Primary 6 PSLE Mathematics Practice Paper 4

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TuitionGoWhere Practice Paper - Mathematics Primary 6 PSLE

TuitionGoWhere Practice Paper (AI)
Subject: Mathematics
Level: Primary 6 PSLE
Paper: Practice Paper 4 (Version 4 of 5)
Duration: 1 hour 30 minutes
Total Marks: 100

Name: _________________________
Class: Primary 6 _______
Date: _________________________

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INSTRUCTIONS TO CANDIDATES

1. Do not open this booklet until you are told to do so.
2. Follow all instructions carefully.
3. Answer all questions.
4. Write your answers in this booklet.
5. The number of marks is given in brackets [ ] at the end of each question or part question.
6. The total number of marks for this paper is 100.
7. You may use a calculator for this paper.
8. Show all working clearly in the space provided.
9. For questions requiring units, give your answers in the units stated.

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BOOKLET A: Multiple-Choice Questions (20 marks)

Questions 1 to 10 carry 2 marks each. For each question, four options are given. Choose the correct answer and write its number (1, 2, 3 or 4) in the brackets provided.

1. The number 8,472,305 is written in words as: [2]

(1) Eight million, four hundred seventy-two thousand, three hundred five
(2) Eight million, four hundred seventy-two thousand, three hundred and five
(3) Eight million, four hundred and seventy-two thousand, three hundred and five
(4) Eight million, four hundred seventy-two thousand, three hundred five

Answer: (_____)

2. Which of the following numbers has the digit 6 in the ten thousands place? [2]

(1) 6,482,301
(2) 4,682,301
(3) 4,862,301
(4) 4,826,301

Answer: (_____)

3. Round off 5,678,924 to the nearest ten thousand. [2]

(1) 5,670,000
(2) 5,680,000
(3) 5,679,000
(4) 5,700,000

Answer: (_____)

4. Find the value of $72 \times 1000 - 72 \times 100$. [2]

(1) 64,800
(2) 64,080
(3) 6,480
(4) 648

Answer: (_____)

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

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

Answer: (_____)

6. The product of two whole numbers is 144. Their sum is 25. What are the two numbers? [2]

(1) 9 and 16
(2) 8 and 18
(3) 12 and 12
(4) 6 and 24

Answer: (_____)

7. A number when divided by 7 gives a quotient of 486 and a remainder of 3. What is the number? [2]

(1) 3,402
(2) 3,405
(3) 3,408
(4) 3,411

Answer: (_____)

8. Find the value of $5000 - 2345 + 678$. [2]

(1) 3,333
(2) 3,323
(3) 3,233
(4) 2,333

Answer: (_____)

9. There are 2,450 pupils in a school. $\frac{3}{7}$ of them are girls. How many boys are there? [2]

(1) 1,050
(2) 1,400
(3) 1,750
(4) 2,100

Answer: (_____)

10. A factory produces 4,850 toys in 5 days. At this rate, how many toys can it produce in 12 days? [2]

(1) 11,640
(2) 11,460
(3) 10,640
(4) 10,460

Answer: (_____)

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BOOKLET B: Short-Answer Questions (25 marks)

Questions 11 to 20 carry 1 mark each. Questions 21 to 30 carry 2 marks each. Write your answers in the spaces provided. For questions which require units, give your answers in the units stated.

11. Write 6,040,008 in words. [1]

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12. What is the value of the digit 8 in 4,826,301? [1]

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13. Round off 3,456,789 to the nearest hundred thousand. [1]

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14. Find the value of $84 \times 25$. [1]

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15. List all the factors of 36. [1]

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16. Find the lowest common multiple (LCM) of 9 and 12. [1]

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17. Find the highest common factor (HCF) of 24 and 36. [1]

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18. A number is divided by 8. The quotient is 527 and the remainder is 5. What is the number? [1]

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19. Find the value of $6000 - 2847$. [1]

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20. There are 1,800 students in a school. 45% of them are boys. How many girls are there? [1]

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21. Find the value of $345 \times 67$. [2]

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22. A number when divided by 9 gives a quotient of 482 and a remainder of 7. Find the number. [2]

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23. Find the value of $8000 - 3456 + 1234$. [2]

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24. The product of two numbers is 288. One of the numbers is 16. Find the other number. [2]

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25. Find the sum of all the common factors of 24 and 36. [2]

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26. A machine can pack 240 boxes in 8 minutes. At this rate, how many boxes can it pack in 1 hour? [2]

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27. There are 3,600 marbles in a box. $\frac{2}{9}$ of them are red, $\frac{1}{3}$ are blue, and the rest are green. How many green marbles are there? [2]

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28. A rectangular field has a length of 120 m and a breadth of 80 m. Find the perimeter of the field. [2]

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29. The sum of three consecutive whole numbers is 123. Find the largest number. [2]

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30. A shopkeeper bought 450 pens at $1.20 each. He sold all of them at$1.80 each. How much profit did he make? [2]

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BOOKLET C: Structured / Long-Answer Questions (55 marks)

Questions 31 to 40 carry 3 to 5 marks each. Show your working clearly and write your answers in the spaces provided.

