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

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Primary 3 Mathematics - SA2 Practice Paper

Version 3 of 5 - Answer Key

Total Marks: 50

Section A: Multiple Choice [10 marks]

1. Answer: (C) 700

Working/Explanation: In 4,728, the digit 7 is in the hundreds place. The value of a digit = digit × place value. So 7 × 100 = 700. Common mistake: Confusing "the digit 7" (which is just 7) with "the value of digit 7" (which is 700). [1 mark]

2. Answer: (C) 3,990

Working/Explanation: Compare digits from left to right. All have 3 in the thousands place. In hundreds place: 0, 9, 9, 0. So 3,909 and 3,990 are larger. Compare tens: 0 vs 9. Therefore 3,990 is greatest. Note: (A) and (D) are identical numbers (3,099), so neither can be the greatest. [1 mark]

3. Answer: (D) 5,700

Working/Explanation: To round 5,678 to the nearest hundred, look at the tens digit (7). Since 7 ≥ 5, round up the hundreds digit from 6 to 7, and change digits to the right to zeros. 5,678 → 5,700. Common mistake: Looking at the ones digit (8) instead of the tens digit. [1 mark]

4. Answer: (B) 4,562

Working/Explanation: The value 50 means the digit 5 must be in the tens place (5 × 10 = 50). In 4,562, the digit 5 is in the hundreds place (value 500). Wait—let me recheck: 4,562 has 5 in the hundreds place (500). Let me verify each option:

• (A) 5,432: 5 is in thousands place (5,000)
• (B) 4,562: 5 is in hundreds place (500)—this gives 500, not 50
• (C) 3,051: 5 is in tens place (50) ✓
• (D) 2,540: 5 is in hundreds place (500)

Correct answer is (C) 3,051. The digit 5 is in the tens place, so its value is 5 × 10 = 50. [1 mark]

5. Answer: (B) 2,750

Working/Explanation: The pattern increases by 100 each time: 2,450 + 100 = 2,550; 2,550 + 100 = 2,650; 2,650 + 100 = 2,750; 2,750 + 100 = 2,850. The missing number is 2,750. [1 mark]

6. Answer: (A) 3,158

Working/Explanation: Convert each part: 3 thousands = 3,000; 15 tens = 15 × 10 = 150; 8 ones = 8. Add: 3,000 + 150 + 8 = 3,158. Common mistake: Writing 15 in the tens place as "15" instead of calculating 15 × 10 = 150. [1 mark]

7. Answer: (B) 50

Working/Explanation: 7,000 + 400 = 7,400. Then 7,450 − 7,400 = 50. Or: 7,000 + 400 + ? = 7,450, so 7,400 + ? = 7,450, therefore ? = 50. [1 mark]

8. Answer: (B) 5,501

Working/Explanation: To round to nearest thousand, look at the hundreds digit. For 6,000: numbers from 5,500 to 6,499 round to 6,000. Check each:

• (A) 5,398: hundreds digit is 3, so rounds down to 5,000
• (B) 5,501: hundreds digit is 5, so rounds up to 6,000 ✓
• (C) 6,498: hundreds digit is 4, so rounds down to 6,000 ✓—wait, this also rounds to 6,000
• (D) 6,502: hundreds digit is 5, so rounds up to 7,000

Both (B) and (C) round to 6,000. However, if only one answer is correct, (B) 5,501 is the intended answer as it demonstrates the "round up" boundary case. Teachers should accept either or clarify if this is used. [1 mark]

9. Answer: (A) 3,900

Working/Explanation: "Difference" means subtraction. Greater number − difference = smaller number. 4,200 − 300 = 3,900. Common mistake: Adding instead of subtracting (getting 4,500, option D). [1 mark]

10. Answer: (B) 1,250

Working/Explanation: 10 hundreds = 10 × 100 = 1,000. 25 tens = 25 × 10 = 250. Total: 1,000 + 250 = 1,250. [1 mark]

Section A Total: 10 marks

Section B: Short Answer [24 marks]

11. (a) Six thousand and eighty-four [1 mark]

Note: "And" is used to indicate the zero in the hundreds place. Some schools accept "six thousand eighty-four" but "six thousand and eighty-four" is preferred for clarity with the zero placeholder.

(b) 4,079 [1 mark]

Explanation: Four thousand = 4,000; seventy = 70; nine = 9. The zero in the hundreds place must be included as a placeholder: 4,000 + 70 + 9 = 4,079. Common mistake: Writing 4,79 or 479.

12. (a) 9 [1 mark]

Explanation: In 8,936, write out the place values: 8 (thousands), 9 (hundreds), 3 (tens), 6 (ones). The hundreds digit is 9.

(b) 900 (or 9 hundreds) [1 mark]

Explanation: In 5,902, the digit 9 is in the hundreds place. Value = 9 × 100 = 900. Common mistake: Answering "9" instead of "900"—this confuses the digit with its value.

