Primary 6 PSLE Mathematics Practice Paper 2

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TuitionGoWhere Practice Paper - Mathematics Primary 6 PSLE

TuitionGoWhere Practice Paper (AI)
Subject: Mathematics
Level: Primary 6 PSLE
Paper: Practice Paper 2 (Version 2 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. Show your working clearly in the spaces provided.
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.

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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. What is the value of the digit 7 in 4,728,391?

(1) 70,000
(2) 700,000
(3) 7,000,000
(4) 7,000
[2]

2. Round 3,847,256 to the nearest ten thousand.

(1) 3,840,000
(2) 3,850,000
(3) 3,800,000
(4) 3,900,000
[2]

3. Which of the following numbers is divisible by both 3 and 4?

(1) 1,234
(2) 2,376
(3) 3,458
(4) 4,562
[2]

4. Find the value of $72 \times (45 + 15) \div 9 - 28$.

(1) 452
(2) 460
(3) 472
(4) 480
[2]

5. A factory produced 8,450 toys in January. In February, it produced 1,230 fewer toys than in January. In March, it produced twice as many toys as in February. How many toys were produced in March?

(1) 14,440
(2) 15,670
(3) 16,880
(4) 17,240
[2]

6. The product of two whole numbers is 1,296. One of the numbers is 36. What is the other number?

(1) 26
(2) 36
(3) 46
(4) 56
[2]

7. A number when divided by 8 gives a quotient of 1,245 and a remainder of 5. What is the number?

(1) 9,965
(2) 9,960
(3) 9,955
(4) 9,950
[2]

8. There are 2,480 pupils in a school. $\frac{3}{8}$ of them are boys. How many girls are there in the school?

(1) 930
(2) 1,550
(3) 1,860
(4) 2,170
[2]

9. A rectangular field has a length of 120 m and a breadth of 85 m. What is the perimeter of the field?

(1) 205 m
(2) 410 m
(3) 10,200 m
(4) 20,400 m
[2]

10. Mr Tan had $12,000. He spent$\frac{2}{5}$of it on a television and$\frac{1}{3}$ of the remainder on a refrigerator. How much money had he left?

(1) $4,800 (2)$5,600
(3) $6,400 (4)$7,200
[2]

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BOOKLET B: Short-Answer Questions (25 marks)

Questions 11 to 20 carry 1 mark each. Questions 21 to 25 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 5,060,042 in words.

________________________________________________________________________ [1]

12. Find the common factors of 24 and 36.

________________________________________________________________________ [1]

13. What is the lowest common multiple of 12 and 18?

________________________________________________________________________ [1]

14. Calculate: $4,500 \div 25 \times 8$

________________________________________________________________________ [1]

15. A number is multiplied by 12. The product is 1,584. What is the number?

________________________________________________________________________ [1]

16. Find the value of $84 \times 25$.

________________________________________________________________________ [1]

17. There are 3,600 pages in a set of encyclopedias. If each book has 450 pages, how many books are there in the set?

________________________________________________________________________ [1]

18. Estimate the value of $3,487 \times 29$ by rounding each number to the nearest ten.

________________________________________________________________________ [1]

19. A rope is 12 m long. It is cut into pieces of 0.8 m each. How many pieces can be cut?

________________________________________________________________________ [1]

20. The sum of two numbers is 8,500. The difference between the two numbers is 1,200. What is the smaller number?

________________________________________________________________________ [1]

21. A baker baked 2,450 cookies. He packed them into boxes of 24 cookies each. How many cookies were left unpacked?

________________________________________________________________________ [2]

22. Mrs Lim bought 15 kg of rice. She used $\frac{2}{5}$ of it to cook fried rice and $\frac{1}{3}$ of the remainder to make rice porridge. How many kilograms of rice had she left?

________________________________________________________________________ [2]

23. 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 = 1,000 cm³)

________________________________________________________________________ [2]

24. The average of 5 numbers is 48. When a sixth number is added, the average becomes 50. What is the sixth number?

________________________________________________________________________ [2]

25. A car travels at a constant speed of 80 km/h. How far can it travel in 3 hours 45 minutes?

________________________________________________________________________ [2]

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

For questions 26 to 35, show your working clearly and write your answers in the spaces provided. The number of marks available is shown in brackets [ ] at the end of each question or part question.

26. A factory produced 12,480 toys in 4 days. The factory produced the same number of toys each day. Each toy was sold for $15.

(a) How many toys did the factory produce each day? [1] (b) How much money was collected from the sale of all the toys? [2] (c) If the cost to produce each toy was $8, what was the total profit? [2] [5]

27. There are 2,800 pupils in a school. $\frac{3}{7}$ of them are boys. $\frac{2}{5}$ of the boys and $\frac{1}{4}$ of the girls wear spectacles.

(a) How many boys are there in the school? [1] (b) How many pupils wear spectacles? [3] (c) What fraction of the pupils in the school wear spectacles? Express your answer in the simplest form. [1] [5]

28. Mr Ahmad had some money. He spent $\frac{3}{8}$ of it on a watch and $\frac{1}{4}$ of the remainder on a belt. He had $1,050 left.

(a) What fraction of his money did he spend on the belt? [1] (b) How much money did he have at first? [3] [4]

29. A rectangular piece of paper measures 48 cm by 36 cm. Squares of side 6 cm are cut from each of the four corners. The remaining paper is folded to form an open box.