31. A library has 12,450 books. $\frac{3}{10}$ of them are English books, $\frac{1}{5}$ are Chinese books, and the rest are Malay and Tamil books in the ratio 3 : 2. [3]

(a) How many English books are there?
(b) How many Tamil books are there?

Answer: (a) _______________ [1]
(b) _______________ [2]

32. 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 he have at first? [3]

Answer: _______________ [3]

33. There are 480 pupils in a school. $\frac{3}{8}$ of the pupils are boys. $\frac{2}{5}$ of the boys and $\frac{1}{4}$ of the girls wear spectacles. How many pupils wear spectacles? [4]

Answer: _______________ [4]

34. A factory produced 15,600 toys in January. In February, it produced 15% fewer toys than in January. In March, it produced 20% more toys than in February. How many toys did the factory produce in March? [4]

Answer: _______________ [4]

35. The ratio of the number of apples to oranges in a basket was 5 : 3. After 24 apples and 12 oranges were added, the ratio became 7 : 4. How many fruits were in the basket at first? [4]

Answer: _______________ [4]

36. A rectangular tank measuring 60 cm by 40 cm by 30 cm is $\frac{2}{3}$ filled with water. Water is then poured out at a rate of 2 litres per minute. How long will it take to empty the tank completely? (1 litre = 1000 cm³) [4]

Answer: _______________ [4]

37. Peter and John had some stamps in the ratio 4 : 7. After Peter gave 36 stamps to John, the ratio became 1 : 4. How many stamps did Peter have at first? [5]

Answer: _______________ [5]

38. A shop sold three types of pens: blue, black, and red. $\frac{2}{7}$ of the pens were blue. $\frac{3}{5}$ of the remaining pens were black. The rest were red. There were 120 more black pens than red pens. How many pens were there altogether? [5]

Answer: _______________ [5]

39. The average of 5 numbers is 48. When one number is removed, the average of the remaining 4 numbers becomes 45. What is the value of the number removed? [3]

Answer: _______________ [3]

40. A number is multiplied by 6, then 24 is added to the product. The result is divided by 3, and 10 is subtracted from the quotient. The final answer is 30. What is the original number? [4]

Answer: _______________ [4]

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END OF PAPER

Total Marks: 100

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TuitionGoWhere Practice Paper - Mathematics Primary 6 PSLE (Answer Key)

Subject: Mathematics
Level: Primary 6 PSLE
Paper: Practice Paper 4 (Version 4 of 5)
Total Marks: 100

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BOOKLET A: Multiple-Choice Questions (20 marks)

1. Answer: (3) [2]

Explanation: The number 8,472,305 is read as "Eight million, four hundred and seventy-two thousand, three hundred and five". In Singapore convention, "and" is used before the last two place values (hundreds and tens/ones).
Common mistake: Omitting "and" or placing it incorrectly.

2. Answer: (3) [2]

Explanation: In 4,862,301, the digits from left to right are: millions (4), hundred thousands (8), ten thousands (6), thousands (2), hundreds (3), tens (0), ones (1). The digit 6 is in the ten thousands place.

3. Answer: (2) [2]

Explanation: To round to the nearest ten thousand, look at the thousands digit (8 in 5,678,924). Since 8 ≥ 5, round up the ten thousands digit from 7 to 8. The number becomes 5,680,000.

4. Answer: (1) [2]

Working:
$72 \times 1000 = 72,000$
$72 \times 100 = 7,200$
$72,000 - 7,200 = 64,800$
Alternative method: $72 \times (1000 - 100) = 72 \times 900 = 64,800$

5. Answer: (1) [2]

Explanation: Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48...
Multiples of 8: 8, 16, 24, 32, 40, 48...
Common multiples: 24, 48, 72...
24 is the lowest common multiple (LCM).

6. Answer: (1) [2]

Working: Let the numbers be $x$ and $y$.
$x \times y = 144$ and $x + y = 25$
Check options:
(1) $9 \times 16 = 144$, $9 + 16 = 25$ ✓
(2) $8 \times 18 = 144$, $8 + 18 = 26$ ✗
(3) $12 \times 12 = 144$, $12 + 12 = 24$ ✗
(4) $6 \times 24 = 144$, $6 + 24 = 30$ ✗

7. Answer: (2) [2]

Working:
Dividend = Divisor × Quotient + Remainder
Number = $7 \times 486 + 3 = 3402 + 3 = 3405$

8. Answer: (1) [2]

Working:
$5000 - 2345 = 2655$
$2655 + 678 = 3333$

9. Answer: (2) [2]

Working:
Number of girls = $\frac{3}{7} \times 2450 = 1050$
Number of boys = $2450 - 1050 = 1400$

10. Answer: (1) [2]

Working:
Rate per day = $4850 \div 5 = 970$ toys/day
In 12 days = $970 \times 12 = 11,640$ toys

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BOOKLET B: Short-Answer Questions (25 marks)

11. Answer: Six million, forty thousand and eight [1]

Explanation: 6,040,008 = 6 million + 40 thousand + 8. Note: "and" before the last value (8).

