23 soalan cuti terancang add maths ting 5

7/31/2019 23 Soalan Cuti Terancang Add Maths Ting 5

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SULIT 3472/1

3472/1

Matematik

Tambahan

Ogos

2009

2 jam

SEKOLAH MENENGAH KEBANGSAAN SS17, SUBANG JAYA

PEPERIKSAAN SEMESTER 2 2009

TINGKATAN 5

MATEMATIK TAMBAHAN

KERTAS 1

JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU

INFORMATION FOR CANDIDATES

1. This question paper consists of 25 questions.

2. Answerall questions.

3. Give only one answer to each question.

4. Write your answers clearly in the spaces provided in the question paper.

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

6. If you wish to change your answer, cross out the work that you have done. Then

write down the new answer.

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

8. The marks allocated for each question are shown in brackets.

9. A list of formulae is provided on pages 2 to 4.

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

11. This question paper must be handed in at the end of the examination.

Kertas soalan ini mengandungi 17 halaman bercetak dan 1 halaman tidak bercetak.

Dua jam


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SULIT 3472/2

3472/2

Matematik

Tambahan

Ogos

2009

2 jam

SEKOLAH MENENGAH KEBANGSAAN SS17, SUBANG JAYA

PEPERIKSAAN SEMESTER 2 2009

TINGKATAN 5

MATEMATIK TAMBAHAN

KERTAS 2

JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU

INFORMATION FOR CANDIDATES

1. This question paper consists of three sections : Section A, Section B and Section C.

2. Answerall questions in Section A, four questions from Section B and

two questions from Section C.

3. Give only one answer/solution for each question.

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

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

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

brackets.

7. A list of formulae is provided on pages 2 to 4.

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

Kertas soalan ini mengandungi 13 halaman bercetak dan 1 halaman tidak bercetak.

Dua jam tiga puluh minit


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1.

Diagram 1

Rajah 1

Diagram 1 shows the relation between set M and set N. StateRajah 1 menunjukkan hubungan antara set M dan N. Nyatakan

( a ) the codomain of the relation,

kodomain hubungan itu,

( b ) the type of the relation.

jenis hubungan itu.

( 2 marks )

( 2 markah )

Answer : ( a ) ..

( b ) ..

Answer all questions.

Jawab semua soalan..

cdefg

a

b

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2. Diagram 2 shows the function g : x mx -1, where m and n are constant

Find the values of m and n. n

Rajah 2 menunjukkan fungsi g : x mx - 1 , dengan m dan n ialah

pemalar. Cari nilai m dan nilai n. n

( 3 marks )x g mx -1

n ( 3 markah )

1

1

3

2

1 Diagram 2

Rajah 2

Answer : ..

3. Given the function g : x 4x + 3 and h : x x2

- 2x + 5, find

Diberi fungsi g : x 4x + 3 dan h : x x2

- 2x + 5, cari

( a ) g-1

( 7 ),

( b ) hg( x ).

( 4 marks )

( 4 markah )

Answer : ( a ) ..

( b ) ..

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4. Given m and 3 are the roots of the quadratic equation ax2

- bx + c = 0.

Diberi m dan 3 ialah punca bagi persamaan kuadratik ax2

- bx + c = 0.

( a ) Express m in terms of a and b.

Ungkapkan m dalam sebutan a dan b.

( b ) Express m in terms of a and c.

Ungkapkan m dalam sebutan a dan c.

( 2 marks )

( 2 markah )

Answer : ( a ) ..

( b )..

5. The quadratic equation 2x ( x - 3 ) = 2x - k has two distinc roots. Find the

range of values of k.

Persamaan kuadratik 2x ( x - 3 ) = 2x - k mempunyai dua punca yang

berbeza. Cari julat nilai k.

( 3 marks )

( 3 markah )

Answer : ..

6. Given ( x + 3 )( x - 2 ) < 6, find the range of values of x.

Diberi ( x + 3 )( x - 2 ) < 6, cari julat nilai x.

( 3 marks )

( 3 markah )

Answer : ..

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7. Diagram 3 shows the graph of a quadratic function f(x ) = -( x + p )2

+ q,

where p and q are constants.

Rajah 3 menunjukkan graf fungsi kuadratik f(x) = -( x + p )2

+ q,

dengan keadaan p dan q ialah pemalar.

f(x)

( 3, 0 ) x

O

r

Diagram 3

Rajah 3

( a ) State the value of p.

Nyatakan nilai p.

( b ) State the equation of the axis of symmetry of the curve.

