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DISEDIAKAN
Panitia Matematik,
Sekolah Menengah Sains Labuan
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Panitia Matematik,
Sekolah Menengah Sains Labuan,
W.P. Labuan.
SEPATAH KATA KETUA PANITIA
Assalamualaikum dan Selamat Sejahtera.
Pelajar-pelajar yang dikasihi sekalian.
Modul Ulangkaji Lengkap Matematik PMR Kertas 2 ini disusun
berpandukan bentuk-bentuk soalan matematik kertas 2 yang pernah
dikeluarkan oleh Lembaga Peperiksaan Malaysia.
Setiap pelajar sepatutnya dapat menguasai dan memahami sepenuhnya
soalan-soalan yang dikemukan dalam modul ini. Adalah dinasihatkan agar
semua pelajar dapat memiliki dan menjawab semua soalan yang
disediakan sebagai persediaan menghadapi PMR 2011.
Kaedah menggunakan modul ini adalah seperti beriku:
1. Jawab soalan mengikut tajuk yang disediakan secara ikhlas.
2. Jumpa guru untuk disemak.
3. Buat pembetulan dengan pen berdakwat merah.
4. Latih Tubi (soalan lain)
5. Simpan modul ini untuk rujukan semasa latih tubi.
6. Ulangkaji modul ini sebelum peperiksaan.
Insyaallah anda akan Berjaya.
Sebenarnya modul ini dipilih daripada ssoalan peperiksaan percubaan
PMR negeri tahun-tahun lepas. Kemudian disusun mengikut tajuk untuk
memudahkan pelajar mengulangkaji. Setiap tajuk disediakan empat
soalan yang hampir sama bagi memberikan latihan yang cukup untuk
pelajar memahami sepenuhnya setiap tajuk dengan baik.
Harapan saya agar semua pelajar mendapat gred A dalam setiap
peperiksaan. Akhirnya mendapat gred A dalam PMR sebenar
Sekian, terima kasih.
“BERKHIDMAT UNTUK NEGARA”
“PANITIA MATEMATIK SMSL BERPRESTASI UNGGUL TAHUN 2015”
Yang Benar,
(ZULKIFLI BIN ZAKARIA)
Ketua Panitia Matematik,
Sek. Men. Sains Labuan.
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1. DIRECTED NUMBER
a. Calculate the value of 933642 [2 marks]
b. Calculate the value of )711(225 [2 marks]
c. Calculate the value of )9416(626 [2 marks]
d. Calculate the value of )432(371 [2 marks]
1
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2. FRACTION
a. Calculate the value of 5
1
4
1(02.0 ) and express the answer
as a fraction in its lowest term. [2 marks]
b. Calculate the value of 6
51)
3
2
2
11( ) and express the answer
as a fraction in its lowest term. [2 marks]
c. Calculate the value of 8
9)
4
1
2
11( ) and express the answer
as a fraction in its lowest term. [2 marks]
d. Calculate the value of 8
11)
5
2
8
5( ) and express the answer
as a fraction in its lowest term. [2 marks]
2
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3. DECIMAL
a. Calculate the value of 9
436.018
[2 marks]
b. Calculate the value of )3()5.0(4
13
[2 marks]
c. Calculate the value of 4.1
704.0
[2 marks]
d. Calculate the value of 56.0)2
1
4
31(
[2 marks]
3
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4. SQUARE, SQUARE ROOTS, CUBE & CUBE ROOTS
a. (i) Find the value of 3 027.0
(ii) Calculate the value of 2)4913(
[3 marks]
b. (i) Find the value of 2
2.1
(ii) Calculate the value of 323 )327(
3
1
[3 marks]
c. (i) Find the value of 327
1
(ii) Calculate the value of 3)2.344.1(
[3 marks]
d. (i) Find the value of 4
16
(ii) Calculate the value of
2
10
61
[3 marks]
4
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5. LINEAR EQUATIONS
a. Solve each of the following linear equations
(i) 96 k
(ii) 113)12(4 y y
[3 marks]
b. Solve each of the following linear equations
(i) 515 x
(ii) 232
95
m
m
[3 marks]
c. Solve each of the following linear equations
(i)3
2
12
n
(ii) 43)1(2 x x
[3 marks]
d. Solve each of the following linear equations
(i) 204 n
(ii) )4(2)2(5 x x
[3 marks]
5
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6. ALGEBARIC EXPRESSIONS ; EXPAND @ SIMPLIFY
a. Expand each of the following expressions
(i) )27(3 n
(ii)2)32( p
[3 marks]
b. Expand each of the following expressions
(i) )4(3 q p
(ii) )2)(24( r r
[3 marks]
c. Simplify mnm 3)43(2
[2 marks]
d. Simplify )5()4(3 y x y x
[2 marks]
6
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7. ALGEBRAIC EXPRESSIONS : FRACTIONS
a. Express x
x
x 6
31
3
5 as a single fraction in its simplest term