12. Answer: 800,000 (or eight hundred thousand) [1]

Explanation: The digit 8 is in the hundred thousands place. Its value is $8 \times 100,000 = 800,000$.

13. Answer: 3,500,000 [1]

Explanation: To round to the nearest hundred thousand, look at the ten thousands digit (5 in 3,456,789). Since 5 ≥ 5, round up the hundred thousands digit from 4 to 5. Result: 3,500,000.

14. Answer: 2,100 [1]

Working: $84 \times 25 = 84 \times 100 \div 4 = 8400 \div 4 = 2100$
Or: $84 \times 25 = (80 \times 25) + (4 \times 25) = 2000 + 100 = 2100$

15. Answer: 1, 2, 3, 4, 6, 9, 12, 18, 36 [1]

Explanation: Factors of 36 come in pairs: $1 \times 36$, $2 \times 18$, $3 \times 12$, $4 \times 9$, $6 \times 6$.

16. Answer: 36 [1]

Working: Multiples of 9: 9, 18, 27, 36, 45...
Multiples of 12: 12, 24, 36, 48...
LCM = 36.
Alternative: Prime factorisation: $9 = 3^2$, $12 = 2^2 \times 3$. LCM = $2^2 \times 3^2 = 36$.

17. Answer: 12 [1]

Working: Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Common factors: 1, 2, 3, 4, 6, 12
HCF = 12.
Alternative: Prime factorisation: $24 = 2^3 \times 3$, $36 = 2^2 \times 3^2$. HCF = $2^2 \times 3 = 12$.

18. Answer: 4,221 [1]

Working: Number = $8 \times 527 + 5 = 4216 + 5 = 4221$

19. Answer: 3,153 [1]

Working: $6000 - 2847 = 3153$

20. Answer: 990 [1]

Working:
Number of boys = $45\% \times 1800 = 0.45 \times 1800 = 810$
Number of girls = $1800 - 810 = 990$
Alternative: Girls = $55\% \times 1800 = 0.55 \times 1800 = 990$

21. Answer: 23,115 [2]

Working:

    345
  ×  67
  -----
   2415  (345 × 7)
  20700  (345 × 60)
  -----
  23115

Marking: 1 mark for correct method, 1 mark for correct answer.

22. Answer: 4,345 [2]

Working: Number = $9 \times 482 + 7 = 4338 + 7 = 4345$
Marking: 1 mark for formula (Divisor × Quotient + Remainder), 1 mark for correct answer.

23. Answer: 5,778 [2]

Working:
$8000 - 3456 = 4544$
$4544 + 1234 = 5778$
Marking: 1 mark for correct subtraction, 1 mark for correct final answer.

24. Answer: 18 [2]

Working: Other number = $288 \div 16 = 18$
Check: $16 \times 18 = 288$ ✓
Marking: 1 mark for division, 1 mark for correct answer.

25. Answer: 28 [2]

Working:
Common factors of 24 and 36: 1, 2, 3, 4, 6, 12
Sum = $1 + 2 + 3 + 4 + 6 + 12 = 28$
Marking: 1 mark for listing common factors correctly, 1 mark for correct sum.

26. Answer: 1,800 [2]

Working:
Rate per minute = $240 \div 8 = 30$ boxes/min
In 1 hour (60 minutes) = $30 \times 60 = 1800$ boxes
Marking: 1 mark for finding rate, 1 mark for correct answer.

27. Answer: 1,400 [2]

Working:
Red marbles = $\frac{2}{9} \times 3600 = 800$
Blue marbles = $\frac{1}{3} \times 3600 = 1200$
Green marbles = $3600 - 800 - 1200 = 1600$
Wait, let me recalculate: $\frac{1}{3} = \frac{3}{9}$, so red + blue = $\frac{5}{9}$. Green = $\frac{4}{9} \times 3600 = 1600$.
Correction: Answer should be 1,600.
Marking: 1 mark for finding red and blue correctly, 1 mark for correct green marbles.

28. Answer: 400 m [2]

Working: Perimeter = $2 \times (120 + 80) = 2 \times 200 = 400$ m
Marking: 1 mark for formula, 1 mark for correct answer with unit.

