Primary 6 PSLE Mathematics Practice Paper 3

TuitionGoWhere Practice Paper - Mathematics Primary 6 PSLE

Answer Key and Marking Scheme

Version: 3 of 5
Total Marks: 80

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Section A: Multiple Choice Questions (20 marks)

1. (4) 7 000 000

Concept: Place value up to 10 million. The digit 7 is in the millions place.

Working: In 7 865 432, the place values are:

• 7: millions (7 × 1 000 000 = 7 000 000)
• 8: hundred thousands
• 6: ten thousands
• 5: thousands
• 4: hundreds
• 3: tens
• 2: ones

Common mistake: Choosing 700 000 (confusing hundred thousands with millions).

Marks: 2

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2. (1) 5 678 901

Concept: Comparing whole numbers by place value from left to right.

Working: Compare digit by digit from the millions place:

• All have 5 in millions place
• Compare hundred thousands: 6, 6, 8, 8 → eliminate options (3) and (4)
• Compare ten thousands: 7 vs. 8 → 5 678 901 is smaller

Common mistake: Scanning from right instead of left.

Marks: 2

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3. (4) 8 800 000

Concept: Rounding to the nearest hundred thousand.

Working: 8 765 432

• Hundred thousands digit: 7
• The next digit (ten thousands) is 6, which is ≥ 5, so round up
• 7 becomes 8, and all digits to the right become 0: 8 800 000

Common mistake: Rounding to 8 770 000 (nearest ten thousand) or 8 760 000 (mixing up place values).

Marks: 2

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4. (1) Six million forty-eight thousand

Concept: Reading and writing numbers in words.

Working: 6 048 000

• 6 in millions place → "six million"
• 048 in thousands place → "forty-eight thousand" (note: we don't say zero hundred thousand)
• 000 in ones place → nothing

Common mistake: Saying "four hundred eight thousand" (misreading 048 as 408).

Marks: 2

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5. (3) 24 and (4) 48 — Question requires single answer: (3) 24 is the correct choice if only one answer, but actually both 24 and 48 work. In standard MCQ format, if only one answer allowed, (3) 24 as the least common multiple, or this is a poorly designed question. Assuming standard "which is" with single best answer: (3) 24 as the least common multiple, or if multiple correct: (3) or (4).

Correction for clarity: LCM of 8 and 12 is 24.

Concept: Common multiples. Multiples of 8: 8, 16, 24, 32, 40, 48... Multiples of 12: 12, 24, 36, 48...

Working:

• 8 = 2³, 12 = 2² × 3
• LCM = 2³ × 3 = 24

Both 24 and 48 are common multiples, but 24 is the least.

Marks: 2

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6. (1) 177 822

Concept: Multiplication of large numbers.

Working:

   4 806
 ×    37
 --------
  33 642   (4 806 × 7)
 144 180   (4 806 × 30)
 --------
 177 822

Check: 4 806 × 30 = 144 180; 144 180 + 33 642 = 177 822

Common mistake: Error in multiplication table or place value alignment.

Marks: 2

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7. (3) 28 937

Concept: Relationship between dividend, divisor, quotient, and remainder.

Working:

• Number = (Divisor × Quotient) + Remainder
• Number = (6 × 4 807) + 5
• Number = 28 842 + 5
• Number = 28 847

Apologies, let me recalculate:

• 6 × 4 807 = 28 842
• 28 842 + 5 = 28 847

Answer is (2) 28 847

Correction: Answer is (2) 28 847

Marks: 2

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8. (2) 7

Concept: Factors of a number.

Working: Factors of 48:

• 48 = 1 × 48
• 48 = 2 × 24
• 48 = 3 × 16
• 48 = 4 × 12
• 48 = 6 × 8

Factors: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

7 is not in this list. 48 ÷ 7 = 6 remainder 6.

Marks: 2

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9. (1) 7 624

Concept: Finding an unknown addend.

Working:

• Other number = 12 500 − 4 876
• 12 500 − 4 876 = 7 624

Check: 4 876 + 7 624 = 12 500 ✓

Marks: 2

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10. (1) 1 012 346

Concept: Subtraction of large numbers.

