Primary 5 Mathematics Semestral Assessment 2 (End of Year) Paper 2

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TuitionGoWhere Practice Paper - Mathematics Primary 5

TuitionGoWhere Exam Practice (AI)

Subject: Mathematics
Level: Primary 5
Paper: SA2 (Version 2)
Duration: 1 hour 45 minutes
Total Marks: 100

Name: ________________________
Class: Primary 5 ______
Date: _______________

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INSTRUCTIONS TO CANDIDATES

1. Do not turn over this page 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 use of an approved calculator is expected, where appropriate.
6. Show all working clearly in the space provided.
7. The number of marks is given in brackets [ ] at the end of each question or part question.
8. The total number of marks for this paper is 100.

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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. In the number 6 482 391, what does the digit 8 stand for? [2]

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

2. Round off 4 759 328 to the nearest ten thousand. [2]

(1) 4 750 000
(2) 4 760 000
(3) 4 800 000
(4) 4 700 000

3. Which of the following is equal to 3 000 000 + 400 000 + 50 000 + 6 000 + 700 + 80 + 9? [2]

(1) 3 456 789
(2) 3 465 789
(3) 3 546 789
(4) 3 456 879

4. Find the value of 72 000 ÷ 800. [2]

(1) 9
(2) 90
(3) 900
(4) 9 000

5. What is the product of 4 500 and 60? [2]

(1) 27 000
(2) 270 000
(3) 2 700 000
(4) 27 000 000

6. Evaluate: 48 + 12 × (15 − 9) ÷ 3 [2]

(1) 72
(2) 76
(3) 84
(4) 120

7. A factory produced 8 450 toys in January. In February, it produced 3 280 more toys than in January. How many toys did the factory produce in the two months? [2]

(1) 11 730
(2) 15 180
(3) 20 180
(4) 21 180

8. Mr Tan had $12 500. He spent$\frac{2}{5}$of it on a television and$\frac{1}{4}$ of the remainder on a sound system. How much money had he left? [2]

(1) $4 500 (2)$5 625
(3) $6 875 (4)$7 500

9. The sum of two numbers is 1 200 000. The larger number is 3 times the smaller number. What is the smaller number? [2]

(1) 300 000
(2) 400 000
(3) 600 000
(4) 900 000

10. A number when divided by 12 gives a quotient of 8 500 and a remainder of 7. What is the number? [2]

(1) 102 007
(2) 102 070
(3) 102 700
(4) 120 007

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BOOKLET B: Short-Answer Questions (30 marks)

Questions 11 to 20 carry 2 marks each. Questions 21 to 25 carry 3 marks each. Show your working clearly and write your answers in the spaces provided. For questions which require units, give your answers in the units stated.

11. Write 9 060 405 in words. [2]

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12. What is the value of the digit 7 in 5 728 394? [2]

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13. Arrange the following numbers from the smallest to the greatest. [2]

3 450 000, 3 045 000, 3 504 000, 3 054 000

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14. Round off 6 849 572 to the nearest hundred thousand. [2]

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15. Find the value of 5 600 × 300. [2]

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16. Find the value of 84 000 ÷ 700. [2]

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17. Evaluate: 65 − 18 ÷ 3 × 2 + 24 [2]

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18. Evaluate: (42 + 18) ÷ 6 × 5 − 25 [2]

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19. A library has 4 850 English books. It has 1 280 more Chinese books than English books. How many books are there in the library altogether? [2]

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20. Mrs Lim bought 15 boxes of apples. There were 24 apples in each box. She repacked all the apples into bags of 6. How many bags of apples did she get? [2]

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21. The difference between two numbers is 245 000. The smaller number is 387 500. What is the sum of the two numbers? [3]

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22. A number is multiplied by 8. Then 1 200 is added to the product. The result is 28 400. What is the number? [3]

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23. Mr Kumar had some money. He spent $\frac{3}{8}$ of it on a laptop and $\frac{2}{5}$ of the remainder on a printer. He had $2 100 left. How much money did he have at first? [3]

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24. There are 4 560 pupils in a school. $\frac{5}{12}$ of them are boys. How many more girls than boys are there in the school? [3]

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25. A factory packs 360 bottles of juice into each carton. If the factory produced 28 800 bottles of juice, how many cartons are needed? [3]

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BOOKLET C: Structured / Long-Answer Questions (50 marks)

Questions 26 to 35 carry 2 to 5 marks each. Show your working clearly and write your answers in the spaces provided.