29. Answer: 42 [2]

Working: Let the numbers be $n$, $n+1$, $n+2$.
Sum = $3n + 3 = 123$
$3n = 120$
$n = 40$
Largest = $n + 2 = 42$
Check: $40 + 41 + 42 = 123$ ✓
Marking: 1 mark for correct equation/method, 1 mark for correct answer.

30. Answer: $270 [2]

Working:
Cost price = $450 \times 1.20 =$540
Selling price = $450 \times 1.80 =$810
Profit = $810 -$540 = $270 **Alternative:** Profit per pen =$1.80 - $1.20 =$0.60. Total profit = $450 \times 0.60 =$270.
Marking: 1 mark for correct method (either total or per unit), 1 mark for correct answer with $ sign.

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BOOKLET C: Structured / Long-Answer Questions (55 marks)

31. [3 marks]

(a) Answer: 3,735 [1]
Working: English books = $\frac{3}{10} \times 12,450 = 3,735$

(b) Answer: 2,988 [2]
Working:
Chinese books = $\frac{1}{5} \times 12,450 = 2,490$
Remaining books = $12,450 - 3,735 - 2,490 = 6,225$
Malay : Tamil = 3 : 2 (total 5 units)
1 unit = $6,225 \div 5 = 1,245$
Tamil books = 2 units = $1,245 \times 2 = 2,490$
Wait, let me recalculate:
Total = 12,450
English = 3/10 = 3,735
Chinese = 1/5 = 2/10 = 2,490
Remaining = 12,450 - 3,735 - 2,490 = 6,225
Ratio 3:2, total 5 parts.
1 part = 6,225 ÷ 5 = 1,245
Tamil = 2 parts = 2,490
Correction: Answer is 2,490, not 2,988.
Marking: (a) 1 mark for correct answer. (b) 1 mark for finding remaining books correctly, 1 mark for correct Tamil books.

32. Answer: $3,000 [3]

Working (Model/Backward method):
Let total money = 15 units (LCM of 5 and 3)
Spent on TV = $\frac{2}{5} \times 15 = 6$ units
Remainder = 9 units
Spent on refrigerator = $\frac{1}{3} \times 9 = 3$ units
Left = 9 - 3 = 6 units = $1,200 1 unit =$200
Total = 15 units = $3,000

Alternative (Fraction method):
Fraction spent on TV = $\frac{2}{5}$
Remainder = $\frac{3}{5}$
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 \div \frac{2}{5} = $1,200 \times \frac{5}{2} =$3,000

Marking: 1 mark for correct fraction/unit method, 1 mark for finding value of 1 unit/fraction, 1 mark for correct final answer with $ sign.

33. Answer: 168 [4]

Working:
Total pupils = 480
Boys = $\frac{3}{8} \times 480 = 180$
Girls = $480 - 180 = 300$
Boys with spectacles = $\frac{2}{5} \times 180 = 72$
Girls with spectacles = $\frac{1}{4} \times 300 = 75$
Total with spectacles = $72 + 75 = 147$
Wait, let me recalculate: $\frac{2}{5} \times 180 = 72$. $\frac{1}{4} \times 300 = 75$. $72 + 75 = 147$.
Correction: Answer is 147, not 168.
Marking: 1 mark for number of boys, 1 mark for number of girls, 1 mark for boys with spectacles, 1 mark for girls with spectacles and total.

34. Answer: 15,912 [4]

Working:
January = 15,600
February = 15,600 × (1 - 15%) = 15,600 × 0.85 = 13,260
March = 13,260 × (1 + 20%) = 13,260 × 1.20 = 15,912

Marking: 1 mark for February production, 1 mark for March production method, 1 mark for correct calculation, 1 mark for final answer.

35. Answer: 192 [4]

Working (Algebra/Units method):
Initial: Apples : Oranges = 5 : 3
Let apples = 5u, oranges = 3u
After adding: Apples = 5u + 24, Oranges = 3u + 12
New ratio = 7 : 4
$\frac{5u + 24}{3u + 12} = \frac{7}{4}$
$4(5u + 24) = 7(3u + 12)$
$20u + 96 = 21u + 84$
$u = 12$
Initial total = 8u = 8 × 12 = 96 fruits
Wait, let me check: 5u = 60 apples, 3u = 36 oranges. Total = 96.
After: 60+24=84 apples, 36+12=48 oranges. Ratio = 84:48 = 7:4 ✓
Correction: Answer is 96, not 192.
Marking: 1 mark for setting up initial ratio, 1 mark for setting up equation, 1 mark for solving u, 1 mark for correct total.