Nyatakan persamaan paksi simetri bagi lengkung itu.

( c ) Find the value of r.

Cari nilai r.

( 4 marks )

( 4 markah )

Answer : ( a ) ..

( b )..

( c )..

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8. Solve the equation 3x+2

- 3x

= 16.

Selesaikan persamaan 3x+2

- 3x

= 16.

( 4 marks )

( 4 markah )

Answer : ..

9. Given that log2 k = r and log2 3 = s, express logk12 in terms of r and s .

Diberi log 2 k = r and log 2 3 = s, ungkapkan log k 12 dalam sebutan r dan s .

( 4 marks )

( 4 markah )

Answer : ..

10. Given the first four terms of a geometric progression are -32, -16, -8 and y.

Find the value of y.

Diberi empat sebutan pertama suatu janjang geometri ialah -32, -16, -8

dan y. Cari nilai y.

( 2 marks )

( 2 markah )

Answer : ..

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11. Find the sum of the terms in the arithmetic progression, 42, 49, 56, .259.

Cari hasil tambah sebutan dalam janjang aritmetik, 42, 49, 56, ..259.

( 4 marks )

( 4 markah )

Answer : ..

12. In a geometric progression, the first term is 5 and the common ratio is r.

Given the sum to infinity of the progression is 25. Find the value of r.

Dalam suatu janjang geometri, sebutan pertama ialah 5 dan nisbah

sepunya ialah r. Diberi hasil tambah hingga sebutan ketakterhinggaan

bagi janjang itu ialah 25. Cari nilai bagi r.

( 2 marks )

( 2 markah )

Answer : ..

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13. ( a ) The variables x and y are related by the equation y = axb, where

a and b are constants. Convert the equation y = axb

to linear form.

Pemboleh ubah x dan y dihubungkan oleh persamaan y = axb,

dengan a dan b ialah pemalar. Tukarkan persamaan y = axb

kepada bentuk linear.

( b ) Diagram 4 shows a straight line graph obtained by plotting log10y

against log10x. Find the value of the following.

Rajah 4 menunjukkan graf garis lurus yang diperoleh dengan

memplot log 10y melawan log 10x. Cari nilai yang berikut.

( i ) log10 a

( ii ) b

( 4 marks )

log10y ( 4 markah )

( 5, 6 )

log10x

0 ( 2, 0 )

Diagram 4Rajah 4

Answer : ( a ) ..

( b )( i ).

( ii )

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14. Diagram 5 shows a straight line PQ which is perpendicular to a straight line

RQ at point Q. The equation of the straight line RQ is y = x + 1. Find the

coordinates of the point Q.

Rajah 5 menunjukkan garis lurus PQ yang berserenjang dengan garis

lurus RQ pada titik Q. Persamaan garis lurus RQ ialah y = x + 1. Cari koordinat titik Q.

( 3 marks )

y ( 3 markah )

P( 0, 5 )

Q

R

x0

Diagram 5

Rajah 5

Answer : ..

15. The points ( -3, 2 ) , ( 2, t ) and ( 1, 0 ) are the vertices of a triangle. Given

the area of the triangle is 11 unit2. Find the possible values of t.

Titik ( -3, 2 ), ( 2, t ) dan ( 1, 0 ) ialah bucu-bucu sebuah segi tiga.

Diberi luas segi tiga itu ialah 11 unit2

. Cari nilai-nilai yang mungkin

bagi t.

( 4 marks )

( 4 markah )

Answer : ..

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16. Diagram 6 shows a rectangle OPQR and a point S lies on the straight line OQ.

Rajah 6 menunjukkan sebuah segi empat tepat OPQR dan titik S terletak

pada garis lurus OQ.

O 6y R

10x

P Q

Diagram 6 Rajah 6

Given OS = 4SQ, express OS in terms of x and y.

Diberi OS = 4SQ , ungkapkan OS dalam sebutan x dan y.

( 3 marks )

( 3 markah )

Answer : ..

S

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17. Given OP = i + 2j and OQ = 3i +j are two vectors in a Cartesian plane,

where O is the origin.

Diberi OP = i + 2j dan OQ = 3i + j ialah dua vektor pada satu satah

Cartesan, dimana O ialah asalan.

( a ) Find the magnitude of the vector PQ.

Cari magnitud bagi vektor PQ.

( b ) Find the unit vector in the direction of PQ.

Cari vektor unit dalam arah PQ.

( 4 marks )

( 4 markah )

Answer : ( a ) ..

( b ) ..

