1. PPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPP
MATHEMATIC
FORM 5
MODUL 1
PPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPP
NUMBER BASES
KEMENTERIAN PELAJARAN MALAYSIA

2. NUMBER BASES
Arahan :
1. Modul ini mengandungi tiga puluh lima soalan.
2. Modul merangkumi tujuh konstruk yang diuji
K1 - Memahami soalan dalam bahasa Inggeris
K3 - Memahami istilah matematik dalam bahasa Inggeris
K5 - Menguasai konstruk pengetahuan
K6 - Menguasai konstruk kefahaman
K7 – Menguasai konstruk kemahiran
K8 – Mengungkapkan idea/informasi dalam bahasa Inggeris
K10 – Memahami pengajaran dan pembelajaran dalam bahasa Inggeris
3. Murid hendaklah menulis maklumat diri dalam kertas jawapan objektif
disediakan. Murid juga perlu mengisikan maklumat konstruk, nombor soalan dan
jumlah soalan seperti yang dibaca oleh guru di dalam ruangan disediakan dalam
kertas jawapan objektif sebelum ujian.
4. Bagi soalan objektif, anda perlu menandakan jawapan dengan menghitamkan
pilihan jawapan pada pilihan jawapan A , B , C atau D pada kertas jawapan
objektif.
Contoh:
Antara berikut, yang manakah haiwan?
A. Pokok B. Kambing C. Kereta D. Pen
A B C D E
5. Untuk soalan subjektif, jawapan hendaklah ditulis pada kertas berasingan
yang disediakan oleh guru.
6. Soalan 31 hingga 35 akan dibaca oleh guru. Murid perlu mendengar dengan
teliti dan menjawab di dalam kertas jawapan objektif.
7. Jawab semua soalan.
Modul ini mengandungi 12 halaman bercetak
2

3. Answer all questions given.
1. The number 110102 is a number in base two. The number 4215 is in base
A two
B five
C eight
D ten
2. A number in base five uses any of these digits 0, 1, 2, 3 and 4.
Which of the following is a possible number in base five?
A 5
B 24
C 25
D 54
3. What are the three consecutive numbers after 8?
A 5, 6, 7
B 8, 9, 10
C 8, 10, 12
D 9, 10, 11
4. 368 denotes a number written in base eight.
Which of the following denotes a number in base five?
A 15
B 51
C 245
D 358
3

4. 5. The value of a digit of a number is the product of the digit and its place value.
Place 125 25 5 1
value
Digit 1 2 3 4
`
The value of the digit 2 in the number 12345 is the product of
A 1 and 125
B 2 and 25
C 3 and 5
D 1 and 4
6. Express 1012 in expanded notation.
A 1x0+1
B =2 + 21 + 20
C 1x2+0x2+1x2
D 1 x 22 + 0 x 21 + 1 x 20
7. The process below is used to convert 73 to base five.
5 73
5 14…3 P
5 2…4
0…2
The numbers 2, 4, and 3 in group P are known as
A divisors
B quotients
C dividends
D remainders
4

5. 8. Which of the following is true about the number 2435 ?
A 2 is the coefficient
B 3 is a multiple
C 4 is a factor
D 5 is the base
9. ‘x is less than 10012’ can be written as
A x < 10012
B x ≤ 10012
C x > 10012
D x ≥ 10012
10. Which of the following is false?
Number Type of number
A 1012 Binary
B 47.5 Decimal
C 246 Even
D 121 Prime
11. The place value for the underlined digit in 1368 is
A 80
B 81
C 82
D 83
12. 11011 is a number expressed in base
A two
B five
C eight
D ten
5

6. 13. What is the largest digit used to form a number in base five?
A 2
B 3
C 4
D 5
14. What are the digits that can be used to form a number in base eight?
A 0, 1, 2, 3 and 4
B 0, 1, 2, 3, 4, 5, 6 and 7
C 0, 1, 2, 3, 4, 5, 6, 7 and 8
D 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.
15. 10201x is a number in a certain base. Which of the following is not a possible value
of x?
A two
B five
C eight
D ten
16. Given 42015 = (4 x 53) + (2 x 5m) + 1, what is the value of m?
A 2
B 3
C 4
D 5
17. Express (1 x 23) + (0 x 22) + (1 x 21) + (1 x 20) as a number in base two.
A 10002
B 10112
C 11012
D 11112
6