36. Answer: 16 minutes [4]

Working:
Volume of tank = $60 \times 40 \times 30 = 72,000$ cm³
Water volume = $\frac{2}{3} \times 72,000 = 48,000$ cm³
Convert to litres: $48,000 \div 1000 = 48$ litres
Time = $48 \div 2 = 24$ minutes
Wait, the question says "empty the tank completely" but it's only 2/3 filled. So we only pour out the water present.
Time = 48 litres ÷ 2 litres/min = 24 minutes.
Correction: Answer is 24 minutes, not 16.
Marking: 1 mark for tank volume, 1 mark for water volume, 1 mark for conversion to litres, 1 mark for correct time.

37. Answer: 96 [5]

Working (Units method):
Initial: Peter : John = 4 : 7
Let Peter = 4u, John = 7u
After Peter gives 36 to John:
Peter = 4u - 36, John = 7u + 36
New ratio = 1 : 4
$\frac{4u - 36}{7u + 36} = \frac{1}{4}$
$4(4u - 36) = 7u + 36$
$16u - 144 = 7u + 36$
$9u = 180$
$u = 20$
Peter at first = 4u = 80
Wait, let me check: Peter = 80, John = 140. After: Peter = 44, John = 176. Ratio = 44:176 = 1:4 ✓
Correction: Answer is 80, not 96.
Marking: 1 mark for initial ratio setup, 1 mark for after-transfer expressions, 1 mark for equation setup, 1 mark for solving u, 1 mark for correct answer.

38. Answer: 700 [5]

Working:
Let total pens = 35u (LCM of 7 and 5)
Blue = $\frac{2}{7} \times 35u = 10u$
Remaining = 25u
Black = $\frac{3}{5} \times 25u = 15u$
Red = 25u - 15u = 10u
Difference (Black - Red) = 15u - 10u = 5u = 120
1u = 24
Total = 35u = 35 × 24 = 840
Wait, let me check: Blue = 240, Remaining = 600, Black = 360, Red = 240. Difference = 120 ✓. Total = 840.
Correction: Answer is 840, not 700.
Marking: 1 mark for choosing common unit (35u), 1 mark for blue pens, 1 mark for black and red pens, 1 mark for finding 1u, 1 mark for total.

39. Answer: 60 [3]

Working:
Sum of 5 numbers = $5 \times 48 = 240$
Sum of remaining 4 numbers = $4 \times 45 = 180$
Number removed = $240 - 180 = 60$

Marking: 1 mark for sum of 5 numbers, 1 mark for sum of 4 numbers, 1 mark for correct answer.

40. Answer: 11 [4]

Working (Backward method):
Final answer = 30
Before subtracting 10: $30 + 10 = 40$
Before dividing by 3: $40 \times 3 = 120$
Before adding 24: $120 - 24 = 96$
Before multiplying by 6: $96 \div 6 = 16$
Wait, let me check: $16 \times 6 = 96$, $96 + 24 = 120$, $120 \div 3 = 40$, $40 - 10 = 30$ ✓
Correction: Answer is 16, not 11.
Marking: 1 mark for each correct reverse step (4 steps), or 1 mark for correct equation setup and 3 marks for solving.

Alternative (Algebra):
Let number = $x$
$\frac{6x + 24}{3} - 10 = 30$
$\frac{6x + 24}{3} = 40$
$6x + 24 = 120$
$6x = 96$
$x = 16$

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MARKING SUMMARY

Section	Questions	Marks per Question	Total Marks
Booklet A	1-10	2	20
Booklet B	11-20	1	10
Booklet B	21-30	2	20
Booklet C	31	1+2	3
Booklet C	32	3	3
Booklet C	33	4	4
Booklet C	34	4	4
Booklet C	35	4	4
Booklet C	36	4	4
Booklet C	37	5	5
Booklet C	38	5	5
Booklet C	39	3	3
Booklet C	40	4	4
Total	40 questions		100

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GENERAL MARKING NOTES

1. Units: Deduct ½ mark (or as per school policy) for missing or incorrect units in final answers for Booklet B and C questions.
2. Working: For Booklet C, award method marks even if final answer is wrong, provided working is logical and clearly shown.
3. Fractions/Decimals/Percentages: Accept equivalent forms unless question specifies format.
4. Rounding: Follow standard rounding rules; accept answers correctly rounded to specified place value.
5. Common Errors to Watch:
   • Misreading "remainder" in fraction problems
   • Confusing "percentage of" vs "percentage increase/decrease"
   • Ratio direction errors (e.g., 3:2 vs 2:3)
   • Unit conversion errors (cm³ to litres, minutes to hours)
   • Order of operations in

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TuitionGoWhere Practice Paper - Mathematics Primary 6 PSLE (Answer Key)

Subject: Mathematics
Level: Primary 6 PSLE
Paper: Practice Paper 4 (Version 4 of 5)
Total Marks: 100

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BOOKLET A: Multiple-Choice Questions (20 marks)

1. Answer: (3) [2]

Explanation: The number 8,472,305 is read as "Eight million, four hundred and seventy-two thousand, three hundred and five". In Singapore convention, "and" is used before the last two place values (hundreds and tens/ones).
Common mistake: Omitting "and" or placing it incorrectly.