Working:

  2 000 000
−   987 654
-----------
  1 012 346

Check: 987 654 + 1 012 346 = 2 000 000 ✓

Common mistake: Borrowing errors across multiple zeros.

Marks: 2

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Section A Total: 20 marks

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Section B: Short Answer Questions (30 marks)

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11. 4 206 015

Concept: Writing numbers in figures from words.

Working:

• "four million" → 4 000 000
• "two hundred and six thousand" → 206 000 (note: "and" indicates the hundreds place within thousands)
• "fifteen" → 015

Total: 4 000 000 + 206 000 + 15 = 4 206 015

Common mistake: Writing 4 200 615 or 4 260 015 (misplacing the "six").

Marking: 3 marks for correct answer. Deduct 1 mark for place value error if working shows understanding.

Marks: 3

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12. No, Maria is not correct. The correct answer is 15 590.

Concept: Order of operations (BODMAS/PEMDAS).

Working: According to order of operations, multiplication comes before addition:

• 3 456 × 2 = 6 912
• 5 678 + 6 912 = 15 590

Maria did: 5 678 + 3 456 = 9 134, then 9 134 × 2 = 18 268 (wrong order).

Explanation: In mixed operations, multiplication and division take priority over addition and subtraction. You must multiply first, then add.

Marking:

• 1 mark: stating Maria is incorrect
• 1 mark: correct method (multiply first)
• 1 mark: correct answer 15 590

Marks: 3

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13. 18 000

Concept: Using known facts and multiplication properties.

Working:

• 375 = 3 × 125
• So 48 × 375 = 48 × (3 × 125) = 3 × (48 × 125) = 3 × 6 000 = 18 000

Alternatively: 48 × 375 = 48 × 125 × 3 = 6 000 × 3 = 18 000

Explanation: This uses the associative property of multiplication. Breaking down problems using known facts is efficient and reduces calculation errors.

Marking:

• 1 mark: recognizing 375 = 3 × 125
• 1 mark: setting up correct calculation
• 1 mark: correct answer

Marks: 3

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14. 18

Concept: Greatest Common Factor (HCF / GCD).

Working: Method 1 - Listing factors:

• 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
• Greatest: 18

Method 2 - Prime factorization:

• 36 = 2² × 3²
• 54 = 2 × 3³
• HCF = 2¹ × 3² = 2 × 9 = 18

Marking:

• 1 mark: finding factors or prime factorization of both numbers
• 1 mark: identifying common factors
• 1 mark: correct HCF

Marks: 3

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15. 4 980 books

Concept: Multiplication and addition in word problems.

Working:

• Tuesday: 1 245 × 3 = 3 735 books
• Total: 1 245 + 3 735 = 4 980 books

Or: 1 245 × (1 + 3) = 1 245 × 4 = 4 980

Marking:

• 1 mark: Tuesday's sales correct
• 1 mark: correct addition
• 1 mark: correct answer with units

Marks: 3

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16. (a) 800 000; (b) 2 654 322

Concept: Place value decomposition and missing subtrahends.

(a) Working:

• 7 865 432 − 7 000 000 − 60 000 − 5 000 − 400 − 30 − 2
• = 865 432 − 60 000 − 5 000 − 400 − 30 − 2
• = 805 432 − 5 000 − 400 − 30 − 2
• = 800 432 − 400 − 30 − 2
• = 800 032 − 30 − 2
• = 800 002 − 2
• = 800 000

Or simply: the hundred thousands digit is 8, so 800 000.

(b) Working:

• Missing number = 5 000 000 − 2 345 678
• = 2 654 322

Check: 2 345 678 + 2 654 322 = 5 000 000 ✓

Marking: 1½ marks each. Deduct ½ mark for arithmetic error with correct method.

Marks: 3 (1½ + 1½)

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17. 211 250 toy cars

Concept: Multiplication in context.

Working:

• 8 450 × 25
• = 8 450 × 100 ÷ 4
• = 845 000 ÷ 4
• = 211 250

Or:

   8 450
 ×    25
 --------
  42 250   (× 5)
 169 000   (× 20)
 --------
 211 250

Marking:

• 1 mark: correct setup
• 1 mark: correct calculation method
• 1 mark: correct answer with units

Marks: 3

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18. 48

Concept: Finding an unknown factor.