26. A stadium has 45 680 seats. During a match, $\frac{7}{8}$ of the seats were occupied. How many seats were empty? [3]

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27. The total mass of 6 identical boxes and 4 identical crates is 1 840 kg. The mass of each box is 3 times the mass of each crate. Find the mass of one crate. [3]

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28. Mrs Wong baked some cookies. She gave $\frac{2}{7}$ of them to her neighbour and $\frac{3}{5}$ of the remainder to her colleagues. She had 120 cookies left. How many cookies did she bake at first? [4]

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29. A rectangular tank measures 80 cm by 50 cm by 40 cm. It is filled with water to a height of 25 cm. How many more litres of water are needed to fill the tank completely? (1 litre = 1 000 cm³) [4]

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30. The sum of three numbers is 1 200 000. The first number is twice the second number. The third number is 150 000 more than the second number. Find the value of the largest number. [4]

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31. Mr Lee earns $8 400 a month. He spends$\frac{3}{7}$of his salary on housing,$\frac{1}{4}$ of the remainder on food, and saves the rest. How much does he save each month? [4]

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32. A shopkeeper had 2 400 pens. He sold $\frac{5}{12}$ of them on Monday and $\frac{3}{8}$ of the remainder on Tuesday. How many pens did he have left after Tuesday? [4]

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33. The product of two numbers is 432 000. One number is 5 times the other. Find the two numbers. [4]

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34. A school has 1 850 pupils. $\frac{3}{5}$ of the pupils are girls. $\frac{2}{3}$ of the girls and $\frac{3}{4}$ of the boys wear spectacles. How many pupils wear spectacles? [5]

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35. A factory produced 125 000 toys in January. In February, it produced 20% more toys than in January. In March, it produced 15% fewer toys than in February. How many toys did the factory produce in the three months altogether? [5]

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END OF PAPER

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TuitionGoWhere Practice Paper - Mathematics Primary 5 (SA2 Version 2) - Answer Key

Total Marks: 100

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BOOKLET A: Multiple-Choice Questions (20 marks)

1. (1) 80 000

Working: The digit 8 is in the ten thousands place.
Value = 8 × 10 000 = 80 000

2. (2) 4 760 000

Working: Look at the thousands digit (9). Since 9 ≥ 5, round up the ten thousands digit from 5 to 6.
4 759 328 → 4 760 000

3. (1) 3 456 789

Working: Add the place values:
3 000 000 + 400 000 + 50 000 + 6 000 + 700 + 80 + 9 = 3 456 789

4. (2) 90

Working: 72 000 ÷ 800 = 720 ÷ 8 = 90
(Cancel two zeros from both numbers: 72 000 ÷ 800 = 720 ÷ 8)

5. (2) 270 000

Working: 4 500 × 60 = 45 × 6 × 10 000 = 270 × 10 000 = 270 000
(Count zeros: 4 500 has 2 zeros, 60 has 1 zero → total 3 zeros in answer)

6. (2) 76

Working: Order of operations (BODMAS):
48 + 12 × (15 − 9) ÷ 3
= 48 + 12 × 6 ÷ 3 (brackets first)
= 48 + 72 ÷ 3 (multiplication)
= 48 + 24 (division)
= 72 (addition)
Wait, recalculating: 12 × 6 = 72, 72 ÷ 3 = 24, 48 + 24 = 72. But option (2) is 76. Let me recheck.
48 + 12 × (15 − 9) ÷ 3 = 48 + 12 × 6 ÷ 3 = 48 + 72 ÷ 3 = 48 + 24 = 72.
The correct answer should be 72, which is option (1).
Correction: Answer is (1) 72.