13. 3,012, 3,102, 3,201, 3,210 [2 marks]

Working: Compare from left to right. All have 3 in thousands place. Compare hundreds: 0, 1, 2, 2. So 3,012 is smallest. Of 3,102 and the rest: 3,102 has 1 in hundreds, so it's next. Compare 3,201 and 3,210: both have 2 in hundreds, so compare tens: 0 vs 1. Thus 3,201 < 3,210.

Marking: 1 mark for correct order with one number misplaced; 0 marks if more than one error or fundamental misunderstanding.

14. (a) 2,740 [1 mark]

Working: Round 2,739 to nearest ten. Look at ones digit: 9. Since 9 ≥ 5, round up tens digit from 3 to 4: 2,740.

(b) 6,600 [1 mark]

Working: Round 6,551 to nearest hundred. Look at tens digit: 5. Since 5 ≥ 5, round up hundreds digit from 5 to 6: 6,600.

15. 4,821 [2 marks]

Working:

  1,876
+ 2,945
-------
  4,821

Step by step:

• Ones: 6 + 5 = 11, write 1, carry 1 to tens
• Tens: 7 + 4 + 1 (carried) = 12, write 2, carry 1 to hundreds
• Hundreds: 8 + 9 + 1 (carried) = 18, write 8, carry 1 to thousands
• Thousands: 1 + 2 + 1 (carried) = 4

Marking: 1 mark for correct method with calculation error; 2 marks for correct answer.

16. 2,413 [2 marks]

Working:

  4,000
- 1,587
-------
  2,413

Step by step (with regrouping):

• Ones: 0 − 7 (can't do), regroup from tens. But tens is 0, so regroup from hundreds. But hundreds is 0, so regroup from thousands.
  • Thousands: 4 → 3, hundreds: 0 → 9, tens: 0 → 9, ones: 0 → 10
• Ones: 10 − 7 = 3
• Tens: 9 − 8 = 1
• Hundreds: 9 − 5 = 4
• Thousands: 3 − 1 = 2

Common mistake: Forgetting the double regrouping needed. Marking: 1 mark for correct method with error; 2 marks for correct answer.

17. 5,750 [2 marks]

Working: Numbers that round to 5,800 when rounded to nearest hundred are from 5,750 to 5,849 (inclusive). The smallest possible number in this range is 5,750.

Explanation: The boundary for rounding to 5,800 is 5,750. At 5,750, the tens digit is 5, so we round up to 5,800. Any number from 5,750 to 5,849 rounds to 5,800. The smallest is 5,750.

Common mistake: Answering 5,800 (the rounded number itself, not the smallest number that rounds to it) or 5,849 (the largest).

Marking: 2 marks for correct answer; 1 mark for stating range 5,750–5,849 but not identifying smallest.

18. Based on image placeholder Q18-fig1: number line from 4,500 to 5,500 with 100-interval markings, arrow between 4,800 and 4,900, closer to 4,800.

(a) 5,100 (accepting estimated position: if arrow is approximately 2/5 of the way from 4,800, estimate is ~4,832, which rounds to 4,800). [1 mark]

Revised interpretation: Given "closer to 4,800" and rounding to nearest hundred, the answer is 4,800 regardless of exact position, since any position between 4,800 and 4,900 that is closer to 4,800 would round to 4,800.

Wait—let me re-read: The arrow position "between 4,800 and 4,900, closer to 4,800" suggests approximately 4,830–4,840 range. Rounded to nearest hundred: 4,800.

Corrected answer: 4,800

(b) 5,000 [1 mark]

Working: 4,800 + 200 = 5,000.

19. From image placeholder Q19-fig1: pattern shows Input + 100 = Output.

Answers: 2,133; 2,143; 2,153 [3 marks]

Pattern: Add 100 to each input. Or observe that output = input + 100.

Marking: 1 mark for each correct answer.

20. 2,779 beads [3 marks]

Working:

Starting amount:        2,450 beads
Given away:           -   876 beads
Remains:                1,574 beads
Bought more:          + 1,205 beads
Final amount:           2,779 beads

Or as one calculation: 2,450 − 876 + 1,205 = 2,779

Step by step:

• 2,450 − 876: 2,450 − 800 = 1,650; 1,650 − 70 = 1,580; 1,580 − 6 = 1,574
• 1,574 + 1,205: 1,574 + 1,000 = 2,574; 2,574 + 200 = 2,774; 2,774 + 5 = 2,779

Marking: 1 mark for correct method with one operation; 2 marks for correct method with both operations attempted; 3 marks for correct final answer with clear working.

Section B Total: 24 marks

Section C: Problem Solving [16 marks]

21. From image placeholder Q21-fig1:

• Bukit Library: 3,456 books
• Town Library: 2,089 books
• Central Library: 4,567 books

(a) 5,545 books [2 marks]

Working:

  3,456
+ 2,089
-------
  5,545

Bukit Library + Town Library = 3,456 + 2,089 = 5,545

Step by step: 3,456 + 2,000 = 5,456; 5,456 + 80 = 5,536; 5,536 + 9 = 5,545

Marking: 1 mark for correct method with calculation error; 2 marks for correct answer.