Working:

• Other number = 720 ÷ 15
• 720 ÷ 15 = 720 ÷ 3 ÷ 5 = 240 ÷ 5 = 48

Or: 15 × 48 = 720 (by inspection or long division)

Check: 15 × 48 = 15 × 50 − 15 × 2 = 750 − 30 = 720 ✓

Marking:

• 1 mark: recognizing division is needed
• 1 mark: correct working
• 1 mark: correct answer

Marks: 3

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19. 77

Concept: Prime numbers.

Working: Prime numbers between 20 and 40:

• 23 (prime: only divisible by 1 and 23)
• 29 (prime)
• 31 (prime)
• 37 (prime)

Note: 21 = 3 × 7, 22 = 2 × 11, 24 = 2 × 12, 25 = 5 × 5, 26 = 2 × 13, 27 = 3 × 9, 28 = 2 × 14, 30 = 2 × 15, 32 = 2 × 16, 33 = 3 × 11, 34 = 2 × 17, 35 = 5 × 7, 36 = 2 × 18, 38 = 2 × 19, 39 = 3 × 13

Sum: 23 + 29 + 31 + 37 = 120

Wait, let me recheck: 23 + 29 = 52; 52 + 31 = 83; 83 + 37 = 120

Correction: Answer is 120

Marking:

• 1 mark: identifying correct prime numbers
• 1 mark: complete list (may lose ½ mark for one missing)
• 1 mark: correct sum

Marks: 3

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20. 3 605

Concept: Division algorithm (finding dividend).

Working:

• Number = (Divisor × Quotient) + Remainder
• Number = (23 × 156) + 17
• 23 × 156 = 23 × 100 + 23 × 50 + 23 × 6 = 2 300 + 1 150 + 138 = 3 588
• Number = 3 588 + 17 = 3 605

Check: 3 605 ÷ 23 = 156 remainder 17 ✓

Marking:

• 1 mark: correct formula
• 1 mark: correct multiplication
• 1 mark: correct final answer

Marks: 3

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Section B Total: 30 marks

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Section C: Problem Sums (30 marks)

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21. (a) $32 400**; **(b)$25 350

Concept: Multi-step money problems with deposits and withdrawals.

(a) After buying the car:

• Starting amount: $45 000
• After withdrawal: $45 000 −$12 600 = $32 400

(b) Final amount:

• After depositing salary: $32 400 +$8 750 = $41 150
• After paying university fees: $41 150 −$15 800 = $25 350

Working shown clearly:

Start:           $45 000
Withdraw car:   −$12 600
                --------
After car:       $32 400  ← (a)

Deposit salary:  +$8 750
                --------
                 $41 150
Pay fees:       −$15 800
                --------
Final:           $25 350  ← (b)

Marking:

• (a) 2 marks: 1 mark method, 1 mark answer
• (b) 4 marks: 2 marks method (both steps), 2 marks answer

Common mistake: Forgetting to add the salary before subtracting fees, or sign errors.

Marks: 6 (2 + 4)

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22. 1 415 boys

Concept: Solving with the "big and small" or "sum and difference" method.

Working: Method - Sum and difference:

• Total pupils: 2 450
• Difference: boys − girls = 380

If we subtract the difference from the total, we get twice the number of girls:

• 2 450 − 380 = 2 070
• Girls: 2 070 ÷ 2 = 1 035
• Boys: 1 035 + 380 = 1 415

Or using algebra:

• Let girls = g, then boys = g + 380
• g + (g + 380) = 2 450
• 2g = 2 070
• g = 1 035
• Boys = 1 035 + 380 = 1 415

Check: 1 415 + 1 035 = 2 450 ✓; 1 415 − 1 035 = 380 ✓

Marking:

• 2 marks: correct method setup (sum and difference or equation)
• 2 marks: finding number of girls
• 2 marks: correct number of boys with check/verification

Marks: 6

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23. (a) $290**; **(b)$68 more

Concept: Reading tables and calculating costs.

Generated table for Q23.

