Level 1 — RecognitionArithmetic & Number Systems

Arithmetic & Number Systems

⏱ 20 minutes30 marksprintable — key stays hidden on paper

Level: 1 (Recognition — MCQ, Matching, True/False with justification) Time limit: 20 minutes Total marks: 30

Section A — Multiple Choice (1 mark each) — 10 marks

Choose the correct option.

Q1. Which of the following is a whole number but not a natural number? (a) 1 (b) 0 (c) $-1$ (d) 5

Q2. In the number $63{,}47{,}812$ (Indian system), the digit 3 stands for: (a) 3 thousands (b) 3 lakhs (c) 30 lakhs (d) 3 crores

Q3. The value of $12 - 4 \times 2 + 6 \div 3$ is: (a) 8 (b) 6 (c) 18 (d) 10

Q4. All the factors of 18 are: (a) 1, 2, 3, 6, 18 (b) 1, 2, 3, 6, 9, 18 (c) 2, 3, 6, 9 (d) 1, 3, 9, 18

Q5. Which of the following is a prime number? (a) 21 (b) 27 (c) 29 (d) 33

Q6. The prime factorization of 60 is: (a) $2^2 \times 3 \times 5$ (b) $2 \times 3 \times 5$ (c) $2^3 \times 5$ (d) $2^2 \times 15$

Q7. The HCF of 12 and 18 is: (a) 2 (b) 3 (c) 6 (d) 36

Q8. The fraction $\dfrac{7}{4}$ written as a mixed number is: (a) $1\frac{3}{4}$ (b) $1\frac{1}{4}$ (c) $2\frac{1}{4}$ (d) $\frac{4}{7}$

Q9. $0.25$ expressed as a percentage is: (a) 2.5% (b) 25% (c) 0.25% (d) 250%

Q10. The value of $|-7|$ is: (a) $-7$ (b) 7 (c) 0 (d) $\frac{1}{7}$

Section B — Matching (1 mark each) — 6 marks

Q11. Match Column A with Column B.

Column A	Column B
(i) 45 written as a fraction of 100 in %	(P) $\frac{1}{2}$
(ii) LCM of 4 and 6	(Q) 12
(iii) $0.5$ as a fraction	(R) 45%
(iv) Simplest form of $\frac{9}{12}$	(S) $\frac{3}{4}$

Write pairs like (i)–(?), (ii)–(?), (iii)–(?), (iv)–(?). (1 mark each pair, 4 marks; +2 for full accuracy)

Match these too:

Column C	Column D
(v) Dividend ÷ Divisor	(T) Quotient
(vi) Ratio $2:4$ in simplest form	(U) $1:2$

Section C — True / False WITH Justification (2 marks each) — 14 marks

State True or False (1 mark) and give a one-line justification (1 mark).

Q12. Every natural number is an integer.

Q13. The number 1 is a prime number.

Q14. $\dfrac{2}{3} = \dfrac{6}{9}$ .

Q15. For any two numbers, $\text{HCF} \times \text{LCM} =$ product of the two numbers.

Q16. A 20% discount on an item marked ₹500 means you pay ₹400.

Q17. In inverse proportion, when one quantity increases the other also increases.

Q18. $|{-3}| > |2|$ .

Answer keyMark scheme & solutions

Section A (1 mark each)

Q1. (b) 0 — whole numbers include 0; naturals start at 1. [1]

Q2. (b) 3 lakhs — in Indian place value 63,47,812, the 3 sits in the lakhs place. [1]

Q3. (b) 6 — BODMAS: $4\times2=8$ , $6\div3=2$ ; $12-8+2=6$ . [1]

Q4. (b) 1, 2, 3, 6, 9, 18 — factor pairs $1\times18, 2\times9, 3\times6$ . [1]

Q5. (c) 29 — 21=3×7, 27=3³, 33=3×11; only 29 has no proper factors. [1]

Q6. (a) $2^2\times3\times5$ — $60=4\times15=2^2\times3\times5$ . [1]

Q7. (c) 6 — $12=2^2\times3$ , $18=2\times3^2$ ; common $2\times3=6$ . [1]

Q8. (a) $1\frac34$ — $7\div4=1$ rem $3$ . [1]

Q9. (b) 25% — $0.25\times100=25$ . [1]

Q10. (b) 7 — modulus is distance from 0. [1]

Section B (1 mark each)

Q11.

(i)–(R) 45%
(ii)–(Q) 12 (LCM of 4,6)
(iii)–(P) $\frac12$
(iv)–(S) $\frac34$ ( $9/12$ ÷ 3/3)
(v)–(T) Quotient
(vi)–(U) $1:2$

[6 marks — 1 each]

Section C (2 marks each: 1 T/F + 1 justification)

Q12. True. Integers include all natural numbers (…,1,2,3,…). [1+1]

Q13. False. A prime has exactly two factors; 1 has only one factor. [1+1]

Q14. True. $\frac23\times\frac33=\frac69$ — equivalent fractions. [1+1]

Q15. True. This is the standard HCF–LCM product relationship for two numbers. [1+1]

Q16. True. 20% of 500 = 100; $500-100=400$ . [1+1]

Q17. False. In inverse proportion, as one increases the other decreases. [1+1]

Q18. True. $|-3|=3$ , $|2|=2$ , and $3>2$ . [1+1]

[
  {"claim":"Q3: 12 - 4*2 + 6/3 = 6","code":"result = (12 - 4*2 + Integer(6)/3) == 6"},
  {"claim":"Q6: prime factorization of 60 is 2^2*3*5","code":"from sympy import factorint; result = factorint(60) == {2:2,3:1,5:1}"},
  {"claim":"Q7: HCF(12,18)=6","code":"from sympy import gcd; result = gcd(12,18) == 6"},
  {"claim":"Q15: HCF*LCM = product for 12,18","code":"from sympy import gcd, lcm; result = gcd(12,18)*lcm(12,18) == 12*18"},
  {"claim":"Q16: 20% discount on 500 gives 400","code":"result = 500 - Rational(20,100)*500 == 400"}
]