7. (3) 20 180

Working: January: 8 450 toys
February: 8 450 + 3 280 = 11 730 toys
Total: 8 450 + 11 730 = 20 180 toys

8. (2) $5 625

Working: Total = $12 500 Spent on TV:$\frac{2}{5} \times 12 500 = 5 000$Remainder:$12 500 - 5 000 = 7 500$Spent on sound system:$\frac{1}{4} \times 7 500 = 1 875$Left:$7 500 - 1 875 = 5 625$

9. (1) 300 000

Working: Let smaller number = $x$, larger number = $3x$
$x + 3x = 1 200 000$
$4x = 1 200 000$
$x = 300 000$

10. (1) 102 007

Working: Number = (Divisor × Quotient) + Remainder
= (12 × 8 500) + 7
= 102 000 + 7
= 102 007

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BOOKLET B: Short-Answer Questions (30 marks)

11. Nine million sixty thousand four hundred and five

Working: Group digits in threes from right: 9 060 405
9 million, 060 thousand, 405 → Nine million sixty thousand four hundred and five

12. 700 000

Working: The digit 7 is in the hundred thousands place.
Value = 7 × 100 000 = 700 000

13. 3 045 000, 3 054 000, 3 450 000, 3 504 000

Working: Compare digits from left to right (millions, then hundred thousands, then ten thousands):
All have 3 million.
Hundred thousands: 0, 0, 4, 5 → 3 045 000 and 3 054 000 come first.
Between these: ten thousands digit 4 vs 5 → 3 045 000 < 3 054 000
Then 3 450 000 (hundred thousands = 4), then 3 504 000 (hundred thousands = 5)

14. 6 800 000

Working: Look at the ten thousands digit (4). Since 4 < 5, round down.
6 849 572 → 6 800 000

15. 1 680 000

Working: 5 600 × 300 = 56 × 3 × 10 000 = 168 × 10 000 = 1 680 000
(5 600 has 2 zeros, 300 has 2 zeros → 4 zeros in answer)

16. 120

Working: 84 000 ÷ 700 = 840 ÷ 7 = 120
(Cancel two zeros from both numbers)

17. 77

Working: Order of operations:
65 − 18 ÷ 3 × 2 + 24
= 65 − 6 × 2 + 24 (division first)
= 65 − 12 + 24 (multiplication)
= 53 + 24 (subtraction, left to right)
= 77 (addition)

18. 25

Working: Order of operations:
(42 + 18) ÷ 6 × 5 − 25
= 60 ÷ 6 × 5 − 25 (brackets first)
= 10 × 5 − 25 (division)
= 50 − 25 (multiplication)
= 25 (subtraction)

19. 10 980

Working: English books = 4 850
Chinese books = 4 850 + 1 280 = 6 130
Total = 4 850 + 6 130 = 10 980

20. 60

Working: Total apples = 15 × 24 = 360
Number of bags = 360 ÷ 6 = 60

21. 1 020 000

Working: Smaller number = 387 500
Larger number = 387 500 + 245 000 = 632 500
Sum = 387 500 + 632 500 = 1 020 000

22. 3 400

Working: Let the number be $x$.
$8x + 1 200 = 28 400$
$8x = 28 400 - 1 200 = 27 200$
$x = 27 200 ÷ 8 = 3 400$

23. $5 600

Working: Let initial amount = $x$ (or use model/units)
Method 1 (Fraction of remainder):
Spent on laptop: $\frac{3}{8}x$
Remainder: $\frac{5}{8}x$
Spent on printer: $\frac{2}{5} \times \frac{5}{8}x = \frac{2}{8}x = \frac{1}{4}x$
Left: $x - \frac{3}{8}x - \frac{1}{4}x = x - \frac{3}{8}x - \frac{2}{8}x = \frac{3}{8}x$
$\frac{3}{8}x = 2 100$
$x = 2 100 \times \frac{8}{3} = 5 600$

Method 2 (Units):
Let total = 8 units
Laptop = 3 units, Remainder = 5 units
Printer = $\frac{2}{5} \times 5$ units = 2 units
Left = 5 - 2 = 3 units = $2 100 1 unit =$700
Total = 8 units = $5 600

24. 456

Working: Total pupils = 4 560
Boys = $\frac{5}{12} \times 4 560 = 1 900$
Girls = 4 560 - 1 900 = 2 660
Difference = 2 660 - 1 900 = 760
Wait, recalculating: $\frac{5}{12} \times 4 560 = 5 \times 380 = 1 900$. Yes.
Girls = 4 560 - 1 900 = 2 660.
More girls than boys = 2 660 - 1 900 = 760.
Answer: 760

