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Primary 6 PSLE Mathematics Semestral Assessment 2 (End of Year) Paper 1
Free P6 PSLE Maths SA2 Paper 1, LongCat Exam version, with questions, answers, and PSLE-focused practice for Singapore students.
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TuitionGoWhere Practice Paper - Mathematics Primary 6 SA2 — Answer Key
Paper: Version 1 of 5 | Total Marks: 50
Section A: Short Answer Questions [20 marks]
1. Write in numerals: Five million, two hundred and three thousand, six hundred and forty-eight.
Answer: 5,203,648
Working:
- Five million = 5,000,000
- Two hundred and three thousand = 203,000
- Six hundred and forty-eight = 648
- Total = 5,000,000 + 203,000 + 648 = 5,203,648
(2 marks)
2. What is the value of the digit 7 in 3,728,456?
Answer: 700,000 (seven hundred thousand)
Working:
- The digit 7 is in the hundred thousands place.
- Value = 7 × 100,000 = 700,000
(2 marks)
3. Round 4,678,352 to the nearest hundred thousand.
Answer: 4,700,000
Working:
- The hundred thousands digit is 6 (in 4,678,352).
- The digit to the right (ten thousands place) is 7, which is ≥ 5.
- Round up: 4,600,000 → 4,700,000
(2 marks)
4. Find the HCF of 36 and 54.
Answer: 18
Working:
- Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
- Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54
- Common factors: 1, 2, 3, 6, 9, 18
- Highest common factor = 18
Alternative method (prime factorisation):
- 36 = 2² × 3²
- 54 = 2 × 3³
- HCF = 2¹ × 3² = 2 × 9 = 18
(2 marks)
5. List all prime numbers between 40 and 60.
Answer: 41, 43, 47, 53, 59
Working:
- Check each number between 40 and 60 for factors other than 1 and itself.
- 41 ✓, 42 ✗, 43 ✓, 44 ✗, 45 ✗, 46 ✗, 47 ✓, 48 ✗, 49 = 7×7 ✗, 50 ✗, 51 = 3×17 ✗, 52 ✗, 53 ✓, 54 ✗, 55 = 5×11 ✗, 56 ✗, 57 = 3×19 ✗, 58 ✗, 59 ✓
(2 marks)
6. Find the LCM of 8 and 14.
Answer: 56
Working:
- Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64…
- Multiples of 14: 14, 28, 42, 56, 70…
- LCM = 56
Alternative method:
- 8 = 2³; 14 = 2 × 7
- LCM = 2³ × 7 = 8 × 7 = 56
(2 marks)
7. Express 84 as a product of its prime factors in index notation.
Answer: 2² × 3 × 7
Working:
84 ÷ 2 = 42
42 ÷ 2 = 21
21 ÷ 3 = 7
7 ÷ 7 = 1
- 84 = 2 × 2 × 3 × 7 = 2² × 3 × 7
(2 marks)
8.
(a) 15 × 240 = 3,600
(b) 3,600 ÷ 12 = 300
Working:
- (a) 15 × 240 = 15 × 24 × 10 = 360 × 10 = 3,600
- (b) 3,600 ÷ 12 = 300 (since 12 × 300 = 3,600)
(2 marks)
9. Arrange from least to greatest.
Answer: A (2,345,678), C (2,345,768), D (2,354,678), B (2,435,678)
Working:
- All start with 2 million.
- Compare hundred thousands: A and C have 3, D has 3, B has 4 → B is largest.
- Compare A vs C: both 2,345,xxx → A has 678, C has 768 → A < C.
- Compare C vs D: C = 2,345,768; D = 2,354,678 → ten thousands: 4 vs 5 → C < D.
- Order: A < C < D < B
(2 marks)
10. Toys produced in March.
Answer: 387,500 toys
Working:
- March has 31 days.
- 12,500 × 31 = 12,500 × 30 + 12,500 = 375,000 + 12,500 = 387,500
(2 marks)
Section B: Structured Questions [20 marks]
11.
(a) Books after new books added:
Answer: 40,254 books
Working:
- 24,816 + 15,438 = 40,254
(b) Books remaining after donation:
Answer: 30,979 books
Working:
- 40,254 − 9,275 = 30,979
(4 marks: 2 marks for each part)
12. Product of two numbers is 2,016. One number is 48. Find the other.
Answer: 42
Working:
- Other number = 2,016 ÷ 48
- 2,016 ÷ 48 = 42
- Check: 48 × 42 = 48 × 40 + 48 × 2 = 1,920 + 96 = 2,016 ✓
(4 marks)
13. Smallest number divisible by 6, 9, and 15.
Answer: 90
Working:
- Find LCM of 6, 9, and 15.
- 6 = 2 × 3
- 9 = 3²
- 15 = 3 × 5
- LCM = 2 × 3² × 5 = 2 × 9 × 5 = 90
(4 marks)
14.
(a) Bags of 8 at first:
Answer: 60 bags
Working:
- 480 ÷ 8 = 60
(b) Bags of 12:
Answer: 40 bags
Working:
- 480 ÷ 12 = 40
(4 marks: 2 marks for each part)
15. Three bells ring at intervals of 6, 8, and 12 minutes. They ring together at 8:00 a.m. When next together?
Answer: 8:24 a.m.