(b) 2,478 books [2 marks]

Working:

  4,567
- 2,089
-------
  2,478

Central Library − Town Library = 4,567 − 2,089 = 2,478

With regrouping: 4,567 − 2,089

• Ones: 7 − 9, regroup: 17 − 9 = 8
• Tens: 5 − 8 (after regroup, 6 became 5), regroup: 15 − 8 = 7
• Hundreds: 4 − 0 (after regroup, 5 became 4), wait—let me redo: 4,567 − 2,089
  • 4,567: 4 thousands, 5 hundreds, 6 tens, 7 ones
  • Need to regroup: 4,567 = 3 thousands, 15 hundreds, 6 tens, 7 ones = 3, 15, 5, 17 (after ones regroup) = 3, 14, 15, 17 (after tens regroup)...

Correct step:

• Ones: 7 < 9, borrow from tens: 17 − 9 = 8, tens becomes 5
• Tens: 5 < 8, borrow from hundreds: 15 − 8 = 7, hundreds becomes 4
• Hundreds: 4 − 0 = 4, wait—need to borrow for tens, so hundreds was 5, becomes 4. Then 4 − 0? No, it's 4 − 0? Actually 2,089 has 0 in hundreds. So 4 − 0 = 4? But we need 4 − 0... wait 2,089 means: 2 thousands, 0 hundreds, 8 tens, 9 ones.

After regrouping: 3 thousands, 14 hundreds, 15 tens, 17 ones

• Thousands: 3 − 2 = 1? Hmm, that gives 1,478. Let me check: 4,567 − 2,089.

Alternative: 4,567 − 2,000 = 2,567; 2,567 − 80 = 2,487; 2,487 − 9 = 2,478. ✓

The column method with careful regrouping: 4,567 − 2,089 = 2,478.

Marking: 1 mark for correct method with error; 2 marks for correct answer.

(c) 6,023 books [3 marks]

Working: Library A = Central Library − 1,000 = 4,567 − 1,000 = 3,567

Library A + Bukit Library = 3,567 + 3,456 = 7,023

Wait—let me recheck: 3,567 + 3,456

• 3,567 + 3,000 = 6,567
• 6,567 + 400 = 6,967
• 6,967 + 50 = 7,017
• 7,017 + 6 = 7,023

Corrected answer: 7,023

Marking: 1 mark for finding Library A's books (3,567); 1 mark for attempting addition; 1 mark for correct final answer.

22. From image placeholder Q22-fig1: digits 7, 0, 5, 2.

(a) 7,520 [1 mark]

Explanation: To make the greatest number, place the largest digit in the highest place value: 7 in thousands, 5 in hundreds, 2 in tens, 0 in ones.

(b) 2,057 [1 mark]

Explanation: To make the smallest number, place the smallest non-zero digit in the highest place value (2 in thousands, since 0 cannot lead), then 0 in hundreds, 5 in tens, 7 in ones. Common mistake: 2,057 not 0,257 (which is a 3-digit number).

(c) 5,463 [2 marks]

Working:

  7,520
- 2,057
-------
  5,463

Step by step:

• Ones: 0 − 7, borrow: 10 − 7 = 3, tens becomes 1
• Tens: 1 − 5, borrow: 11 − 5 = 6, hundreds becomes 4
• Hundreds: 4 − 0 = 4
• Thousands: 7 − 2 = 5

Check: 7,520 − 2,057 = 5,463

Marking: 1 mark for correct method with error; 2 marks for correct answer.

23. (a) 125 marbles [2 marks]

Working: Container holds: 2,000 marbles Currently has: 1,875 marbles Space remaining: 2,000 − 1,875 = 125

  2,000
- 1,875
-------
    125

Marking: 1 mark for correct method with error; 2 marks for correct answer.

(b) 525 marbles [2 marks]

Working: Final amount: 1,875 marbles Starting amount: 1,350 marbles Ali added: 1,875 − 1,350 = 525

  1,875
- 1,350
-------
    525

Or: 1,350 + ? = 1,875, so ? = 525

Marking: 1 mark for correct method with error; 2 marks for correct answer.

24. (a) 9,590 [2 marks]

Working:

• Thousands: greatest single digit = 9
• Hundreds: 4 less than thousands digit = 9 − 4 = 5
• Tens: same as thousands digit = 9
• Ones: 0

Number: 9,590

Marking: 1 mark for correct digits identified; 1 mark for correct number formed.

(b) 90 (or 9 tens) [1 mark]

Explanation: The digit in the tens place is 9. Its value is 9 × 10 = 90.

(c) 9,600 [1 mark]

Working: 9,590 rounded to nearest hundred. Tens digit is 9, which is ≥ 5, so round up: 9,590 → 9,600.

Section C Total: 16 marks

Grand Total: 50 marks

Summary of Marks Distribution

Recommended: 5 minutes for checking. Total paper time: 60 minutes (1 hour).