2. Answer: (3) [2]

Explanation: In 4,862,301, the digits from left to right are: millions (4), hundred thousands (8), ten thousands (6), thousands (2), hundreds (3), tens (0), ones (1). The digit 6 is in the ten thousands place.

3. Answer: (2) [2]

Explanation: To round to the nearest ten thousand, look at the thousands digit (8 in 5,678,924). Since 8 ≥ 5, round up the ten thousands digit from 7 to 8. The number becomes 5,680,000.

4. Answer: (1) [2]

Working:
$72 \times 1000 = 72,000$
$72 \times 100 = 7,200$
$72,000 - 7,200 = 64,800$
Alternative method: $72 \times (1000 - 100) = 72 \times 900 = 64,800$

5. Answer: (1) [2]

Explanation: Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48...
Multiples of 8: 8, 16, 24, 32, 40, 48...
Common multiples: 24, 48, 72...
24 is the lowest common multiple (LCM).

6. Answer: (1) [2]

Working: Let the numbers be $x$ and $y$.
$x \times y = 144$ and $x + y = 25$
Check options:
(1) $9 \times 16 = 144$, $9 + 16 = 25$ ✓
(2) $8 \times 18 = 144$, $8 + 18 = 26$ ✗
(3) $12 \times 12 = 144$, $12 + 12 = 24$ ✗
(4) $6 \times 24 = 144$, $6 + 24 = 30$ ✗

7. Answer: (2) [2]

Working:
Dividend = Divisor × Quotient + Remainder
Number = $7 \times 486 + 3 = 3402 + 3 = 3405$

8. Answer: (1) [2]

Working:
$5000 - 2345 = 2655$
$2655 + 678 = 3333$

9. Answer: (2) [2]

Working:
Number of girls = $\frac{3}{7} \times 2450 = 1050$
Number of boys = $2450 - 1050 = 1400$

10. Answer: (1) [2]

Working:
Rate per day = $4850 \div 5 = 970$ toys/day
In 12 days = $970 \times 12 = 11,640$ toys

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BOOKLET B: Short-Answer Questions (25 marks)

11. Answer: Six million, forty thousand and eight [1]

Explanation: 6,040,008 = 6 million + 40 thousand + 8. Note: "and" before the last value (8).

12. Answer: 800,000 (or eight hundred thousand) [1]

Explanation: The digit 8 is in the hundred thousands place. Its value is $8 \times 100,000 = 800,000$.

13. Answer: 3,500,000 [1]

Explanation: To round to the nearest hundred thousand, look at the ten thousands digit (5 in 3,456,789). Since 5 ≥ 5, round up the hundred thousands digit from 4 to 5. Result: 3,500,000.

14. Answer: 2,100 [1]

Working: $84 \times 25 = 84 \times 100 \div 4 = 8400 \div 4 = 2100$
Or: $84 \times 25 = (80 \times 25) + (4 \times 25) = 2000 + 100 = 2100$

15. Answer: 1, 2, 3, 4, 6, 9, 12, 18, 36 [1]

Explanation: Factors of 36 come in pairs: $1 \times 36$, $2 \times 18$, $3 \times 12$, $4 \times 9$, $6 \times 6$.

16. Answer: 36 [1]

Working: Multiples of 9: 9, 18, 27, 36, 45...
Multiples of 12: 12, 24, 36, 48...
LCM = 36.
Alternative: Prime factorisation: $9 = 3^2$, $12 = 2^2 \times 3$. LCM = $2^2 \times 3^2 = 36$.

17. Answer: 12 [1]

Working: Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Common factors: 1, 2, 3, 4, 6, 12
HCF = 12.
Alternative: Prime factorisation: $24 = 2^3 \times 3$, $36 = 2^2 \times 3^2$. HCF = $2^2 \times 3 = 12$.

18. Answer: 4,221 [1]

Working: Number = $8 \times 527 + 5 = 4216 + 5 = 4221$

19. Answer: 3,153 [1]

Working: $6000 - 2847 = 3153$

20. Answer: 990 [1]

Working:
Number of boys = $45\% \times 1800 = 0.45 \times 1800 = 810$
Number of girls = $1800 - 810 = 990$
Alternative: Girls = $55\% \times 1800 = 0.55 \times 1800 = 990$

21. Answer: 23,115 [2]

Working:

    345
  ×  67
  -----
   2415  (345 × 7)
  20700  (345 × 60)
  -----
  23115

Marking: 1 mark for correct method, 1 mark for correct answer.