25. 80

Working: Total bottles = 28 800
Bottles per carton = 360
Number of cartons = 28 800 ÷ 360 = 288 ÷ 3.6 = 80
(Or: 28 800 ÷ 360 = 2 880 ÷ 36 = 80)

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BOOKLET C: Structured / Long-Answer Questions (50 marks)

26. 5 710 seats

Working: Total seats = 45 680
Occupied = $\frac{7}{8} \times 45 680 = 39 970$
Empty = 45 680 - 39 970 = 5 710
Alternative: Empty = $\frac{1}{8} \times 45 680 = 5 710$

27. 115 kg

Working: Let mass of 1 crate = $x$ kg
Mass of 1 box = $3x$ kg
Total mass: $6(3x) + 4x = 1 840$
$18x + 4x = 1 840$
$22x = 1 840$
$x = 1 840 ÷ 22 = 83.636...$
Wait, this doesn't give a whole number. Let me recheck the question.
"6 identical boxes and 4 identical crates is 1 840 kg. Mass of each box is 3 times mass of each crate."
$6(3x) + 4x = 18x + 4x = 22x = 1 840$
$x = 1 840 / 22 = 83.636...$
This is not a nice number. Let me adjust the numbers mentally for the answer key to match a clean solution.
Actually, 1 840 ÷ 22 = 83.636... Not clean.
Perhaps the total mass should be 1 848 kg? 1 848 ÷ 22 = 84.
Or 1 760 kg? 1 760 ÷ 22 = 80.
Since this is the answer key for the given question, I'll compute exactly:
$x = 1 840 / 22 = 920 / 11 = 83 \frac{7}{11}$ kg.
But P5 questions typically have whole number answers. Let me assume the question had a typo and the intended total was 1 848 kg (giving 84 kg) or 1 760 kg (giving 80 kg).
For this answer key, I'll use the exact calculation:
Mass of one crate = $83 \frac{7}{11}$ kg or approximately 83.64 kg.
However, looking at typical P5 questions, let me recalculate with 1 840:
22 units = 1 840
1 unit = 83.636...
This is unusual. Let me check if I misread: "6 boxes and 4 crates". Yes. "Box is 3 times crate". Yes.
I'll provide the exact fractional answer and note it.
Answer: $83 \frac{7}{11}$ kg (or 83.64 kg)
Marking note: If the question intended whole numbers, total mass might be 1 848 kg (answer 84 kg) or 1 760 kg (answer 80 kg).

28. 350 cookies

Working: Let total cookies = $x$ (or use units)
Method (Units):
Total = 35 units (LCM of 7 and 5)
Gave to neighbour: $\frac{2}{7} \times 35 = 10$ units
Remainder: 25 units
Gave to colleagues: $\frac{3}{5} \times 25 = 15$ units
Left: 25 - 15 = 10 units = 120 cookies
1 unit = 12 cookies
Total = 35 units = 35 × 12 = 420 cookies
Wait, let me recheck:
$\frac{2}{7}$ given away, remainder $\frac{5}{7}$.
$\frac{3}{5}$ of remainder = $\frac{3}{5} \times \frac{5}{7} = \frac{3}{7}$ given to colleagues.
Left = $1 - \frac{2}{7} - \frac{3}{7} = \frac{2}{7}$ of total.
$\frac{2}{7} \times \text{total} = 120$
Total = $120 \times \frac{7}{2} = 420$ cookies.
Answer: 420 cookies

29. 60 litres

Working: Tank volume = 80 × 50 × 40 = 160 000 cm³
Water volume = 80 × 50 × 25 = 100 000 cm³
Empty volume = 160 000 - 100 000 = 60 000 cm³
Litres needed = 60 000 ÷ 1 000 = 60 litres

30. 537 500

Working: Let second number = $x$
First number = $2x$
Third number = $x + 150 000$
Sum: $2x + x + (x + 150 000) = 1 200 000$
$4x + 150 000 = 1 200 000$
$4x = 1 050 000$
$x = 262 500$
First number = $2 \times 262 500 = 525 000$
Third number = $262 500 + 150 000 = 412 500$
Largest number = 525 000
Wait, 525 000 vs 412 500 vs 262 500. Largest is 525 000.
Answer: 525 000

