1449/1

SEKOLAH MENENGAH INTEGRASI SAINS TAHFIZMAJLIS AGAMA ISLAM WILAYAH PERSEKUTUAN

PEPERIKSAAN PENILAIAN SPM TINGKATAN 5 2015

MATEMATIK Kertas 1

Satu jam lima belas minit

JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU.

1. Kertas soalan ini mengandungi 40 soalan.

2. Jawab semua soalan.

3. Jawab setiap soalan dengan menghitamkan ruangan yang betul pada kertas jawapan objektif.

4. Hitamkan satu ruangan sahaja bagi setiap soalan.

5. Sekiranya anda hendak menukar jawapan, padamkan tanda yang telah dibuat. Kemudian tandakan jawapan yang baru.

6. Rajah yang mengiringi soalan tidak dilukis mengikut skala kecuali dinyatakan.

7. Satu senarai rumus disediakan di halaman 2 hingga 4.

8. Penggunaan kalkulator saintifik yang tidak boleh diprogramkan adalah dibenarkan.

Kertas soalan ini mengandungi 19 halaman bercetak [Lihat sebelah

SULIT

SULIT1449/1MatematikKertas 1Mei 2014 1 jam 15 minit

SULIT 3472/2

INFORMATION FOR CANDIDATES

1. 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.

ALGEBRA1. 5.

2. 6.

3. 7.

4. 8.

GEOMETRY1. Distance between two points

=

2. Midpoint of two points

3. A point dividing a line segment

4.Area of triangle =

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Section ABahagian A[45 marks]

Answer all questions in this section.

1. Solve the following simultaneous equations

i- y + 2x = 7

y 2 = xy 1[5 marks]

ii- x + 3y = 1x2 + 3x +5y = 20

[5 marks]

iii- 2x + 3y = 10 = [5 marks]

2. Function f is defined by . Function gf is defined as .Find (i) the function g(x) [2 marks]

(ii) the values of p if g(-2p) = f(p) - 2 [5 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. Given that 2 and are roots of the quadratic equation = 0, finda) the value of and p [ 3 marks ]b) a new quadratic equation whose roots are and 4 [ 4 marks ]

5. 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

[ 5 marks ]

Section B

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SULIT 3472/2

Bahagian B[55 marks]

Answer all questions in this section

6. 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]

7. (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]

8. The quadratic function f is defined by .

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1 3

11

23

x

y

y= f(x)

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SULIT 3472/2

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 ]

9. a) Solve the equation .

b) Find the value of x and of y that satisfy both the equations below.

,

[6 marks]

10. a) Express in the simplest form.

[3 marks]

b) Solve the equation [3 marks]

c) Given that log10 x = m and log10 y = n, express log10 in terms of m and n.

[3 marks]

11. Given that ,

a) express in the form of in terms of m, where a, p and q

are constants [3 marks]

b) hence, find the value of m if the minimum value of is 5. [2 marks]

c) sketch the graph of the function [2 marks]

d) state the equation of the curve formed when the graph function of is reflected

on the x-axis [3 marks]END OF QUESTION PAPER

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PREPARED BY CHECKED BY VERIFIED BY

……………………………… ………………………………… ………………………………(MOHD ZULHANIF IDRIS) (MOHD FAEZ MOHTAR) (PN NURA’AFIFAH MARNI)ADDITIONAL MATHEMATIC VICE PRINCIPAL OF PRINCIPALTEACHER ADMINISTRATION