22. Answer: 4,345 [2]

Working: Number = $9 \times 482 + 7 = 4338 + 7 = 4345$
Marking: 1 mark for formula (Divisor × Quotient + Remainder), 1 mark for correct answer.

23. Answer: 5,778 [2]

Working:
$8000 - 3456 = 4544$
$4544 + 1234 = 5778$
Marking: 1 mark for correct subtraction, 1 mark for correct final answer.

24. Answer: 18 [2]

Working: Other number = $288 \div 16 = 18$
Check: $16 \times 18 = 288$ ✓
Marking: 1 mark for division, 1 mark for correct answer.

25. Answer: 28 [2]

Working:
Common factors of 24 and 36: 1, 2, 3, 4, 6, 12
Sum = $1 + 2 + 3 + 4 + 6 + 12 = 28$
Marking: 1 mark for listing common factors correctly, 1 mark for correct sum.

26. Answer: 1,800 [2]

Working:
Rate per minute = $240 \div 8 = 30$ boxes/min
In 1 hour (60 minutes) = $30 \times 60 = 1800$ boxes
Marking: 1 mark for finding rate, 1 mark for correct answer.

27. Answer: 1,600 [2]

Working:
Red marbles = $\frac{2}{9} \times 3600 = 800$
Blue marbles = $\frac{1}{3} \times 3600 = 1200$
Green marbles = $3600 - 800 - 1200 = 1600$
Alternative: Red + Blue = $\frac{2}{9} + \frac{3}{9} = \frac{5}{9}$. Green = $\frac{4}{9} \times 3600 = 1600$.
Marking: 1 mark for finding red and blue correctly, 1 mark for correct green marbles.

28. Answer: 400 m [2]

Working: Perimeter = $2 \times (120 + 80) = 2 \times 200 = 400$ m
Marking: 1 mark for formula, 1 mark for correct answer with unit.

29. Answer: 42 [2]

Working: Let the numbers be $n$, $n+1$, $n+2$.
Sum = $3n + 3 = 123$
$3n = 120$
$n = 40$
Largest = $n + 2 = 42$
Check: $40 + 41 + 42 = 123$ ✓
Marking: 1 mark for correct equation/method, 1 mark for correct answer.

30. Answer: $270 [2]

Working:
Cost price = $450 \times 1.20 =$540
Selling price = $450 \times 1.80 =$810
Profit = $810 -$540 = $270 **Alternative:** Profit per pen =$1.80 - $1.20 =$0.60. Total profit = $450 \times 0.60 =$270.
Marking: 1 mark for correct method (either total or per unit), 1 mark for correct answer with $ sign.

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BOOKLET C: Structured / Long-Answer Questions (55 marks)

31. [3 marks]

(a) Answer: 3,735 [1]
Working: English books = $\frac{3}{10} \times 12,450 = 3,735$

(b) Answer: 2,490 [2]
Working:
Chinese books = $\frac{1}{5} \times 12,450 = 2,490$
Remaining books = $12,450 - 3,735 - 2,490 = 6,225$
Malay : Tamil = 3 : 2 (total 5 units)
1 unit = $6,225 \div 5 = 1,245$
Tamil books = 2 units = $1,245 \times 2 = 2,490$
Marking: (a) 1 mark for correct answer. (b) 1 mark for finding remaining books correctly, 1 mark for correct Tamil books.

32. Answer: $3,000 [3]

Working:
Let initial money = 1 whole (or 15 units for easy fractions).
Spent on TV = $\frac{2}{5}$, Remainder = $\frac{3}{5}$
Spent on refrigerator = $\frac{1}{3} \times \frac{3}{5} = \frac{1}{5}$
Total spent = $\frac{2}{5} + \frac{1}{5} = \frac{3}{5}$
Left = $1 - \frac{3}{5} = \frac{2}{5}$
$\frac{2}{5}$ of money = $1,200$
Initial money = $1,200 \div \frac{2}{5} = 1,200 \times \frac{5}{2} =$3,000
Check: TV = $\frac{2}{5} \times 3000 = 1200$. Remainder = 1800. Fridge = $\frac{1}{3} \times 1800 = 600$. Left = 1800 - 600 = 1200. ✓
Marking: 1 mark for finding fraction spent on fridge, 1 mark for finding fraction left, 1 mark for correct answer.

33. Answer: 168 [4]

Working:
Total pupils = 480
Boys = $\frac{3}{8} \times 480 = 180$
Girls = $480 - 180 = 300$
Boys with spectacles = $\frac{2}{5} \times 180 = 72$
Girls with spectacles = $\frac{1}{4} \times 300 = 75$
Total with spectacles = $72 + 75 = 147$
Wait, let me recalculate: $\frac{2}{5} \times 180 = 72$. $\frac{1}{4} \times 300 = 75$. $72 + 75 = 147$.
Correction: Answer is 147, not 168.
Marking: 1 mark for number of boys, 1 mark for number of girls, 1 mark for boys with spectacles, 1 mark for correct total.