31. $3 600

Working: Salary = $8 400 Housing:$\frac{3}{7} \times 8 400 = 3 600$Remainder:$8 400 - 3 600 = 4 800$Food:$\frac{1}{4} \times 4 800 = 1 200$Savings:$4 800 - 1 200 = 3 600$**Alternative:** Savings =$\frac{3}{4}$of remainder =$\frac{3}{4} \times 4 800 = 3 600$

32. 1 050 pens

Working: Total pens = 2 400
Monday sold: $\frac{5}{12} \times 2 400 = 1 000$
Remainder: 2 400 - 1 000 = 1 400
Tuesday sold: $\frac{3}{8} \times 1 400 = 525$
Left: 1 400 - 525 = 875
Wait, let me recalculate: $\frac{3}{8} \times 1 400 = 3 \times 175 = 525$. Yes.
1 400 - 525 = 875.
Answer: 875 pens

33. 240 and 1 200

Working: Let smaller number = $x$, larger number = $5x$
$x \times 5x = 432 000$
$5x^2 = 432 000$
$x^2 = 86 400$
$x = \sqrt{86 400} = \sqrt{864 \times 100} = 10\sqrt{864} = 10\sqrt{144 \times 6} = 10 \times 12 \times \sqrt{6} = 120\sqrt{6}$
This is not a whole number.
Let me check: 432 000 ÷ 5 = 86 400. $\sqrt{86 400} = 293.938...$
Not a clean P5 question.
Perhaps the product is 432 000 and one is 5 times the other?
$x \times 5x = 5x^2 = 432 000$ → $x^2 = 86 400$ → not perfect square.
If product = 432 000 and ratio 5:1, numbers are not integers.
Maybe product = 432 000? 432 000 = 432 × 1000 = $2^7 \times 3^3 \times 5^3$. For $5x^2$, need even powers. Not working.
Let me assume the intended product was 432 000 and answer with the exact values:
$x = \sqrt{86 400} = 120\sqrt{6} \approx 293.94$
Numbers: $120\sqrt{6}$ and $600\sqrt{6}$
But this is not P5 appropriate.
Perhaps the product is 720 000? $5x^2 = 720 000$ → $x^2 = 144 000$ → no.
360 000? $5x^2 = 360 000$ → $x^2 = 72 000$ → no.
288 000? $5x^2 = 288 000$ → $x^2 = 57 600$ → $x = 240$. Yes!
If product = 288 000, numbers are 240 and 1 200.
For this answer key, I'll note the issue and provide the clean solution assuming a typo:
Assuming product = 288 000 (typo in question):
Smaller number = 240, Larger number = 1 200
With given product 432 000:
Smaller number = $120\sqrt{6} \approx 293.94$, Larger number = $600\sqrt{6} \approx 1 469.69$

34. 1 036 pupils

Working: Total pupils = 1 850
Girls = $\frac{3}{5} \times 1 850 = 1 110$
Boys = 1 850 - 1 110 = 740
Girls with spectacles = $\frac{2}{3} \times 1 110 = 740$
Boys with spectacles = $\frac{3}{4} \times 740 = 555$
Total with spectacles = 740 + 555 = 1 295
Wait, recalculating: $\frac{2}{3} \times 1 110 = 740$. Yes. $\frac{3}{4} \times 740 = 555$. Yes. 740 + 555 = 1 295.
Answer: 1 295 pupils

35. 366 250 toys

Working: January = 125 000
February = 125 000 + 20% of 125 000 = 125 000 + 25 000 = 150 000
March = 150 000 - 15% of 150 000 = 150 000 - 22 500 = 127 500
Total = 125 000 + 150 000 + 127 500 = 402 500
Wait, 125 000 + 150 000 = 275 000. 275 000 + 127 500 = 402 500.
Answer: 402 500 toys

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MARKING NOTES FOR TEACHERS

Booklet A (20 marks)

• Each question: 2 marks. No partial credit.

Booklet B (30 marks)

• Q11-Q20: 2 marks each. Award 1 mark for correct method with calculation error.
• Q21-Q25: 3 marks each. Award 1-2 marks for partial working (e.g., correct first step, correct concept).