Working:
- Find LCM of 6, 8, and 12.
- 6 = 2 × 3
- 8 = 2³
- 12 = 2² × 3
- LCM = 2³ × 3 = 8 × 3 = 24 minutes
- 8:00 a.m. + 24 minutes = 8:24 a.m.
(4 marks)
Section C: Problem Sums [10 marks]
16. Mr Tan's money problem (backward working).
Answer: ₹15,660
Working (backward method):
- After donating ₹950, he had ₹2,400 left.
- Before donation: ₹2,400 + ₹950 = ₹3,350
- This ₹3,350 is half of what remained before giving to wife.
- Before giving to wife: ₹3,350 × 2 = ₹6,700
- He spent ₹3,250 + ₹1,780 = ₹5,030 on groceries and transport.
- Original amount: ₹6,700 + ₹5,030 = ₹11,730
Correction — re-check:
- Let original = X
- After groceries and transport: X − 3,250 − 1,780 = X − 5,030
- Gave half to wife: remaining = (X − 5,030) ÷ 2
- After donating ₹950: (X − 5,030) ÷ 2 − 950 = 2,400
- (X − 5,030) ÷ 2 = 2,400 + 950 = 3,350
- X − 5,030 = 3,350 × 2 = 6,700
- X = 6,700 + 5,030 = ₹11,730
Answer: ₹11,730
(5 marks: 1 mark each for correct backward steps, 1 mark for final answer)
17. Box A + Box B = 8,400 g. Box A is 1,250 g heavier than Box B.
(a) Mass of Box B:
Answer: 3,575 g
(b) Mass of Box A:
Answer: 4,825 g
Working:
- If we subtract the difference: 8,400 − 1,250 = 7,150
- Box B = 7,150 ÷ 2 = 3,575 g
- Box A = 3,575 + 1,250 = 4,825 g
- Check: 3,575 + 4,825 = 8,400 ✓
(5 marks: 2 marks for (a), 2 marks for (b), 1 mark for correct method)
18. Concert hall: 1,250 seats. Friday: 785 filled. Saturday: 920 filled. Seats not filled over two days?
Answer: 800 seats
Working:
- Total seats available over 2 days = 1,250 × 2 = 2,500 seats
- Total filled = 785 + 920 = 1,705 seats
- Not filled = 2,500 − 1,705 = 795 seats
Correction:
- 785 + 920 = 1,705
- 2,500 − 1,705 = 795
Answer: 795 seats
(5 marks: 1 mark for total seats, 1 mark for total filled, 1 mark for subtraction, 1 mark for final answer, 1 mark for unit)
19. 7-digit number N.
(a) Write down N.
Answer: 5,300,080
Working:
- Millions place: 5
- Hundred thousands place: 3
- Tens place: 8
- All other digits: 0
- N = 5,300,080
(b) Round N to the nearest million.
Answer: 5,000,000
Working:
- 5,300,080 → hundred thousands digit is 3 (< 5), so round down.
- Rounded = 5,000,000
(5 marks: 3 marks for (a), 2 marks for (b))
20. Three fields.
(a) Field B:
Answer: 4,225 kg
Working:
- Field B = 2,350 + 1,875 = 4,225 kg
(b) Field C:
Answer: 8,450 kg
Working:
- Field C = 4,225 × 2 = 8,450 kg
(c) Total rice from all three fields:
Answer: 15,025 kg
Working:
- Total = 2,350 + 4,225 + 8,450 = 15,025 kg
(5 marks: 1 mark for (a), 1 mark for (b), 2 marks for (c), 1 mark for correct method across all parts)
Mark Summary
| Section | Marks |
|---|---|
| A: Questions 1–10 | 20 |
| B: Questions 11–15 | 20 |
| C: Questions 16–20 | 10 |
| Total | 50 |
Common Mistakes & Marking Notes
- Q2: Award full marks for "700,000" or "seven hundred thousand". Do not accept just "7".
- Q3: Common error — rounding to nearest ten thousand (4,680,000). This is wrong; the question asks for hundred thousand.
- Q4: Accept any valid method (listing factors, prime factorisation, or Euclidean algorithm).
- Q7: Award 1 mark for correct prime factorisation even if index notation is not used; award full marks only for index notation form.
- Q9: Award 1 mark for correct order, 1 mark for showing comparison reasoning.
- Q11: Award 1 mark for each correct part even if the other part is wrong (no carry-over penalty).
- Q15: Award 2 marks for finding LCM = 24, 1 mark for adding to 8:00, 1 mark for correct time format.
- Q16: This is a backward-working problem. Award marks for each correct backward step even if arithmetic slips occur. Accept model-drawing method as alternative.
- Q18: Common error — students may only consider one day. Award marks for showing understanding of two days.
- Q20: Award marks independently for each part. If (a) is wrong but (b) correctly uses (a)'s answer, award follow-through marks for (b) and (c).