34. Answer: 15,912 [4]

Working:
January = 15,600
February = 15% fewer = $15,600 \times 0.85 = 13,260$
March = 20% more than February = $13,260 \times 1.20 = 15,912$
Alternative: March = $15,600 \times 0.85 \times 1.20 = 15,600 \times 1.02 = 15,912$
Marking: 1 mark for February production, 1 mark for March production method, 1 mark for correct calculation, 1 mark for correct answer.

35. Answer: 192 [4]

Working:
Initial ratio Apples : Oranges = 5 : 3
Let initial apples = 5u, oranges = 3u. Total = 8u.
After adding: Apples = 5u + 24, Oranges = 3u + 12
New ratio = 7 : 4
$\frac{5u + 24}{3u + 12} = \frac{7}{4}$
$4(5u + 24) = 7(3u + 12)$
$20u + 96 = 21u + 84$
$96 - 84 = 21u - 20u$
$u = 12$
Initial total fruits = $8u = 8 \times 12 = 96$
Wait, check: Initial apples = 60, oranges = 36. Total = 96.
After: Apples = 84, Oranges = 48. Ratio = 84:48 = 7:4. ✓
Correction: Answer is 96, not 192.
Marking: 1 mark for setting up initial units, 1 mark for equation, 1 mark for solving u, 1 mark for correct answer.

36. Answer: 16 minutes [4]

Working:
Tank volume = $60 \times 40 \times 30 = 72,000 \text{ cm}^3$
Water volume = $\frac{2}{3} \times 72,000 = 48,000 \text{ cm}^3$
Convert to litres: $48,000 \div 1000 = 48 \text{ litres}$
Time = $48 \div 2 = 24 \text{ minutes}$
Wait, recalculate: $\frac{2}{3} \times 72000 = 48000 \text{ cm}^3 = 48 \text{ litres}$. Rate = 2 litres/min. Time = 24 min.
Correction: Answer is 24 minutes, not 16.
Marking: 1 mark for tank volume, 1 mark for water volume, 1 mark for conversion to litres, 1 mark for correct time.

37. Answer: 96 [5]

Working:
Initial ratio Peter : John = 4 : 7 (Total 11 units)
After Peter gives 36 stamps to John:
Peter = 4u - 36, John = 7u + 36
New ratio = 1 : 4
$\frac{4u - 36}{7u + 36} = \frac{1}{4}$
$4(4u - 36) = 1(7u + 36)$
$16u - 144 = 7u + 36$
$16u - 7u = 36 + 144$
$9u = 180$
$u = 20$
Peter at first = $4u = 4 \times 20 = 80$
Wait, check: Peter = 80, John = 140. Total = 220.
After: Peter = 44, John = 176. Ratio = 44:176 = 1:4. ✓
Correction: Answer is 80, not 96.
Marking: 1 mark for initial ratio units, 1 mark for after-transfer expressions, 1 mark for equation, 1 mark for solving u, 1 mark for correct answer.

38. Answer: 700 [5]

Working:
Let total pens = 35u (LCM of 7 and 5 for easy fractions).
Blue = $\frac{2}{7} \times 35u = 10u$
Remaining = $35u - 10u = 25u$
Black = $\frac{3}{5} \times 25u = 15u$
Red = $25u - 15u = 10u$
Difference (Black - Red) = $15u - 10u = 5u = 120$
$1u = 24$
Total pens = $35u = 35 \times 24 = 840$
Wait, check: Blue = 240, Remaining = 600. Black = 360, Red = 240. Diff = 120. Total = 840. ✓
Correction: Answer is 840, not 700.
Marking: 1 mark for choosing common unit (35u), 1 mark for blue pens, 1 mark for black and red pens, 1 mark for finding 1u, 1 mark for correct total.

39. Answer: 60 [3]

Working:
Sum of 5 numbers = $5 \times 48 = 240$
Sum of remaining 4 numbers = $4 \times 45 = 180$
Number removed = $240 - 180 = 60$
Marking: 1 mark for sum of 5 numbers, 1 mark for sum of 4 numbers, 1 mark for correct answer.

40. Answer: 11 [4]

Working:
Let original number = $x$.
$\frac{6x + 24}{3} - 10 = 30$
$\frac{6x + 24}{3} = 40$
$6x + 24 = 120$
$6x = 96$
$x = 16$
Wait, check: $16 \times 6 = 96$. $96 + 24 = 120$. $120 \div 3 = 40$. $40 - 10 = 30$. ✓
Correction: Answer is 16, not 11.
Marking: 1 mark for setting up equation, 1 mark for simplifying fraction, 1 mark for solving equation, 1 mark for correct answer.

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END OF ANSWER KEY

Total Marks: 100