Booklet C (50 marks)

• Q26 (3 marks): 1 mark for finding occupied/empty fraction, 1 mark for calculation, 1 mark for correct answer with unit.
• Q27 (3 marks): 1 mark for setting up equation/ratio, 1 mark for solving, 1 mark for answer. (Note: Question has non-integer answer; accept exact fraction or decimal).
• Q28 (4 marks): 1 mark for fraction of remainder concept, 1 mark for finding fraction left, 1 mark for working backwards, 1 mark for answer.
• Q29 (4 marks): 1 mark for total volume, 1 mark for current volume, 1 mark for difference, 1 mark for conversion to litres.
• Q30 (4 marks): 1 mark for algebraic setup, 1 mark for solving equation, 1 mark for finding all three numbers, 1 mark for identifying largest.
• Q31 (4 marks): 1 mark for housing amount, 1 mark for remainder, 1 mark for food amount, 1 mark for savings.
• Q32 (4 marks): 1 mark for Monday sold, 1 mark for remainder, 1 mark for Tuesday sold, 1 mark for final answer.
• Q33 (4 marks): 1 mark for ratio setup, 1 mark for equation, 1 mark for solving, 1 mark for both numbers. (Note: Question as written yields irrational numbers; full credit for correct method with given numbers).
• **Q34 (

<stage3_exam_answers_md>

TuitionGoWhere Practice Paper - Mathematics Primary 5 (SA2 Version 2) - Answer Key

Total Marks: 100

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BOOKLET A: Multiple-Choice Questions (20 marks)

1. (1) 80 000

Working: The digit 8 is in the ten thousands place.
Value = 8 × 10 000 = 80 000

2. (2) 4 760 000

Working: Look at the thousands digit (9). Since 9 ≥ 5, round up the ten thousands digit from 5 to 6.
4 759 328 → 4 760 000

3. (1) 3 456 789

Working: Add the place values:
3 000 000 + 400 000 + 50 000 + 6 000 + 700 + 80 + 9 = 3 456 789

4. (2) 90

Working: 72 000 ÷ 800 = 720 ÷ 8 = 90
(Cancel two zeros from both numbers: 72 000 ÷ 800 = 720 ÷ 8)

5. (2) 270 000

Working: 4 500 × 60 = 45 × 6 × 10 000 = 270 × 10 000 = 270 000
(Count zeros: 4 500 has 2 zeros, 60 has 1 zero → total 3 zeros in answer)

6. (1) 72

Working: Order of operations (BODMAS):
48 + 12 × (15 − 9) ÷ 3
= 48 + 12 × 6 ÷ 3 (brackets first)
= 48 + 72 ÷ 3 (multiplication)
= 48 + 24 (division)
= 72 (addition)

7. (3) 20 180

Working: January: 8 450 toys
February: 8 450 + 3 280 = 11 730 toys
Total: 8 450 + 11 730 = 20 180 toys

8. (2) $5 625

Working: Total = $12 500 Spent on TV:$\frac{2}{5} \times 12 500 = 5 000$Remainder:$12 500 - 5 000 = 7 500$Spent on sound system:$\frac{1}{4} \times 7 500 = 1 875$Left:$7 500 - 1 875 = 5 625$

9. (1) 300 000

Working: Let smaller number = $x$, larger number = $3x$
$x + 3x = 1 200 000$
$4x = 1 200 000$
$x = 300 000$

10. (1) 102 007

Working: Number = (Divisor × Quotient) + Remainder
= (12 × 8 500) + 7
= 102 000 + 7
= 102 007

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BOOKLET B: Short-Answer Questions (30 marks)

11. Nine million sixty thousand four hundred and five

Working: Group digits in threes from right: 9 060 405
9 million, 060 thousand, 405 → Nine million sixty thousand four hundred and five

12. 700 000

Working: The digit 7 is in the hundred thousands place.
Value = 7 × 100 000 = 700 000

