Sample Quizzes For Preparation: Types of Number
O Level and IGCSE Mathematics – Chapter 1.1: Types of Number – Quiz
Multiple Choice Questions
1. Which of the following is a rational number?
A. √2
B. π
C. 0.75
D. √3
2. What is the smallest prime number?
A. 0
B. 1
C. 2
D. 3
3. What is the HCF of 18 and 24?
A. 3
B. 6
C. 12
D. 36
4. Which of the following numbers is a cube number?
A. 9
B. 27
C. 49
D. 64
5. What is the reciprocal of 5?
A. 5
B. 0.5
C. 1/5
D. 1/25
6. Which number is irrational?
A. 2/5
B. √3
C. 0.4
D. 1/3
7. The product of prime factors of 90 is:
A. 2 × 3² × 5
B. 2² × 3 × 5
C. 3 × 5 × 6
D. 2 × 3 × 15
8. A number that can be written in the form a/b where a and b are integers and b ≠ 0 is:
A. An irrational number
B. A prime number
C. A rational number
D. A composite number
9. What is the LCM of 6 and 8?
A. 12
B. 18
C. 24
D. 48
10. Which number is NOT a natural number?
A. 1
B. 2
C. 0
D. 5
11. Which number is both a square and a cube?
A. 4
B. 16
C. 64
D. 36
12. Which of the following is a composite number?
A. 13
B. 17
C. 21
D. 29
13. The square root of which of the following numbers is NOT an integer?
A. 1
B. 4
C. 8
D. 9
14. How is 72 written as a product of prime factors?
A. 2² × 3³
B. 2³ × 3²
C. 2 × 3⁴
D. 2⁴ × 3
15. Which of the following is not an integer?
A. -5
B. 0
C. 1.5
D. 3
16. Which number has no reciprocal?
A. 1
B. 0
C. 2
D. -1
17. What is the HCF of 45 and 75?
A. 5
B. 15
C. 25
D. 75
18. A square number always has:
A. Only one factor
B. Two equal factors
C. Three digits
D. A prime factor
19. Which number is NOT a cube number?
A. 8
B. 27
C. 64
D. 81
20. What is the LCM of 12 and 18?
A. 36
B. 48
C. 72
D. 60
21. Which of the following is a natural number but not a square number?
A. 4
B. 5
C. 9
D. 16
22. Which number below is a prime?
A. 20
B. 31
C. 35
D. 39
23. Which of the following is both an integer and a rational number?
A. π
B. 0
C. √5
D. e
24. The cube of 3 is:
A. 6
B. 9
C. 27
D. 81
25. The lowest common multiple of 9 and 12 is:
A. 18
B. 36
C. 27
D. 48
26. What is the reciprocal of 1/4?
A. 1/4
B. 4
C. 1
D. 0.25
27. The prime numbers between 10 and 20 are:
A. 11, 13, 17, 19
B. 12, 14, 16
C. 11, 15, 18
D. 13, 14, 15, 17
28. Which of these is a factor of both 30 and 45?
A. 2
B. 3
C. 4
D. 6
29. How many digits are in 1 billion?
A. 6
B. 9
C. 10
D. 12
30. 10007 written in words is:
A. One thousand and seven
B. Ten thousand seven
C. Ten thousand and seven
D. Ten thousand seven hundred
Marking Key and Explanations – Chapter 1.1: Types of Number
1. C. 0.75
→ 0.75 = 3/4, which is a rational number (can be expressed as a fraction a/b).
2. C. 2
→ 2 is the smallest prime number. 1 is not considered prime.
3. B. 6
→ 18 = 2 × 3², 24 = 2³ × 3. Common factors: 2, 3 → HCF = 6.
4. B. 27
→ 27 = 3³. A cube number.
5. C. 1/5
→ The reciprocal of a number n is 1/n.
6. B. √3
→ √3 is a non-terminating, non-repeating decimal = irrational number.
7. A. 2 × 3² × 5
→ 90 = 2 × 3 × 3 × 5 = 2 × 3² × 5.
8. C. A rational number
→ A rational number is any number that can be written as a/b.
9. C. 24
→ Multiples of 6: 6, 12, 18, 24…
→ Multiples of 8: 8, 16, 24… → LCM = 24.
10. C. 0
→ Natural numbers start from 1, 2, 3…
11. C. 64
→ 64 = 8² and 4³ → both a square and a cube.
12. C. 21
→ 21 has factors other than 1 and itself → it is composite.
13. C. 8
→ √8 ≈ 2.828… is not an integer.
14. B. 2³ × 3²
→ 72 = 8 × 9 = 2³ × 3².
15. C. 1.5
→ 1.5 is a decimal, not an integer.
16. B. 0
→ 1/0 is undefined. Zero has no reciprocal.
17. B. 15
→ 45 = 3² × 5, 75 = 3 × 5² → Common: 3 × 5 = 15.
18. B. Two equal factors
→ A square number is a number multiplied by itself.
19. D. 81
→ 81 = 3⁴ → not a cube number.
20. A. 36
→ Multiples of 12: 12, 24, 36…
→ Multiples of 18: 18, 36… → LCM = 36.
21. B. 5
→ 5 is natural, not a perfect square.
22. B. 31
→ Prime numbers between 20 and 40 include 23, 29, 31, 37.
23. B. 0
→ 0 is an integer and also a rational number (0 = 0/1).
24. C. 27
→ 3³ = 27.
25. B. 36
→ LCM of 9 and 12 = 36.
26. B. 4
→ Reciprocal of 1/4 = 4/1 = 4.
27. A. 11, 13, 17, 19
→ These are all prime numbers between 10 and 20.
28. B. 3
→ 30 = 2 × 3 × 5, 45 = 3² × 5 → common = 3, 5 → 3 is valid.
29. B. 9
→ 1 billion = 1,000,000,000 → 9 digits.
30. C. Ten thousand and seven
→ 10007 = 10,007 → “Ten thousand and seven.”