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SULIT 3472/1

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NAMA : ___________________________________________________TINGKATAN :___________

NO.KAD PENGENALAN : ________________________________________

SEKOLAH BERASRAMA PENUH INTEGRASI RAWANG

BANDAR TASIK PUTERI,48020 RAWANG,

SELANGOR DARUL EHSAN.

PEPERIKSAAN PERTENGAHAN TAHUN 2011 3472/1

ADDITIONAL MATHEMATICS FORM FOUR

Kertas 1

Mei 2010

2 jam Dua jam

JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU

1. Tulis nama,no kad pengenalan dan tingkatan anda pada ruang yang disediakan.

2. Kertas soalan ini adalah dalam bahasa Inggeris.

3. Kertas soalan ini mengandungi 25 soalan.

4. Jawab semua soalan. 5. Tulis jawapan anda dalam ruang

yang disediakan dalam kertas soalan anda.

6. Show your workings.It may help you to get marks.

7. A list of formulae is provided on page 2.

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

SOALAN MARKAH PENUH

MARKAH DIPEROLEH

1 2 2 2

3 4 4 2 5 3 6 3 7 3 8 3 9 4 10 3

11 3 12 3 13 3 14 4 15 4 16 4 17 3

18 3 19 3 20 3 21 3 22 4 23 3 24 4 25 4

JUMLAH 80

Kertas soalan ini mengandungi 16 halaman bercetak termasuk muka hadapan ini.

http://www.tutormansor.wordpress.com

SULIT 3472/1

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

ALGEBRA

1. √

2.

3.

4.

5.

6.

7.

8.

GEOMETRY

1. Distance =

2. Midpoint = , ,

3. A point dividing a segment of a line = , ,

4. Area of triangle = | |


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1. In Diagram 1, the function h maps x to y and the function g maps y to z.

–2 ●

Diagram 1

Determine

(a) g1(5) ,

(b) gh(–2).

[2 marks]

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SULIT 3472/1

Answer all questions.

3472/1 © SEPINTAR 2011 SULIT

1

2

●5 ● 3

x y z h g


5

2. Given the function f : x → │2x – 3│, find the values of x such that f (x) = 7.

[2 marks]

3. Solve the quadratic equation 3 – 8(x – 1) = 2x (x + 1). Give your answers correct to four

significant figures.

[4 marks]

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[ Lihat Sebelah


2

2

4

3


6

4. Given that –5 is one of the roots of the quadratic equation 15 – px = 2x2 .

Find the value of p. [2 marks]

5. The quadratic function f (x) = p (x + q)2 + r where p , q and r are constants, has a

maximum value of 16 . The equation of the axis of symmetry is x = 2.

State

(a) the range of the values of p,

(b) the value of q,

(c) the value of r.

[ 3 marks]

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3

5

2

4


7

6. Given f (x) = 4x 2 – 1. Find the range of value of x so that f (x) is always positive.

[3 marks]

7. Given 38 x = 24

64

x

. Find the value of x. [3 marks]

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3

6

3

7


8

8. Solve the equation 32x + 1 (4x – 2) = 32. [3 marks]

9. Given logm 5 = p and logm 3 = t. Express logm

m3

125 in terms of t and p.

[4 marks]

SULIT 3472/1


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3

8

4

9


9

10. Find the range of the values of 𝑥 for (2𝑥 − 1)(𝑥 + 4) > 4 + 𝑥 [3 marks]

11. The quadratic equation 𝑥(𝑥 + 1) = 𝑝𝑥 − 4 has two distinct roots.Find the range of

values of 𝑝 . [3 marks]

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3

3

10

11


10

12. The straight line 𝑦 = 5𝑥 − 3 does not intersect the curve 𝑦 = 2𝑥2 − 𝑥 + 𝑝.Find the

range of the values of p. [ 3 marks]

13. Solve the equation 324𝑥 = 48𝑥+6. [ 3 marks]

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3

12

3

13


11

14. Solve the equation 2𝑥+4 − 2𝑥+3 = 1 [ 4 marks]

15. Solve the equation 𝑙𝑜𝑔𝑥81 − 𝑙𝑜𝑔𝑥3 = 3 [ 4 marks ]

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4

15

4

14


12

16. Given 𝑙𝑜𝑔9𝑥 = 𝑙𝑜𝑔32.Find the value of 𝑥 . [ 4 marks ]

17. Diagram 5 shows the graph of a quadratic function 𝑦 = 𝑓(𝑥).The straight line

𝑦 = −4 is a tangent to the curve 𝑦 = 𝑓(𝑥). [ 3 marks ]

a) Write the equationof the axis of symmetry of the curve.

b) Express 𝑓(𝑥) in the form (𝑥 + 𝑏)2 + 𝑐 where b and c are constants

a) __________________

b) __________________

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4


SULIT 3472/1

y

x

𝑦 = f(x)

𝑦 = −4 1 O 5

Diagram 2

17

3


13

18. Diagram 4 shows the graph of the function 𝑦 = −(𝑥 − 𝑘)2 − 2 , where k is a constant.

[ 3 marks ]

Find, a) The value of k

b) The equation of the axis of symmetry,

c) The coordinates of the maximum point.

Answer : a) k = ______________

b) _________________

c) _________________

19. Find the range of values of 𝑥 for which 𝑥(𝑥 − 4) ≤ 12 [ 3 marks ]

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3

18

y

x O

• (2 ,- 3 )

-3

Diagram 3

19

3


14

20. If 𝛼 and 𝛽 are the roots of the quadratic equation 2𝑥2 − 6𝑥 + 5 = 0 ,form the quadratic

equation which has the roots 𝛼 + 1 and 𝛽 + 1. [ 3 marks ]

]

21. Form the quadratic equation which has the roots – 3 and 1

2 .Give your answer in the form of

𝑎𝑥2 + 𝑏𝑥 + 𝑐 = 0, where a , b and c are constants. [ 3 marks ]

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3

20

21

3


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22. The quadratic equation 𝑥2 + 𝑝𝑥 + 16 = 4𝑥 has two equal roots .Find the possible values of 𝑝.

[ 4 marks ]

23. Solve the quadratic equation 2𝑥(𝑥 − 4) = (1 − 𝑥)(𝑥 + 2).Give your answer correct to four

significant figures.

[3 marks]

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22

3

23


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24. The function m is defined as 𝑚(𝑥) =3

5−𝑥, 𝑥 ≠ 5.Find

a) 𝑚−1(𝑥)

b) 𝑚−1(6) [ 4 marks ]

25. Given that function ℎ(𝑥) =6

𝑥, 𝑥 ≠ 0 and the composite function ℎ𝑔(𝑥) = 3𝑥 ,find

a) 𝑔(𝑥)

b) The value of x when 𝑔ℎ(𝑥) = 5 [ 4 marks ]

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4

24

4


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