My Name is Red

Topics: Linear equation, Line, Elementary algebra Pages: 25 (1464 words) Published: October 28, 2013
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Mathematics
Kertas 1
September 2012
1.
1-Jam
4

PEPERIKSAAN PERCUBAAN SPM 2012

TINGKATAN LIMA

MATEMATIK
Kertas 1

Satu jam lima belas minit

JANGAN BUKA KERTAS SOALAN INI
SEHINGGA DIBERITAHU

I.

Kertas soalan ini ada/ah dalam dwibahasa.

2.

Soalan dalam bahasa /nggeris mendahului soalan yang sepadan
dalam bahasa Melayu.

3. CaJon dikehendaki membaca maklumat di halaman belakang
Kertas soalan ini.

halaman bercetak.

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2
MATHEMATICAL FORMULAE
RUMUS MATEMATIK
The following formulae may be helpful in answering the questions. The symbols given are the ones commonly used.

Rumus-rumus berikut boleh membantu anda menjawab soalan. Simbolsimbol yang diberi adalah yang biasa digunakan. RELATIONS
PERKAITAN
Pythagoras Theorem:

amX a =am+n

10

2

am +a" =am-n

11

P(A) = n(A)
n(S)

3

(amr =a

12

P(A') = 1- P(A)

4

A-'-

13

m=

11

I

mn

I

(d

ad -be -c

-:)

Y2- Yt
x 2 -x1

y-intercept
x-intercept
pintas an-y .
m=.
pintasan-x

m=-..;__--~

Distance I Jarak =

5

Teorem Pithagoras:
c2 = a2 +b2

J(x, -x 2 +(y,- Y2Y
Y

14

Midpoint I Titik tengah,
6

( x ,y)=(x,+x2 ' y,+y2J
2
2

distance travelled
.
k
time ta en
7
jarak yang _ __
.
Purata l aJU = .::..__ _..::._..:::.....dilalui
masa yang diambil
sum of data
Mean= - - - - - number of data
8
hasil tam bah nilai data
Min=---------~~.... -3 or 52 = 10
-2 > -3 atau 5 2 = 10
b. Write down two implications based on the following sentence: Tulis dua implikasi berdasarkan pernyataan berikut:

Vm = 4 if and only if m = 64.
Vm = 4 jikadan hanyajika m = 64.
c. Make a general conclusion by induction for the sequence of numbers 5, II, 21 , 35 , ... which follows the following pattern:
Buat satu kesimpulan secara aruhan untuk urutan nombor 5, 11, 21, 35, .. . yang mengikut pola berikut :

5 = 2(li + 3

11

=

2(2)2 + 3

21

=

2(3i + 3

35

=

2(4i + 3
[ 5 marks I 5 markah ]

Answer I Jawapan

a)

b) Implication l I lmplikasi 1 :

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5. Calculate the value of m and n that satisfy the following simultaneous linear equations:
Hi tung nilai m dan n yang memuaskan persamaan linear serentak berikut:

3
=8
2
m - 2n = 8

-m + n

[ 4 marks I 4 markah ]

Answer I Jawapan:

1449/2

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For
Examiner 's
Use

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10

For

144912

·

Examiner's
Use

6. In Diagram 6 , JK , KL and LM are straight lines . J is on they-axis and K is on the x-axis. KL is parallel to y-axis and JK is parallel to LM.
Dalam Rajah 6, JK, KL dan LM adalah garis lurus . J terletak pada paksi-y dan K terletak pada paksi-x. KL adalah selari dengan paksi-y dan JK adalah selari dengan LM
y

M ( 8, 5)

J

L
Diagram 6 I Rajah 6

The equation of JK is 3x- y = 7 .
Persamaan JK adalah 3x- y = 7.
a.) State the equation of the straight line KL.
Nyatakan persamaan gar is lurus KL.
b.) Find the equation of straight line LM and hence, x-intercept. Cari persamaan garis lurus LM dan seterusnya nyatakan pintasan-x.

[6 marks/ 6 markah]
Answer/Jawapan
(a)

(b)

1 49/2

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7.

1449/2

Using factorisation , solve the following quadratic equation : Menggunakan pemfaktoran, selesaikan persamaan kuadratik berikut: 2

3x + 3x
2

For
Examiner "
s
Use

=x + 2
[ 4 marks I 4 markah]

Answer I Jawapan :

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For
Examiner's
Use

8.

The inverse matrix of (

Matriks songsang bagi (

a)

7

2

-5

-3...
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