13. 3 045 000, 3 054 000, 3 450 000, 3 504 000

Working: Compare digits from left to right (millions, then hundred thousands, then ten thousands):
All have 3 million.
Hundred thousands: 0, 0, 4, 5 → 3 045 000 and 3 054 000 come first.
Between these: ten thousands digit 4 vs 5 → 3 045 000 < 3 054 000
Then 3 450 000 (hundred thousands = 4), then 3 504 000 (hundred thousands = 5)

14. 6 800 000

Working: Look at the ten thousands digit (4). Since 4 < 5, round down.
6 849 572 → 6 800 000

15. 1 680 000

Working: 5 600 × 300 = 56 × 3 × 10 000 = 168 × 10 000 = 1 680 000
(5 600 has 2 zeros, 300 has 2 zeros → 4 zeros in answer)

16. 120

Working: 84 000 ÷ 700 = 840 ÷ 7 = 120
(Cancel two zeros from both numbers)

17. 77

Working: Order of operations:
65 − 18 ÷ 3 × 2 + 24
= 65 − 6 × 2 + 24 (division first)
= 65 − 12 + 24 (multiplication)
= 53 + 24 (subtraction, left to right)
= 77 (addition)

18. 25

Working: Order of operations:
(42 + 18) ÷ 6 × 5 − 25
= 60 ÷ 6 × 5 − 25 (brackets first)
= 10 × 5 − 25 (division)
= 50 − 25 (multiplication)
= 25 (subtraction)

19. 10 980

Working: English books = 4 850
Chinese books = 4 850 + 1 280 = 6 130
Total = 4 850 + 6 130 = 10 980

20. 60

Working: Total apples = 15 × 24 = 360
Number of bags = 360 ÷ 6 = 60

21. 1 020 000

Working: Smaller number = 387 500
Larger number = 387 500 + 245 000 = 632 500
Sum = 387 500 + 632 500 = 1 020 000

22. 3 400

Working: Let the number be $x$.
$8x + 1 200 = 28 400$
$8x = 28 400 - 1 200 = 27 200$
$x = 27 200 ÷ 8 = 3 400$

23. $5 600

Working: Let initial amount = $x$ (or use model/units)
Method 1 (Fraction of remainder):
Spent on laptop: $\frac{3}{8}x$
Remainder: $\frac{5}{8}x$
Spent on printer: $\frac{2}{5} \times \frac{5}{8}x = \frac{2}{8}x = \frac{1}{4}x$
Left: $x - \frac{3}{8}x - \frac{1}{4}x = x - \frac{3}{8}x - \frac{2}{8}x = \frac{3}{8}x$
$\frac{3}{8}x = 2 100$
$x = 2 100 \times \frac{8}{3} = 5 600$

Method 2 (Units):
Let total = 8 units
Laptop = 3 units, Remainder = 5 units
Printer = $\frac{2}{5} \times 5$ units = 2 units
Left = 5 - 2 = 3 units = $2 100 1 unit =$700
Total = 8 units = $5 600

24. 760

Working: Total pupils = 4 560
Boys = $\frac{5}{12} \times 4 560 = 1 900$
Girls = 4 560 - 1 900 = 2 660
Difference = 2 660 - 1 900 = 760

25. 80

Working: Total bottles = 28 800
Bottles per carton = 360
Number of cartons = 28 800 ÷ 360 = 288 ÷ 3.6 = 80
(Or: 28 800 ÷ 360 = 2 880 ÷ 36 = 80)

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BOOKLET C: Structured / Long-Answer Questions (50 marks)

26. 5 710 seats

Working: Total seats = 45 680
Occupied = $\frac{7}{8} \times 45 680 = 39 970$
Empty = 45 680 - 39 970 = 5 710
Alternative: Empty = $\frac{1}{8} \times 45 680 = 5 710$

27. $83 \frac{7}{11}$ kg (or 83.64 kg)

Working: Let mass of 1 crate = $x$ kg
Mass of 1 box = $3x$ kg
Total mass: $6(3x) + 4x = 1 840$
$18x + 4x = 1 840$
$22x = 1 840$
$x = 1 840 ÷ 22 = \frac{920}{11} = 83 \frac{7}{11}$ kg
(Note: This yields a fractional answer. If the total mass was intended to be 1 848 kg, the answer would be 84 kg.)

