Primary 6 PSLE Mathematics Semestral Assessment 2 (End of Year) Paper 3

TuitionGoWhere Practice Paper - Mathematics Primary 6 SA2 (Version 3)

Answer Key & Marking Scheme – Whole Numbers

Section A: Short Answer Questions (20 marks)

Q1. Write seven million, three hundred and five thousand, two hundred and six in numerals.

• Answer: 7,305,206
• Marks: 2
• Working: 7,000,000 + 305,000 + 206 = 7,305,206
• Common mistake: Writing 7,350,206 (confusing "three hundred and five thousand" with "three hundred and fifty thousand").

Q2. Round 4,567,892 to the nearest ten thousand.

• Answer: 4,570,000
• Marks: 2
• Working: The ten-thousands digit is 6. The thousands digit is 7 (≥ 5), so round up: 4,560,000 → 4,570,000.
• Common mistake: Rounding to the nearest thousand instead (4,568,000).

Q3. Find the HCF of 72 and 120.

• Answer: 24
• Marks: 2
• Working (prime factorisation method):
  • 72 = 2³ × 3²
  • 120 = 2³ × 3 × 5
  • HCF = 2³ × 3 = 8 × 3 = 24
• Alternative (listing): Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72. Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120. Highest common = 24.

Q4. Find the LCM of 18 and 45.

• Answer: 90
• Marks: 2
• Working:
  • 18 = 2 × 3²
  • 45 = 3² × 5
  • LCM = 2 × 3² × 5 = 2 × 9 × 5 = 90

Q5. Express 84 as a product of its prime factors (index notation).

• Answer: 2² × 3 × 7
• Marks: 2
• Working: 84 ÷ 2 = 42; 42 ÷ 2 = 21; 21 ÷ 3 = 7; 7 ÷ 7 = 1. So 84 = 2 × 2 × 3 × 7 = 2² × 3 × 7.

Q6. A factory produced 3,456,789 toys in January and 2,567,890 in February. Total rounded to nearest hundred thousand.

• Answer: 6,000,000 (or 6,020,000 if rounding after summing — see working)
• Marks: 2
• Working: 3,456,789 + 2,567,890 = 6,024,679. Rounded to nearest hundred thousand: look at the ten-thousands digit (2), which is < 5, so round down → 6,000,000 (to nearest hundred thousand, 6,024,679 → 6,000,000).
  • Note: If the question intends "rounded to the nearest hundred thousand" of the total: 6,024,679 → the hundred-thousands digit is 0 (in 6,000,000), the ten-thousands digit is 2 (< 5), so answer is 6,000,000.
• Common mistake: Rounding each month first before adding.

Q7. Find the value of 15,000 ÷ (25 × 6).

• Answer: 100
• Marks: 2
• Working: 25 × 6 = 150. 15,000 ÷ 150 = 100.

Q8. List all the factors of 96.

• Answer: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
• Marks: 2
• Working: 96 = 2⁵ × 3. Number of factors = (5+1)(1+1) = 12. Listing systematically in pairs: (1, 96), (2, 48), (3, 32), (4, 24), (6, 16), (8, 12).
• Common mistake: Missing factors or listing only some of them. Award 1 mark if at least 8 correct factors are listed.

Q9. Smallest number divisible by both 24 and 36.

• Answer: 72
• Marks: 2
• Working: LCM of 24 and 36.
  • 24 = 2³ × 3
  • 36 = 2² × 3²
  • LCM = 2³ × 3² = 8 × 9 = 72

Q10. A number divisible by both 6 and 8. Smallest possible value.

• Answer: 24
• Marks: 2
• Working: LCM of 6 and 8.
  • 6 = 2 × 3
  • 8 = 2³
  • LCM = 2³ × 3 = 24

Section B: Structured Questions (20 marks)

Q11. Population 2,345,678. Round to:

• (a) Nearest hundred: 2,345,700 [1 mark]
  • Working: The tens digit is 7 (≥ 5), so 2,345,678 → 2,345,700.
• (b) Nearest million: 2,000,000 [1 mark]
  • Working: The hundred-thousands digit is 3 (< 5), so round down.
• (c) 3 significant figures: 2,350,000 [2 marks]
  • Working: First 3 significant figures are 2, 3, 4. The next digit is 5 (≥ 5), so round up: 2,340,000 → 2,350,000.
• Common mistake in (c): Writing 2,340,000 (not rounding up when the 4th digit is 5).

Q12. Find the value of 3⁴ − 2⁵ + 10².

• Answer: 75
• Marks: 4
• Working:
  • 3⁴ = 81
  • 2⁵ = 32
  • 10² = 100
  • 81 − 32 + 100 = 49 + 100 = 149
  • Correction: 81 − 32 = 49; 49 + 100 = 149
• Answer: 149
• Marking: 1 mark for each correct power, 1 mark for correct final answer.
• Common mistake: 3⁴ = 12 (confusing with 3 × 4) or 2⁵ = 10.

Q13. HCF = 12, LCM = 360, one number = 60. Find the other.

• Answer: 72
• Marks: 4
• Working: Product of two numbers = HCF × LCM = 12 × 360 = 4,320. Other number = 4,320 ÷ 60 = 72.
• Marking: 2 marks for formula, 2 marks for correct answer.
• Common mistake: Dividing HCM by the given number instead of using the product formula.

Q14. 4,800 exercise books shared among 24 classes, then each class shares among 40 pupils.

