Primary 6 PSLE Mathematics Whole Numbers Quiz

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Primary 6 PSLE Mathematics Quiz - Whole Numbers

Name: ___________________________
Class: Primary 6 _______
Date: _______________
Score: _______ / 50

Duration: 45 minutes
Total Marks: 50

Instructions:

1. Answer all questions.
2. Show your working clearly in the space provided.
3. Write your answers in the spaces provided.
4. The number of marks is given in brackets [ ] at the end of each question or part question.
5. Calculators are NOT allowed for this quiz.

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Section A: Multiple Choice Questions (10 marks)

Questions 1 to 5 carry 2 marks each. Choose the correct answer and write its number (1, 2, 3 or 4) in the brackets provided.

1. In the number 4 827 391, the digit 8 stands for __________. [2]

(1) 80 000
(2) 800 000
(3) 8 000 000
(4) 80 000 000

Answer: (_____)

2. Round off 3 456 789 to the nearest ten thousand. [2]

(1) 3 450 000
(2) 3 460 000
(3) 3 500 000
(4) 3 400 000

Answer: (_____)

3. Which of the following is a common multiple of 6 and 8? [2]

(1) 24
(2) 36
(3) 42
(4) 54

Answer: (_____)

4. Find the value of $72 \times 1000 + 72 \times 500$. [2]

(1) 108 000
(2) 108 000
(3) 108 000
(4) 108 000

Answer: (_____)

5. A number when divided by 9 gives a quotient of 4 321 and a remainder of 5. What is the number? [2]

(1) 38 889
(2) 38 894
(3) 38 899
(4) 38 904

Answer: (_____)

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Section B: Short Answer Questions (20 marks)

Questions 6 to 15 carry 2 marks each. Show your working clearly and write your answers in the spaces provided.

6. Write 2 050 007 in words. [2]

Answer: ________________________________________________________________

7. Find the value of $5 400 \div 60$. [2]

Answer: ________________________________________________________________

8. Find the product of 324 and 47. [2]

Answer: ________________________________________________________________

9. What is the greatest possible whole number that when rounded off to the nearest hundred gives 8 500? [2]

Answer: ________________________________________________________________

10. List all the factors of 36. [2]

Answer: ________________________________________________________________

11. Find the lowest common multiple (LCM) of 12 and 18. [2]

Answer: ________________________________________________________________

12. A factory produces 2 450 toys each day. How many toys does it produce in 15 days? [2]

Answer: ________________________________________________________________

13. Find the value of $8 000 - 3 456$. [2]

Answer: ________________________________________________________________

14. There are 4 800 marbles in a box. They are packed into packets of 25 marbles each. How many packets are needed to pack all the marbles? [2]

Answer: ________________________________________________________________

15. The sum of two numbers is 12 500. The difference between the two numbers is 2 300. What is the larger number? [2]

Answer: ________________________________________________________________

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

Questions 16 to 20 carry 4 marks each. Show your working clearly and write your answers in the spaces provided.

16. Mr Tan had some money. He spent $\frac{2}{5}$ of it on a television and $\frac{1}{3}$ of the remainder on a refrigerator. He had $1 200 left. How much money did Mr Tan have at first? [4]

Answer: ________________________________________________________________

17. A library has 3 456 fiction books. The number of non-fiction books is 1 234 more than the number of fiction books. The library also has 2 567 reference books. How many books are there in the library altogether? [4]

Answer: ________________________________________________________________

18. There are 48 girls and 60 boys in a hall. They are to be divided into groups such that each group has the same number of girls and the same number of boys. What is the greatest number of groups that can be formed? How many girls and how many boys are there in each group? [4]

Answer: ________________________________________________________________

19. A rectangular tank measures 60 cm by 40 cm by 30 cm. It is filled with water to a height of 20 cm. How many more litres of water are needed to fill the tank completely? (1 litre = 1000 cm³) [4]

Answer: ________________________________________________________________

20. A number is between 50 and 100. It is a multiple of 6. When it is divided by 7, the remainder is 4. What is the number? [4]

Answer: ________________________________________________________________

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End of Quiz

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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