6SULIT 3472/27SULIT 3472/2
3472/2
SEKTOR SEKOLAH BERASRAMA PENUH
KEMENTERIAN PELAJARAN MALAYSIA
PEPERIKSAAN PERTENGAHAN TAHUN TINGKATAN 4 2007MATEMATIK
TAMBAHAN
Kertas 2
Dua jam tiga puluh minit
JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU.
1. Kertas soalan ini mengandungi dua bahagian : Bahagian A dan
Bahagian B.2. Jawab semua soalan dalam Bahagian A dan semua soalan
dalam Bahagian B.3. Tunjukkan langkah-langkah penting dalam kerja
mengira anda. Ini boleh membantu anda untuk mendapatkan markah. 4.
Rajah yang mengiringi soalan ini tidak dilukiskan mengikut skala
kecuali dinyatakan.5. Markah yang diperuntukkan bagi setiap soalan
atau ceraian soalan ditunjukkan dalam kurungan6. Satu senarai rumus
disediakan di halaman 2.7. Buku sifir matematik empat angka boleh
digunakan.8.Penggunaan kalkulator saintifik yang tidak boleh
diprogramkan adalah dibenarkan.
Kertas soalan ini mengandungi 7 halaman bercetak
[Lihat sebelahSULIT
INFORMATION FOR CANDIDATES1.This question paper consists of two
sections: Section A and Section B. 2.Answer all questions in
Section A and all questions in Section B.3.Give only one
answer/solution for each question.
4.Show your working. It may help you to get marks.5.The diagrams
provided in the questions are not drawn to scale unless
stated.6.The marks allocated for each question and sub-part of a
question is shown in brackets.7.A list of formulae is provided on
page 2.8.Four-figure mathematical tables may be used.9.You may use
a non-programmable scientific calculator.
The following formulae may be helpful in answering the
questions. The symbols given are the ones commonly used.
ALGEBRA
1.
5.
2.
6.
3.
7.
4.
8.
GEOMETRY
1.Distance between two points
=
2.Midpoint of two points
3.A point dividing a line segment
4.Area of triangle =
Section A[40 marks]
Answer all questions in this section.
1.Solve the simultaneous equations y + 2x = 7
y 2 = xy ( 1
[5 marks]2.Function g and composite function fg are defined by
and
.
(a)Sketch the graph of y = for the domain (5 x 3.
[3 marks]
(b)Find f(x).
[3 marks]
3. Given and are the roots of quadratic equation while and
are the roots of the quadratic equation , find the values of m
and n.
[6 marks]
4. a) If the line does not meet the curve , find
the range of values of k.[ 5 marks ]
b) f(x) = x2 6hx + 8h 2 + 1 has a minimum value of t + 2h 2,
where t and h are constants. By completing the square, show that t
= 1 3h 2
[ 3 marks ]
5a)Solve the equation .
[2 marks]
b)Mr. Anuar invested RM 5,000 in a unit trust for his new born
sons education in the future. The amount of the invested money will
become
for a period of n years.
i)Find the amount of his investment in the fifth year, correct
to two decimal points.
[2 marks]
ii)Find the minimum number of years required so that the amount
of his investment is more than RM 20,000.
[3 marks]
6. Given points A(4,8) and B( -2, 3). Point P moves such that PA
: PB = 2 : 1.(a)Find the equation of locus P.
[3 marks]
(b)If the locus in (a) intersect the y-axis, find the value of
y-intercepts.
[3 marks]
(c)Determine whether point C(1,2) is on the locus P.
[2 marks]
Section B
[60 marks]Answer all questions in this section.
7.Diagram 2 shows the graph of the function y = f(x).
DIAGRAM 2
It is given that f(x)= ax + b.
Find
(a)the value of a and of b,
[4 marks]
(b)the value of m if m is mapped onto itself under the function
f,
[2 marks]
(c) the value of x if f -1(x) = f 2(x).
[4 marks]8.(a)Given that the quadratic equation has two
equal
roots. Find the values of p, hence find the possible roots of
the quadratic equation.
[6 marks](b) Given that a root is two times the other root of
the quadratic equation
4x 2 18x + k = 0. Find the value of k.
[4 marks]
9. The quadratic function f is defined by.
a) Express the quadratic function in the form , where a , p
and q are constants.
[ 3 marks ]
b) Determine the maximum or minimum value of and state the
corresponding value of x.
[ 2 marks ]
c) Hence, sketch the graph of the function [ 3 marks ]
d) Find the equation of the function if the graph in (c) is
reflected in the x-axis
[ 2 marks ]
10a)Solve the equation .
[4 marks]
b) Find the value of x and of y that satisfy both the equations
below.
,
[6 marks]
11. Diagram 2 shows a triangle PQR with points P ( 0 , 4 ) and Q
( 4 , -2 )
a) If the gradient , find the value of m. [2 marks]b) Given that
the gradient PR and QR are and respectively,findi) the equation of
PRii) the equation of QR
[4 marks]
c) Find the coordinate of R. [2 marks]d) Find the area of a
triangle PQR. [2 marks]
12(a)Solve the simultaneous equations y + 5 = 2x and xy + 1 =
2x
Give your answers correct to three decimal places.
[5 marks]
(b)Functions f and g are defined by and , where h and k are
constants. It is given that f (1(10) = 4 and fg(2) = 16. Find the
value of h and of k.
[5 marks]END OF QUESTION PAPER
SULIT
3472/2
Matematik
Tambahan
Kertas 2
Mei 2007
2 jam
1
3
11
23
x
y
y= f(x)
O
DIAGRAM 2
y
x
O
P (0,4)
Q
R
(4,-2)
3472/2 SULIT3472/2 [Lihat sebelah
SULIT
_1235684095.unknown
_1235684292.unknown
_1235944019.unknown
_1236108085.unknown
_1236166125.unknown
_1236166179.unknown
_1236166039.unknown
_1236109366.unknown
_1235968062.unknown
_1236105197.unknown
_1236105215.unknown
_1235944033.unknown
_1235937313.unknown
_1235939090.unknown
_1235939727.unknown
_1235937816.unknown
_1235937999.unknown
_1235684345.unknown
_1235684199.unknown
_1235684237.unknown
_1235684121.unknown
_1235684167.unknown
_1144873537.unknown
_1232831862.unknown
_1235510287.unknown
_1235636828.unknown
_1235683162.unknown
_1235512013.unknown
_1235512032.unknown
_1235510264.unknown
_1232831932.unknown
_1232831790.unknown
_1232831853.unknown
_1232831781.unknown
_1144873017.unknown
_1144873266.unknown
_1144872827.unknown