• Answer: 5 books per pupil
• Marks: 4
• Working:
  • Books per class = 4,800 ÷ 24 = 200
  • Books per pupil = 200 ÷ 40 = 5
  • Alternative: Total pupils = 24 × 40 = 960. Books per pupil = 4,800 ÷ 960 = 5.
• Marking: 2 marks for books per class, 2 marks for books per pupil.

Q15. Common multiples of 8 and 12 less than 100.

• Answer: 24, 48, 72, 96
• Marks: 4
• Working: LCM of 8 and 12 = 24. Multiples of 24 less than 100: 24, 48, 72, 96.
• Marking: 2 marks for finding LCM = 24, 2 marks for listing all four multiples. Deduct 1 mark for each missing multiple.

Section C: Problem-Solving Questions (20 marks)

Q16. Shopkeeper had 5,400 apples. Sold 2,350 on Monday and 1,680 on Tuesday.

• (a) Total sold: 2,350 + 1,680 = 4,030 [2 marks]
• (b) Apples left: 5,400 − 4,030 = 1,370 [2 marks]
• Marking: 1 mark for correct addition, 1 mark for correct answer in (a); 1 mark for correct subtraction, 1 mark for correct answer in (b).
• Common mistake in (b): Subtracting only one day's sales from the total.

Q17. 3_5,8_2 divisible by both 4 and 9. Find the two missing digits.

• Answer: First missing digit (ten-thousands place) = 7, second missing digit (tens place) = 5. Number: 375,852.
• Marks: 4
• Working:
  • Let the number be 3a5,8b2.
  • Divisibility by 4: Last two digits b2 must be divisible by 4. Possible values for b: 1 (12), 3 (32), 5 (52), 7 (72), 9 (92).
  • Divisibility by 9: Sum of digits = 3 + a + 5 + 8 + b + 2 = 18 + a + b must be divisible by 9.
  • Try b = 5: sum = 18 + a + 5 = 23 + a. For this to be divisible by 9: 23 + a = 27 → a = 4, or 23 + a = 36 → a = 13 (not a digit). So a = 4, b = 5 → number = 345,852. Check: 52 ÷ 4 = 13 ✓. Sum = 3+4+5+8+5+2 = 27 ✓.
  • Wait — rechecking: The number format is 3_5,8_2, so positions are: hundred-thousands=3, ten-thousands=, thousands=5, hundreds=8, tens=, ones=2.
  • Let digits be a and b: number = 3a5,8b2.
  • Divisibility by 4: last two digits = 10b + 2. Must be divisible by 4.
    • b = 1 → 12 ✓; b = 3 → 32 ✓; b = 5 → 52 ✓; b = 7 → 72 ✓; b = 9 → 92 ✓
  • Divisibility by 9: 3 + a + 5 + 8 + b + 2 = 18 + a + b. Must be divisible by 9.
    • If b = 1: 19 + a → a = 8 (27). Number = 385,812. Check: 12 ÷ 4 = 3 ✓, sum = 27 ✓.
    • If b = 5: 23 + a → a = 4 (27). Number = 345,852. Check: 52 ÷ 4 = 13 ✓, sum = 27 ✓.
  • Multiple solutions possible. The question should have a unique answer. Assuming the smallest valid number: a = 4, b = 5 → 345,852.
  • Award marks for any valid pair (a, b) that satisfies both conditions.
• Revised Answer: First digit = 4, second digit = 5 (number: 345,852). Other valid answers: (8,1) → 385,812.
• Marking: 2 marks for correct divisibility-by-4 analysis, 2 marks for correct divisibility-by-9 analysis and final answer.

Q18. Three bells ring at 12s, 18s, 24s intervals. Ring together at 8:00 a.m. Next time together?

• Answer: 8:01:12 a.m. (or 8:01 and 12 seconds a.m.)
• Marks: 4
• Working:
  • LCM of 12, 18, 24.
  • 12 = 2² × 3; 18 = 2 × 3²; 24 = 2³ × 3
  • LCM = 2³ × 3² = 8 × 9 = 72 seconds = 1 minute 12 seconds.
  • 8:00:00 + 0:01:12 = 8:01:12 a.m.
• Marking: 2 marks for LCM, 2 marks for correct time.

Q19. Rectangular hall 48 m × 36 m. Largest square tiles without cutting.

• (a) Side length of tile: HCF of 48 and 36 = 12 m [2 marks]
  • Working: 48 = 2⁴ × 3; 36 = 2² × 3²; HCF = 2² × 3 = 12.
• (b) Number of tiles: (48 ÷ 12) × (36 ÷ 12) = 4 × 3 = 12 tiles [2 marks]
  • Alternative: Area of hall = 48 × 36 = 1,728 m². Area of one tile = 12 × 12 = 144 m². Number of tiles = 1,728 ÷ 144 = 12.
• Marking: 2 marks for HCF in (a), 2 marks for correct calculation in (b).

Q20. Sum of three consecutive odd numbers is 987. Find the largest.

• Answer: 331
• Marks: 4
• Working:
  • Let the three consecutive odd numbers be: n, n + 2, n + 4.
  • n + (n + 2) + (n + 4) = 987
  • 3n + 6 = 987
  • 3n = 981
  • n = 327
  • The three numbers are 327, 329, 331.
  • Largest = 331.
• Alternative method: Middle number = 987 ÷ 3 = 329. Largest = 329 + 2 = 331.
• Marking: 2 marks for correct equation or method, 2 marks for correct answer.
• Common mistake: Dividing 987 by 3 and giving 329 as the answer (the middle number, not the largest).

Mark Summary

End of Answer Key