[3 marks]
b. Expressmn
n
m 18
62
3
2 as a single fraction in its simplest term
[3 marks]
c. Express2
6
8
2
1
n
n
n
as a single fraction in its simplest term
[3 marks]
d. Express xy
y
x 12
23
6
5 as a single fraction in its simplest term
[3 marks]
7
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8. ALGEBRAIC EXPRESSIONS : FACTORISE
a. Factorise completely each of the following expressions
(i) y36
(ii) 91242 x x
[3 marks]
b. Factorise completely each of the fol lowing expressions
(i) p pq 183
(ii) 5022 g
[3 marks]
c. Factorise completely each of the following expressions
(i) 153 y
(ii)3
82 x x
[3 marks]
d. Factorise completely each of the following expressions
(i)2
156 mm
(ii)22
502 y x
[3 marks]
e. Factorise completely each of the following expressions
(i) mnm 318
(ii) wuwvuv 22
[3 marks]
8
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9. ALGEBRAIC FORMULAE
a. Given mk
m 4 , express m in term of k
[3 marks]
b. Given3
532
mn , express m in term of n
[3 marks]
c. Given x y 232
1 , express x in term of y
[3 marks]
d. Given k nm 3 , express n in term of m and k
[3 marks]
9
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10. LINEAR INEQUALITIES
a. List all integer values of x which satisfy both the inequalities
125 x and 24 x
[3 marks]
b. List all integer values of x which satisfy both the inequalities
73 x and 1735 x
[3 marks]
c. Solve each of the following inequalities
(i) 24 x
(ii) 9262
x x
[3 marks]
d. List all integer values of x which satisfy both the inequalities
14
pand 523 p
[3 marks]
10
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11. INDICES : SIMPLIFY
a. Simplify33
5
)2(
32
k
k
[2 marks]
b. Simplify
(i) k k
k
2
4
(ii) 31
368 x x
[3 marks]
c. Simplify h g gh 5422
[2 marks]
d. Simplify3
42
aa
aa
[2 marks]
11
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12. INDICES : CALCULATE THE VALUE
a. Calculate the value of 23
1
3
2
3324
[3 marks]
b. Calculate the value of
(i)32
24
(ii) 21
4493
[3 marks]
c. Find the value of
(i)1
2
3
3
(ii)
3
3
1
2
1
2
1
355
[3 marks]
d. Given that 1231 m
, calculate the value of m
[3 marks]
e. Find the value of 2
3
2
1
2
1
4123
[3 marks]
12
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10. SOLID GEOMETRY : NET
13
(a)
(b)
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12. SCALE DRAWING11. SIMILLAR
14
(a) (a)
(b)
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(b) (c)
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13. TRANSFORMATIONS : TRANSLATIONS
16
(d)
(a)
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(b) (c)
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13. TRANSFORMATIONS : REFLECTIONS
18
(d)
(a)
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13. TRANSFORMATIONS : ROTATIONS
19
(b)
(a)
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(b)(c)
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13. TRANSFORMATIONS ENLARGEMENT
21
(a)
(b)
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14. STATISTIC
22
(a)
(b)
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(c) (d)
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(e) (f)
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15. TRIGONOMETRY
25
(a)
(b)
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(c) (d)
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16. CONGRUENT
27
(a) (b)
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17. LOCI IN TWO DIMENSIONS
28
17.1
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17.2 17.3
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18. CONSTRUCTIONS
30
17.4
18.1
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18.2
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18.3
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18.4
19 GRAPH OF FUNCTIONS
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19. GRAPH OF FUNCTIONS
34
(a)
(b)
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(b)
(c)
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(c)
(d)
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(d)
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