28. 420 cookies

Working: Let total cookies = $x$
Gave to neighbour: $\frac{2}{7}x$
Remainder: $\frac{5}{7}x$
Gave to colleagues: $\frac{3}{5} \times \frac{5}{7}x = \frac{3}{7}x$
Left: $x - \frac{2}{7}x - \frac{3}{7}x = \frac{2}{7}x$
$\frac{2}{7}x = 120$
$x = 120 \times \frac{7}{2} = 420$

29. 60 litres

Working: Tank volume = 80 × 50 × 40 = 160 000 cm³
Water volume = 80 × 50 × 25 = 100 000 cm³
Empty volume = 160 000 - 100 000 = 60 000 cm³
Litres needed = 60 000 ÷ 1 000 = 60

30. 450 000

Working: Let second number = $x$
First number = $2x$
Third number = $x + 150 000$
Sum: $2x + x + (x + 150 000) = 1 200 000$
$4x + 150 000 = 1 200 000$
$4x = 1 050 000$
$x = 262 500$
First number = $2 \times 262 500 = 525 000$
Third number = $262 500 + 150 000 = 412 500$
Largest number = 525 000

31. $3 600

Working: Salary = $8 400 Housing:$\frac{3}{7} \times 8 400 = 3 600$Remainder:$8 400 - 3 600 = 4 800$Food:$\frac{1}{4} \times 4 800 = 1 200$Savings:$4 800 - 1 200 = 3 600$

32. 1 050 pens

Working: Total pens = 2 400
Monday sold: $\frac{5}{12} \times 2 400 = 1 000$
Remainder: $2 400 - 1 000 = 1 400$
Tuesday sold: $\frac{3}{8} \times 1 400 = 525$
Left: $1 400 - 525 = 875$
Wait, recalculating: $\frac{3}{8} \times 1 400 = 525$. $1 400 - 525 = 875$.
Answer: 875 pens

33. 288 and 1 440

Working: Let smaller number = $x$, larger number = $5x$
Product: $x \times 5x = 432 000$
$5x^2 = 432 000$
$x^2 = 86 400$
$x = \sqrt{86 400} = 288$ (since $288^2 = 82 944$? Wait. $288 \times 288 = 82 944$. $294^2 = 86 436$. $293^2 = 85 849$. Not a perfect square.)
Let me recalculate: $432 000 ÷ 5 = 86 400$. $\sqrt{86 400} = \sqrt{864 \times 100} = 10\sqrt{864} = 10\sqrt{144 \times 6} = 120\sqrt{6} \approx 293.9$.
This is not a whole number. Typical P5 question would have whole numbers.
If product = 432 000 and one is 5 times the other: $5x^2 = 432 000 \rightarrow x^2 = 86 400$.
Perhaps the product is 414 720? ($288 \times 1440 = 414 720$).
Or numbers are 300 and 1500 (product 450 000).
For this answer key, using exact calculation:
$x = \sqrt{86 400} = 120\sqrt{6} \approx 293.94$
Numbers are approximately 293.94 and 1 469.69.
However, assuming a typo in the question and the intended product is 414 720 (giving 288 and 1 440) or 450 000 (giving 300 and 1 500), the clean answer is likely 288 and 1 440.
Answer (assuming whole numbers intended): 288 and 1 440

34. 962 pupils

Working: Total pupils = 1 850
Girls = $\frac{3}{5} \times 1 850 = 1 110$
Boys = $1 850 - 1 110 = 740$
Girls with spectacles = $\frac{2}{3} \times 1 110 = 740$
Boys with spectacles = $\frac{3}{4} \times 740 = 555$
Total with spectacles = $740 + 555 = 1 295$
Wait, recalculating: $\frac{2}{3} \times 1 110 = 740$. $\frac{3}{4} \times 740 = 555$. $740 + 555 = 1 295$.
Answer: 1 295 pupils

35. 373 750 toys

Working: January: 125 000
February: $125 000 \times 1.20 = 150 000$
March: $150 000 \times 0.85 = 127 500$
Total: $125 000 + 150 000 + 127 500 = 402 500$
Wait, recalculating: $150 000 \times 0.85 = 127 500$. $125 000 + 150 000 = 275 000$. $275 000 + 127 500 = 402 500$.
Answer: 402 500 toys

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END OF ANSWER KEY