6SULIT 3472/27SULIT 3472/2

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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)

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SULIT

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