Primary 6 PSLE Mathematics Whole Numbers Quiz

Primary 6 PSLE Mathematics Quiz - Whole Numbers (Answer Key)

Total Marks: 50

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Section A: Multiple Choice Questions (10 marks)

1. Answer: (2) 800 000 [2]
Working:
The digit 8 is in the hundred thousands place.
$8 \times 100 000 = 800 000$

Key concept: Place value up to 10 million. The places from right to left are: ones, tens, hundreds, thousands, ten thousands, hundred thousands, millions, ten millions.

2. Answer: (2) 3 460 000 [2]
Working:
To round to the nearest ten thousand, look at the thousands digit (6).
Since 6 ≥ 5, round up the ten thousands digit (5 → 6).
3 456 789 → 3 460 000

Key concept: Rounding rules - if the digit to the right is 5 or more, round up; if less than 5, round down.

3. Answer: (1) 24 [2]
Working:
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48...
Multiples of 8: 8, 16, 24, 32, 40, 48...
Common multiples: 24, 48...
24 is the lowest common multiple (LCM).

Key concept: A common multiple is a number that is a multiple of two or more numbers.

4. Answer: (1) 108 000 [2]
Working:
$72 \times 1000 + 72 \times 500 = 72 \times (1000 + 500)$ (Distributive Law)
$= 72 \times 1500$
$= 72 \times 15 \times 100$
$= 1080 \times 100$
$= 108 000$

Alternative: $72 000 + 36 000 = 108 000$

Key concept: Distributive property of multiplication over addition: $a \times b + a \times c = a \times (b + c)$.

5. Answer: (2) 38 894 [2]
Working:
Dividend = Divisor × Quotient + Remainder
$= 9 \times 4 321 + 5$
$= 38 889 + 5$
$= 38 894$

Key concept: Division algorithm: Dividend = Divisor × Quotient + Remainder (where remainder < divisor).

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Section B: Short Answer Questions (20 marks)

6. Answer: Two million fifty thousand and seven [2]
Working:
2 050 007 = 2 000 000 + 50 000 + 7
= Two million + fifty thousand + seven

Key concept: Reading and writing numbers up to 10 million in words. Note: "and" is used before the last part (ones/tens) in British/Singapore convention.

7. Answer: 90 [2]
Working:
$5 400 \div 60 = 540 \div 6 = 90$
(Cancel one zero from both numbers)

Key concept: Division by multiples of 10 - cancel common zeros.

8. Answer: 15 228 [2]
Working:

    324
  ×  47
  -----
   2268  (324 × 7)
  12960  (324 × 40)
  -----
  15228

Key concept: Multiplication of up to 4-digit by 2-digit numbers using vertical multiplication.

9. Answer: 8 549 [2]
Working:
When rounding to the nearest hundred, numbers from 8 450 to 8 549 round to 8 500.
Greatest possible = 8 549

Key concept: Rounding range - for a rounded value X to the nearest hundred, the original number lies in [X - 50, X + 49].

10. Answer: 1, 2, 3, 4, 6, 9, 12, 18, 36 [2]
Working:
Factor pairs of 36:
1 × 36
2 × 18
3 × 12
4 × 9
6 × 6
Factors: 1, 2, 3, 4, 6, 9, 12, 18, 36

Key concept: Factors are numbers that divide exactly into another number. Always list in ascending order.

11. Answer: 36 [2]
Working:
Multiples of 12: 12, 24, 36, 48, 60...
Multiples of 18: 18, 36, 54, 72...
LCM = 36

Alternative (Prime factorisation):
$12 = 2^2 \times 3$
$18 = 2 \times 3^2$
LCM = $2^2 \times 3^2 = 4 \times 9 = 36$

Key concept: LCM is the smallest common multiple. Can use listing or prime factorisation method.

12. Answer: 36 750 [2]
Working:
$2 450 \times 15$
$= 2 450 \times 10 + 2 450 \times 5$
$= 24 500 + 12 250$
$= 36 750$

Key concept: Multiplication word problem - identify the operation and compute accurately.

13. Answer: 4 544 [2]
Working:

  8 000
- 3 456
-------
  4 544

(Regrouping across zeros: 8000 = 7000 + 900 + 90 + 10)

Key concept: Subtraction with regrouping across zeros.

14. Answer: 192 [2]
Working:
$4 800 \div 25$
$= 4800 \div 100 \times 4$ (since ÷25 = ÷100 × 4)
$= 48 \times 4$
$= 192$

Alternative: $4 800 \div 25 = 192$ exactly (no remainder)

Key concept: Division by 25 shortcut: divide by 100, multiply by 4. Check for remainder in packing problems.

15. Answer: 7 400 [2]
Working:
Let the larger number be $L$, smaller be $S$.
$L + S = 12 500$
$L - S = 2 300$
Adding: $2L = 14 800$
$L = 7 400$

Check: $S = 12 500 - 7 400 = 5 100$; $7 400 - 5 100 = 2 300$ ✓

Key concept: Sum and difference problems - larger number = (sum + difference) ÷ 2.

