soalan daripada bahagian ini.

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13.

Rajah 7

Graf dalam Rajah 7 menunjukkan sisi empat ABCD, sisi empat AGFE, dan sisi empat HJKE.

( a ) Penjelmaan T mewakili translasi 2 . Penjelmaan P mewakili putaran ikut arah jam

-3

melalui 90O

pada titik D. Nyatakan koordinat imej bagi titik E di bawah penjelmaan berikut.( i ) T

( ii ) P

( iii ) TP ( 4 markah )

( b ) Sisi empat AGFE ialah imej bagi sisi empat ABCD di bawah satu penjelmaan V dan sisi

empat HJKE ialah imej bagi sisi empat AGFE di bawah satu penjelmaan W. Huraikan selengkapnya

( i ) penjelmaan V,

( ii ) penjelmaan W. ( 6 markah )

( c ) Diberi bahawa luas sisi empat ABCD ialah 12.5 unit2, hitung luas sisi empat BCDEFG.

( 2 markah )Jawapan :

( a ) ( i )

( ii )

( iii )

( b ) ( i )

( ii )

( c )

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Rajah 8

Poligon kekerapan dalam Rajah 8 menunjukkan elaun harian bagi sekumpulan 100 pekerja

sambilan di Ekspo Perdagangan.

( a ) Berdasarkan poligon kekerapan itu, salin dan lengkapkan jadual di bawah.

Elaun ( RM ) Titik tengah Sempadan Atas Kekerapan Kekerapan longgokan

15 - 19 19.5

20 - 24

25 - 29

30 - 34

35 - 39

40 - 44

45 - 49

50 - 54

55 - 59 100

( 5 markah )

( b ) Dengan menggunakan jadual yang dibina di ( a ),

( i ) nyatakan kelas mod,

( ii ) hitungkan min anggaran. ( 3 markah )

( c ) Untuk ceraian soalan ini, gunakan kertas graf pada halaman 17.

( i ) Dengan menggunakan skala 2 cm kepada RM5 pada paksi-x dan 2 cm kepada 10

orang pekerja sambilan pada paksi-y, binakan satu ogif berdasarkan jadual yang di ( a ).

( ii ) Daripada ogif itu, nyatakan kuartil ketiga.

( 4 markah )

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Jawapan :

( a )

Elaun ( RM ) Titik tengah Sempadan Atas Kekerapan Kekerapan longgokan

15 - 19 19.5

20 - 24

25 - 29

30 - 34

35 - 39

40 - 44

45 - 49

50 - 54

55 - 59 100

( b ) ( i )

( ii )

( c ) ( i ) Rujuk graf di halaman 17.

( ii )

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15.

U

V

T

S

P 34O

R

Q

Rajah 9

( a ) Dalam Rajah 9, PQR ialah tangen kepada bulatan SQVUT di Q. O ialah pusat bulatan dan

PSOV ialah garis lurus. Diberi SPQ = 34O

dan UV = VQ. Hitung

( i ) OVQ,

( ii ) QUV,

( iii ) STU. ( 6 markah )

( b ) ( i ) Cari nilai-nilai bagi x jika 0O

< x < 360O

bagi tan x = 1.25.

( ii ) Cari nilai bagi kos 246O25'.

( iii )

U T

xO

10 cm

S

yO

P Q 5 cm R

Rajah 10

Dalam Rajah 10, PQR dan USR ialah garis lurus. Diberi kos UST = 3 dan S

ialah titik tengah UR. Cari kos xO

dan tan yO. 5

( 6 markah )

O

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Jawapan :

( a ) ( i )

( ii )

( iii )

( b ) ( i )

( ii )

( iii ) kos xO

=

tan yO

= .

KERTAS SOALAN TAMAT

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KERTAS SOALAN TAMAT

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KERTAS SOALAN TAMAT

22 soalan cuti terancang add maths ting 4

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