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19. Two variables, x and y, are related by the equation y = 2x + 3 . Given that

x

y increases at a constant rate of 2 units per second, find the rate of change o

x when x = 3.

Dua pemboleh ubah, x dan y, adalah dihubungkan oleh persamaany = 2x + 3 . Diberi y bertambah dengan kadar malar 2 unit sesaat.

x

Cari kadar perubahan x apabila x = 3.

( 3 marks )

( 3 markah )

Answer : ..

20. The gradient function of a curve is px + 3, where p is a constant. The straight

line y = 5 - 2x is a tangent to the curve at the point ( -2, 1 ).

Find the value of p.

Fungsi kecerunan suatu lengkung ialah px +3, dengan keadaan p ialah

pemalar. Garis lurus y = 5 - 2x ialah tangen kepada lengkung itu pada

titik ( -2, 1 ). Cari nilai p.

( 3 marks )( 3 markah )

Answer : ..

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21. Given y = 4 , find the value of dy when x = 2. Hence, estimate the value of 4 .

x3

dx ( 1.99 )3

Diberi y = 4 , cari nilai dy bila x = 2. Seterusnya, anggarkan nilai bagi 4 .

x3

dx ( 1.99 )3

( 3 marks )( 3 markah )

Answer : ..

22. Given f (x) dx = 12 and [ f (x) - kx ] dx = 4, find the value of k.Diberi f (x) dx = 12 dan [ f (x) - kx ] dx = 4, cari nilai k.

( 3 marks )

( 3 markah )

Answer : ..

23. Given the gradient function of a curve is 3x2

- 2 and the curve passes

x2

through the point ( 1, 2 ). Find the equation of the curve.

Diberi fungsi kecerunan suatu lengkung ialah 3x2

- 2 dan lengkung

x2

itu melalui titik ( 1, 2 ). Cari persamaan bagi lengkung itu.

( 3 marks )

( 3 markah )

Answer : ..

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24. The standard deviation of a set of six numbers, 10, x, 9, 19, 13, 14, is 113 .

Find the possible values of x. 3

Sisihan piawai bagi set enam nombor 10, x, 9, 19, 13, 14 ialah 113

Cari nilai yang mungkin bagi x. 3

( 3 marks ) ( 3 markah )

Answer : ..

25. Table 1 shows the frequency distribution of employees in a company.

Jadual 1 menunjukkan taburan kekerapan umur pekerja-pekerjadi dalam sebuah syarikat.

Table 1

Jadual 1

If the median age of the distribution is 35.5 years, calculate the value of m.

Jika umur median taburan itu ialah 35.5 tahun, hitung nilai m.

( 3 marks )

( 3 markah )

Answer : ..

END OF QUESTION PAPER

Age ( years ) Number of employees

Umur ( tahun ) Bilangan pekerja

20 - 24

25 - 29

2

3

30 - 34

35 - 39

40 - 44

44 - 49

7

m

6

3

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ADDITIONAL MATHEMATICS FORM FIVE (26 MAY 2012 TO 10 JUNE 2012)

1. Solve the following simultaneous equations and give your answers correct to three

decimal places.

2x + 3y + 1 = 0

x2

+ 6xy + 6 = 0 ( 5 marks )

2. Diagram 1 shows the curve of a quadratic equation f(x) = -x2

+ kx -10. The curve

has a maximum point at B ( -2, p ) and intersects the f(x)-axis at point A.

f(x)

x

O

B( -2, p )

A

Diagram 1

Rajah 1

( a ) State the coordinates of point A. ( 1 marks )

( b ) Using the method of completing the square, find the values of k and p. ( 4 marks )

( c ) Determine the range the values of x if f(x) > -10. ( 2 marks )

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3. Diagram 2 shows an arrangement of the first three of an infinite series of similar rectangles.

The first rectangle has breadth and length of p cm and q cm respectively. The measurements

of the breadth and length of each subsequent rectangle is 1/3 the measurement of the

previous rectangle.

Diagram 2p cm

q cm

( a ) Show that the areas of the rectangles form a geometric progression.

State the common ratio of the progression. ( 3 marks )

( b ) Given p = 60 cm and q = 54 cm,

( i ) determine which rectangle has an area of 40 cm2. ( 3 marks )

81

( ii ) find the sum to infinity for the area, in cm2, of all the rectangles. ( 2 marks )

4. A curve with gradient function x - 8 has a turning point at x = m.x

2

( a ) Find the value of m. ( 2 marks )

( b ) Determine whether the turning point is a maximum or a minimum point. ( 3 marks )

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23 soalan cuti terancang add maths ting 5

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