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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.
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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) g 1(5) ,
(b) gh( – 2).
[2 marks]
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Answer al l questions.
3472/1 © SEPINTAR 2011 SULIT
1
2
●5● 3
x y zh g
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2. Given the function f : x → │2 x – 3│, find the values of x such that f ( x) = 7.[2 marks]
3. Solve the quadratic equation 3 – 8( x – 1) = 2 x ( x + 1). Give your answers correct to foursignificant figures.
[4 marks]
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2
4
3
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4. Given that – 5 is one of the roots of the quadratic equation 15 – px = 2 x2 .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
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6. Given f ( x) = 4 x 2 – 1. Find the range of value of x so that f ( x) is always positive.[3 marks]
7. Given 38 x =2
4
64
x
. Find the value of x. [3 marks]
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Use/Untuk
Keguna
Pemerik
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3
6
3
7
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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]
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3
8
4
9
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10. Find the range of the values of for (2 1)( 4) > 4 [3 marks]
11. The quadratic equation ( 1) = 4 has two distinct roots.Find the range of
values of . [3 marks]
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11
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12. The straight line = 5 3 does not intersect the curve = 2 .Find therange of the values of p. [ 3 marks]
13. Solve the equation 32 = 4+. [ 3 marks]
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12
3
13
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14. Solve the equation 2+ 2+ = 1 [ 4 marks]
15. Solve the equation 81 3 = 3 [ 4 marks ]
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UsUn
Kegu
Peme
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15
4
14
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16. Given 9 = 2.Find the value of . [ 4 marks ]
17. Diagram 5 shows the graph of a quadratic function = ().The straight line
= 4 is a tangent to the curve = (). [ 3 marks ]
a)
Write the equationof the axis of symmetry of the curve. b) Express () in the form ( ) where b and c are constants
a) __________________
b) __________________
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16
4
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SULIT 3472/1
y
x
= f(x)
= 4 1O 5
Diagram 2
17
3
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18. Diagram 4 shows the graph of the function = ( ) 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 for which ( 4) ≤ 12 [ 3 marks ]
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y
xO
• (2 ,- 3 )-3
Diagram 3
19
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20. If and are the roots of the quadratic equation 2 6 5 = 0 ,form the quadratic
equation which has the roots 1 and 1. [ 3 marks ]
]
21.
Form the quadratic equation which has the roots – 3 and .Give your answer in the form of
= 0, where a , b and c are constants. [ 3 marks ]
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21
3
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24. The function m is defined as () =
−, ≠ 5.Find
a) −()
b) −(6) [ 4 marks ]
25.
Given that function ℎ() =
, ≠ 0 and the composite function ℎ() = 3 ,find
a)
()
b) The value of x when ℎ() = 5 [ 4 marks ]
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4
24
4
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