(a) Weekday cost:

• Adults: 2 × $45 =$90
• Children: 2 × $28 =$56
• Senior citizens: 2 × $32 =$64
• Total: $90 +$56 + $64 = **$290**

(b) Weekend cost:

• Adults: 2 × $55 =$110
• Children: 2 × $35 =$70
• Senior citizens: 2 × $38 =$76
• Total: $110 +$70 + $76 =$256

Difference: $256 −$290 = Wait, this gives negative. Let me recheck weekend total: $110 +$70 + $76 =$256

Actually: $110 +$70 = $180;$180 + $76 =$256

But weekday is $290, weekend is$256? That means weekend is cheaper, which contradicts "how much more."

Rechecking values from placeholder: Weekend prices are higher per ticket. Let me recalculate weekend:

• Adults: 2 × $55 =$110
• Children: 2 × $35 =$70
• Senior citizens: 2 × $38 =$76
• Weekend total: $110 +$70 + $76 =$256

Hmm, $256 <$290. The difference is $290 −$256 = $34, but this is "how much less."

The answer should be that they pay MORE on weekend. Let me recheck my arithmetic.

Weekday: $90 +$56 + $64 =$210 + $64? No:$90 + $56 =$146; $146 +$64 = $210? No,$146 + $64 =$210.

Wait: $90 +$56 = $146.$146 + $64 = **$210**

Let me recalculate: 90 + 56 + 64

• 90 + 56 = 146
• 146 + 64 = 210

Weekday total: $210

Weekend total: $110 +$70 + $76 =$256

Difference: $256 −$210 = $46

My earlier addition was wrong. The correct weekday total is $210.

Corrected answers:

• (a) $210
• (b) $46

Marking:

• (a) 3 marks: 1 mark per ticket type calculation, or 2 marks method + 1 mark answer
• (b) 3 marks: 1 mark weekend total, 1 mark method for difference, 1 mark answer

Marks: 6 (3 + 3)

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24. $1 335

Concept: Multi-step problem with division, multiplication, and subtraction.

Working:

• Number of packets: 3 840 ÷ 24

  • 3 840 ÷ 24 = 3 840 ÷ 12 ÷ 2 = 320 ÷ 2 = 160 packets

  Or: 24 × 160 = 24 × 100 + 24 × 60 = 2 400 + 1 440 = 3 840 ✓

• Money from sales: 160 × $8 =$1 280

• Money left after buying supplies: $1 280 −$945 = $335

Wait, let me recheck: 160 × $8

• 160 × 8 = 1280

$1 280 −$945 = $335

Hmm, but $1 280 <$945? No, $1 280 >$945.

$1 280 −$945:

• $1 280 −$900 = $380
• $380 −$45 = $335

Answer is $335

Marking:

• 2 marks: finding number of packets (division)
• 2 marks: finding total money (multiplication)
• 2 marks: finding final amount (subtraction)

Marks: 6

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25. (a) June; (b) 800 books; (c) 9 450 books

Generated chart for Q25.

(a) The tallest bar is June (2 050 books).

(b) June − January = 2 050 − 1 250 = 800 books

(c) Total = 1 250 + 1 480 + 1 360 + 1 590 + 1 720 + 2 050

Working:

• 1 250 + 1 480 = 2 730
• 2 730 + 1 360 = 4 090
• 4 090 + 1 590 = 5 680
• 5 680 + 1 720 = 7 400
• 7 400 + 2 050 = 9 450

Or grouping: (1 250 + 2 050) + (1 480 + 1 720) + (1 360 + 1 590) = 3 300 + 3 200 + 2 950 = 9 450

Marking:

• (a) 1 mark: correct month
• (b) 2 marks: 1 mark method, 1 mark answer
• (c) 3 marks: 2 marks method (grouping or clear addition), 1 mark answer

Marks: 6 (1 + 2 + 3)

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Section C Total: 30 marks

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Grand Total: 80 marks

Mark Distribution Summary

Section	Marks	Percentage
A: MCQ	20	25%
B: Short Answer	30	37.5%
C: Problem Sums	30	37.5%
Total	80	100%

Difficulty Breakdown (Estimated)

Level	Questions	Marks
Easy	1–5, 11–14	~22
Medium	6–10, 15–19	~28
Challenging	20–25	~30