peperiksaan pertengahan tahun 2011 3472/1 · pdf filepeperiksaan pertengahan tahun 2011 3472/1...
Post on 02-Mar-2018
246 Views
Preview:
TRANSCRIPT
SULIT 3472/1
1
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
2
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 = | |
http://www.tutormansor.wordpress.com
SULIT 3472/1
3
http://www.tutormansor.wordpress.com
4
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]
For
Examiner’s
Use/
Untuk
Kegunaan
Pemeriksa
SULIT 3472/1
Answer all questions.
3472/1 © SEPINTAR 2011 SULIT
1
2
●5 ● 3
x y z h g
http://www.tutormansor.wordpress.com
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]
For
Examiner’s
Use/
Untuk
Kegunaan
Pemeriksa
SULIT 3472/1
[ Lihat Sebelah
3472/1 © SEPINTAR 2011 SULIT
2
2
4
3
http://www.tutormansor.wordpress.com
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]
SULIT 3472/1
3472/1 © SEPINTAR 2011 SULIT
For
Examiner’s
Use/
Untuk
Kegunaan
Pemeriksa
3
5
2
4
http://www.tutormansor.wordpress.com
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]
For
Examiner’s
Use/
Untuk
Kegunaan
Pemeriksa
SULIT 3472/1
[ Lihat Sebelah
3472/1 © SEPINTAR 2011 SULIT
3
6
3
7
http://www.tutormansor.wordpress.com
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
3472/1 © SEPINTAR 2011 SULIT
For
Examiner’s
Use /
Untuk
Kegunaan
Pemeriksa
3
8
4
9
http://www.tutormansor.wordpress.com
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]
For
Examiner’s
Use/
Untuk
Kegunaan
Pemeriksa
SULIT 3472/1
[ Lihat Sebelah
3472/1 © SEPINTAR 2011 SULIT
3
3
10
11
http://www.tutormansor.wordpress.com
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]
For
Examiner’s
Use/
Untuk
Kegunaan
Pemeriksa
SULIT 3472/1
3472/1 © SEPINTAR 2011 SULIT
3
12
3
13
http://www.tutormansor.wordpress.com
11
14. Solve the equation 2𝑥+4 − 2𝑥+3 = 1 [ 4 marks]
15. Solve the equation 𝑙𝑜𝑔𝑥81 − 𝑙𝑜𝑔𝑥3 = 3 [ 4 marks ]
For
Examiner’s
Use/
Untuk
Kegunaan
Pemeriksa
SULIT 3472/1
[ Lihat Sebelah
3472/1 © SEPINTAR 2011 SULIT
4
15
4
14
http://www.tutormansor.wordpress.com
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) __________________
For
Examiner’s
Use/
Untuk
Kegunaan
Pemeriksa
16
4
3472/1 © SEPINTAR 2011 SULIT
SULIT 3472/1
y
x
𝑦 = f(x)
𝑦 = −4 1 O 5
Diagram 2
17
3
http://www.tutormansor.wordpress.com
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 ]
For
Examiner’s
Use/
Untuk
Kegunaan
Pemeriksa
SULIT 3472/1
[ Lihat Sebelah
3472/1 © SEPINTAR 2011 SULIT
3
18
y
x O
• (2 ,- 3 )
-3
Diagram 3
19
3
http://www.tutormansor.wordpress.com
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 ]
SULIT 3472/1
3472/1 © SEPINTAR 2011 SULIT
For
Examiner’s
Use/
Untuk
Kegunaan
Pemeriksa
3
20
21
3
http://www.tutormansor.wordpress.com
15
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]
For
Examiner’s
Use/
Untuk
Kegunaan
Pemeriksa
SULIT 3472/1
[ Lihat Sebelah
3472/1 © SEPINTAR 2011 SULIT
4
22
3
23
http://www.tutormansor.wordpress.com
16
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 ]
For
Examiner’s
Use/
Untuk
Kegunaan
Pemeriksa
SULIT 3472/1
3472/1 © SEPINTAR 2011 SULIT
25
4
24
4
http://www.tutormansor.wordpress.com
17
For
Examiner’s
Use/
Untuk
Kegunaan
Pemeriksa
SULIT BLANK PAGE 3472/1
3472/1 © SEPINTAR 2011 SULIT
END OF QUESTION PAPER
KERTAS SOALAN TAMAT
http://www.tutormansor.wordpress.com
top related