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Section C: Structured / Long Answer Questions (20 marks)

16. Answer: $3 000 [4]

Method 1: Fraction Model (Backward)
Let total money = 1 whole = 15 units (LCM of 5 and 3)

Spent on TV: $\frac{2}{5} = \frac{6}{15}$ → 6 units
Remainder: $15 - 6 = 9$ units

Spent on refrigerator: $\frac{1}{3}$ of remainder = $\frac{1}{3} \times 9 = 3$ units
Left: $9 - 3 = 6$ units

6 units = $1 200 1 unit =$1 200 ÷ 6 = $200 15 units =$200 × 15 = $3 000

Method 2: Fraction Calculation
Fraction spent on TV = $\frac{2}{5}$
Remainder = $1 - \frac{2}{5} = \frac{3}{5}$
Fraction spent on refrigerator = $\frac{1}{3} \times \frac{3}{5} = \frac{1}{5}$
Fraction left = $1 - \frac{2}{5} - \frac{1}{5} = \frac{2}{5}$

$\frac{2}{5}$ of money = $1 200 Total money =$1 200 ÷ \frac{2}{5} = $1 200 × \frac{5}{2} =$3 000

Marking notes:

• 1 mark for correct fraction of remainder / fraction left
• 1 mark for correct unit value or fraction division
• 1 mark for correct total calculation
• 1 mark for final answer with unit ($)

Key concept: Fraction of remainder problems - track the changing whole. "Of the remainder" means multiply by the remaining fraction.

17. Answer: 10 713 [4]

Working:
Fiction books = 3 456
Non-fiction books = 3 456 + 1 234 = 4 690
Reference books = 2 567

Total = 3 456 + 4 690 + 2 567
= 8 146 + 2 567
= 10 713

Check:
3 456 + 4 690 = 8 146
8 146 + 2 567 = 10 713 ✓

Marking notes:

• 1 mark for correct non-fiction calculation
• 1 mark for correct addition of all three categories
• 1 mark for correct total
• 1 mark for clear working presentation

Key concept: Multi-step word problem - identify each quantity, compute step by step, then combine.

18. Answer: Greatest number of groups = 12; Each group has 4 girls and 5 boys [4]

Working:
To find greatest number of groups with equal girls and equal boys per group, find HCF of 48 and 60.

Prime factorisation:
$48 = 2^4 \times 3$
$60 = 2^2 \times 3 \times 5$
HCF = $2^2 \times 3 = 4 \times 3 = 12$

Or listing factors:
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
HCF = 12

Greatest number of groups = 12
Girls per group = 48 ÷ 12 = 4
Boys per group = 60 ÷ 12 = 5

Marking notes:

• 1 mark for identifying HCF method
• 1 mark for correct HCF (12)
• 1 mark for correct girls per group (4)
• 1 mark for correct boys per group (5)

Key concept: HCF (Highest Common Factor) for grouping problems - largest number that divides both quantities exactly.

19. Answer: 24 litres [4]

Working:
Volume of tank = $60 \times 40 \times 30 = 72 000 \text{ cm}^3$
Volume of water currently = $60 \times 40 \times 20 = 48 000 \text{ cm}^3$
Volume needed = $72 000 - 48 000 = 24 000 \text{ cm}^3$

Convert to litres: $24 000 \div 1 000 = 24 \text{ litres}$

Alternative:
Height needed = 30 - 20 = 10 cm
Volume needed = $60 \times 40 \times 10 = 24 000 \text{ cm}^3 = 24 \text{ litres}$

Marking notes:

• 1 mark for correct tank volume or height difference
• 1 mark for correct volume of water needed in cm³
• 1 mark for correct conversion (÷ 1000)
• 1 mark for final answer with unit (litres)

Key concept: Volume of cuboid = length × breadth × height. Unit conversion: 1 litre = 1000 cm³.

20. Answer: 60 [4]

Working:
Conditions:

• Between 50 and 100
• Multiple of 6
• Remainder 4 when divided by 7

Method 1: List multiples of 6 between 50 and 100
Multiples of 6: 54, 60, 66, 72, 78, 84, 90, 96

Check each ÷ 7 remainder 4:
54 ÷ 7 = 7 R 5 ✗
60 ÷ 7 = 8 R 4 ✓
66 ÷ 7 = 9 R 3 ✗
72 ÷ 7 = 10 R 2 ✗
78 ÷ 7 = 11 R 1 ✗
84 ÷ 7 = 12 R 0 ✗
90 ÷ 7 = 12 R 6 ✗
96 ÷ 7 = 13 R 5 ✗

Answer = 60

Method 2: Algebraic
Number = 6k (multiple of 6)
6k ≡ 4 (mod 7)
6k = 7m + 4
Try k = 9: 6 × 9 = 54, 54 ÷ 7 = 7 R 5 ✗
Try k = 10: 6 × 10 = 60, 60 ÷ 7 = 8 R 4 ✓

Marking notes:

• 1 mark for listing multiples of 6 in range
• 1 mark for checking division by 7
• 1 mark for identifying 60 as the only solution
• 1 mark for final answer

Key concept: Systematic listing with multiple conditions. Check each condition step by step.

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End of Answer Key