7. 18. The place value of the digits in 1235 is shown in the table.
`
Place 52 51 50
value
Digit 1 2 3
What is the value of the digit 2?
A 1 x 51
B 1 x 52
C 2 x 51
D 2 x 52
19. 1 × 25 + 1× 22 =
A 112
B 10012
C 100102
D 1001002
20. Which of the following is the correct step to find the value of m in 112 + m2 = 11012?
A 11012 - 112
B 11012 + 112
C 112 - 11012
D 112 + 11012
21. Given that 101102 < x10 < 111102 , a possible value of x is
A 19
B 21
C 25
D 32
7

8. 22. Convert 4025 to base eight.
A 1028
B 1468
C 1128
D 1588
23. Convert 21 to base five.
A 415
B 215
C 145
D 115
24. 101112 is equivalent to
A 238
B 278
C 468
D 628
25. 100102 - 11112 =
A 10112
B 1112
C 1012
D 112
26. Based on the table, make three true statements.
x 1011012
y 45
I. x has six digits.
II. The largest digit of x is 2.
III. y is a number in base ten.
IV. x and y have the same value.
A I, II, III
B I, II , IV
C I, III, IV
D II, III, IV
8

9. 27. Describe the following step that is used to convert 4325 to base ten.
4325 = (4 x 52) + (3 x 51) + (2 x 50)
A Expand the number according to the place value.
B Divide into groups of three digits from right.
C Simplify the expressions.
28. How do you convert 53 to a number in base two?
A Perform repeated division by 2.
B Perform repeated division by 10.
C Expand the number according to its place value.
29. What are the steps to convert a number in base five to base ten?
I Perform repeated division.
II Write the number in expanded notation.
III Simplify the expanded notation.
A I and II
B I and III
C II and III
D I, II and III
30. 4125 is read as
A four thousand and twelve base five.
B four hundred and twelve base five.
C four one two base five.
D four one two five.
9

10. From Question 31 – 35, the teacher reads the questions to the students. Students
choose the correct answer.
31.
A 5
B 15
C 245
D 548
32.
A 7
B 11
C 22
D 35
33.
A 1+0+1
B 1x0x1
C (1 x 22) + (0 x 21) + (1 x 20)
D (1 x 22) x (0 x 21) x (1 x 20)
34.
A 10002
B 10012
C 10102
D 11002
10

11. 35.
A 628
B 508
C 408
D 138
END OF QUESTION PAPER
11

12. KEMENTERIAN PELAJARAN MALAYSIA
KERTAS JAWAPAN OBJEKTIF
Ujian Diagnostik
Nama Pelajar:
Tahun/ Tingkatan : 5 Mata Pelajaran: MATHEMATIC
Nama Sekolah: Modul:
GUNAKAN PENSIL 2B ATAU BB SAHAJA.
TENTUKAN TIAP-TIAP TANDA ITU HITAM DAN MEMENUHI KESELURUHAN RUANG.
PADAMKAN HINGGA HABIS MANA-MANA TANDA YANG ANDA UBAH
SILA HITAMKAN JAWAPAN DI BAWAH MENGIKUT HURUF JAWAPAN YANG ANDA PILIH
1 A B C D E 31 A B C D E 46 A B C D E
2 A B C D E 32 A B C D E 47 A B C D E
3 A B C D E 33 A B C D E 48 A B C D E
4 A B C D E 34 A B C D E 49 A B C D E
5 A B C D E 35 A B C D E 50 A B C D E
6 A B C D E 36 A B C D E 51 A B C D E
7 A B C D E 37 A B C D E 52 A B C D E
8 A B C D E 38 A B C D E 53 A B C D E
9 A B C D E 39 A B C D E 54 A B C D E
10 A B C D E 40 A B C D E 55 A B C D E
11 A B C D E 41 A B C D E 56 A B C D E
12 A B C D E 42 A B C D E 57 A B C D E
A B C D E 43 A B C D E 58 A B C D E
13
14 A B C D E 44 A B C D E 59 A B C D E
15 A B C D E 45 A B C D E 60 A B C D E
A B C D E Konstruk No. Soalan Jumlah Bilangan Soalan Kegunaan Guru
16
Soalan Gagal Dijawab
17 A B C D E
18 A B C D E 1 K1 1-5 5
19 A B C D E
20 A B C D E 2 K3 6 - 10 5
3 K5 11 - 15 5
21 A B C D E
22 A B C D E 4 K6 16 - 20 5
23 A B C D E
A B C D E
5 K7 21 - 25 5
24
25 A B C D E 6 K8 26 - 30 5
26 A B C D E 7 K10 31 - 35 5
27 A B C D E
8
28 A B C D E
29 A B C D E 9
30 A B C D E
10