AzM2 Grade 6 Mathematics 1 — Questions and Answers
Question 1: What is 2/3 ÷ 4/5?
- 8/15
- 5/6 (Correct answer)
- 10/12
- 15/8
Correct answer: 5/6
Dividing fractions: multiply by the reciprocal. 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6.
Fraction division rule (Keep-Change-Flip): Keep 2/3, change ÷ to ×, flip 4/5 to 5/4. Then: 2/3 × 5/4 = (2×5)/(3×4) = 10/12 = 5/6 (simplified by dividing by 2). Answer B is correct. Answer A (8/15) = 2/3 × 4/5 (multiplied without flipping — wrong). Answer C (10/12) is the unsimplified form. Answer D (15/8) flips the wrong fraction.
Question 2: Evaluate: 3 + 4² ÷ 2 × 3
- 24
- 27 (Correct answer)
- 21
- 30
Correct answer: 27
Order of operations (PEMDAS): 4² = 16; 16 ÷ 2 = 8; 8 × 3 = 24; 3 + 24 = 27.
PEMDAS: 1) Exponents: 4² = 16. Expression: 3 + 16 ÷ 2 × 3. 2) Division and Multiplication left to right: 16 ÷ 2 = 8, then 8 × 3 = 24. Expression: 3 + 24. 3) Addition: 27. Answer B is correct. A common error is adding 3 + 4 first (= 7, then 7² = 49...) or doing the operations in wrong order.
Question 3: A store offers 25% off a jacket that originally costs $48. What is the sale price?
- $24.00
- $36.00 (Correct answer)
- $12.00
- $38.00
Correct answer: $36.00
25% of $48 = 0.25 × 48 = $12. Sale price = $48 - $12 = $36.
Step 1: Calculate the discount: 25% of $48 = 0.25 × 48 = $12. Step 2: Subtract from original: $48 - $12 = $36. Answer B is correct. Answer A ($24) is 50% off. Answer C ($12) is the discount amount, not the sale price. Answer D ($38) = $48 - $10 (incorrect discount). Always distinguish between the discount amount and the final price.
Question 4: Which of the following is a prime number?
- 27
- 33
- 41 (Correct answer)
- 49
Correct answer: 41
41 is prime — it has no factors other than 1 and itself. 27 = 3×9, 33 = 3×11, 49 = 7×7.
Prime numbers have exactly two factors: 1 and the number itself. 27 = 3 × 9 (not prime). 33 = 3 × 11 (not prime). 41: try dividing by 2, 3, 5, 7 — none divide evenly. 41 is prime (C). 49 = 7 × 7 (not prime). Answer C is correct. For a quick check, test divisibility by primes up to the square root of the number.
Question 5: A recipe calls for 2¾ cups of flour. If you want to make 2 batches, how much flour do you need?
- 4½ cups
- 5 cups
- 5½ cups (Correct answer)
- 4¾ cups
Correct answer: 5½ cups
2¾ × 2 = 11/4 × 2 = 22/4 = 5½ cups.
Convert 2¾ to improper fraction: (2×4 + 3)/4 = 11/4. Multiply by 2: 11/4 × 2 = 22/4 = 5½. Answer C is correct. Or decompose: 2 batches of 2 cups = 4 cups; 2 batches of ¾ = 3/2 = 1½ cups; total = 4 + 1½ = 5½ cups. Answer A (4½) = 2¼ × 2. Answer B (5) = 2½ × 2. Answer D (4¾) only multiplied the whole number part by 2.
Question 6: Which expression represents 'five less than three times a number n'?
- 5 - 3n
- 3n - 5 (Correct answer)
- 3(n - 5)
- 5(n - 3)
Correct answer: 3n - 5
'Three times a number' = 3n. 'Five less than' means subtract 5 from it: 3n - 5.
Translating word expressions: 'three times a number n' = 3n. 'Five less than 3n' = 3n - 5 (subtract 5 from 3n). Answer B is correct. A common error is writing 5 - 3n (A), which says 5 minus three times n, not the other way around. 'Less than' reverses the order: 'A less than B' = B - A. So 'five less than 3n' = 3n - 5.