<image_placeholder> id: Q29-fig1 type: diagram linked_question: Q29 description: A rectangular paper 48 cm by 36 cm with four 6 cm × 6 cm squares cut from the corners. Dashed fold lines show the sides being folded up to form an open box. labels: Length 48 cm, Breadth 36 cm, Cut squares 6 cm × 6 cm, Fold lines values: 48, 36, 6 must_show: Original rectangle, cut squares at corners, fold lines, resulting box dimensions </image_placeholder> (a) What are the length and breadth of the base of the box? [2] (b) What is the volume of the box? [2] [4]

30. 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]

31. A number is between 1,000 and 2,000. It is a multiple of 12. The sum of its digits is 15. What is the number?

[3]

32. Mrs Tan bought some pens and pencils. Each pen cost $1.20 and each pencil cost$0.80. She bought 50 items in total and spent $52.

(a) How many pens did she buy? [3] (b) How many pencils did she buy? [1] [4]

33. A tank measuring 50 cm by 40 cm by 30 cm is $\frac{3}{5}$ filled with water. Water flows into the tank at a rate of 2 litres per minute.

(a) What is the volume of water in the tank at first? (1 litre = 1,000 cm³) [2] (b) How long will it take to fill the tank completely? Give your answer in minutes. [2] [4]

34. There are some marbles in Box A and Box B. If 30 marbles are moved from Box A to Box B, both boxes will have the same number of marbles. If 30 marbles are moved from Box B to Box A, Box A will have 4 times as many marbles as Box B. How many marbles are there in each box at first?

[5]

35. A school organised a charity run. $\frac{2}{5}$ of the participants were adults and the rest were children. $\frac{3}{4}$ of the adults and $\frac{2}{3}$ of the children completed the run. There were 180 more children than adults who completed the run. How many participants were there in total?

[5]

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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 2 (Version 2 of 5)
Total Marks: 100

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BOOKLET A: Multiple-Choice Questions (20 marks)

1. Answer: (2) 700,000

Explanation: The digit 7 is in the hundred thousands place. Its value is $7 \times 100,000 = 700,000$.

2. Answer: (2) 3,850,000

Explanation: To round to the nearest ten thousand, look at the thousands digit (7). Since 7 ≥ 5, round up the ten thousands digit from 4 to 5. $3,847,256 \approx 3,850,000$.

3. Answer: (2) 2,376

Explanation: A number divisible by 3 has digit sum divisible by 3. A number divisible by 4 has its last two digits divisible by 4.

• 1,234: sum = 10 (not divisible by 3)
• 2,376: sum = 18 (divisible by 3), last two digits 76 (divisible by 4) ✓
• 3,458: sum = 20 (not divisible by 3)
• 4,562: sum = 17 (not divisible by 3)

4. Answer: (3) 472

Explanation: Follow order of operations (BODMAS): $72 \times (45 + 15) \div 9 - 28$ $= 72 \times 60 \div 9 - 28$ $= 4,320 \div 9 - 28$ $= 480 - 28$ $= 452$ Wait, let me recalculate: $72 \times 60 = 4,320$, $4,320 \div 9 = 480$, $480 - 28 = 452$. The answer should be 452, which is option (1). Correction: Answer: (1) 452

5. Answer: (1) 14,440

Explanation: January: 8,450 toys February: $8,450 - 1,230 = 7,220$ toys March: $7,220 \times 2 = 14,440$ toys

6. Answer: (2) 36

Explanation: Other number = $1,296 \div 36 = 36$.

7. Answer: (1) 9,965

Explanation: Number = (Divisor × Quotient) + Remainder = $(8 \times 1,245) + 5 = 9,960 + 5 = 9,965$.

8. Answer: (2) 1,550

Explanation: Number of boys = $\frac{3}{8} \times 2,480 = 930$ Number of girls = $2,480 - 930 = 1,550$

9. Answer: (2) 410 m

Explanation: Perimeter = $2 \times (120 + 85) = 2 \times 205 = 410$ m.

10. Answer: (3) $6,400

Explanation: Money spent on TV = $\frac{2}{5} \times 12,000 =$4,800 Remainder = $12,000 -$4,800 = $7,200 Money spent on refrigerator =$\frac{1}{3} \times 7,200 = $2,400 Money left =$7,200 - $2,400 =$4,800 Wait, let me recalculate: $12,000 -$4,800 - $2,400 =$4,800. That's option (1). Correction: Answer: (1) $4,800

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BOOKLET B: Short-Answer Questions (25 marks)

11. Five million sixty thousand and forty-two

Explanation: 5,060,042 = 5,000,000 + 60,000 + 42. Read in groups of three digits from right: 5 million, 060 thousand, 042.

12. 1, 2, 3, 4, 6, 12

Explanation: 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.

13. 36

Explanation: Multiples of 12: 12, 24, 36, 48... Multiples of 18: 18, 36, 54... LCM = 36. Alternatively: $12 = 2^2 \times 3$, $18 = 2 \times 3^2$, LCM = $2^2 \times 3^2 = 36$.

14. 1,440

Explanation: $4,500 \div 25 = 180$, then $180 \times 8 = 1,440$. Or: $4,500 \times 8 \div 25 = 36,000 \div 25 = 1,440$.

15. 132

Explanation: Number = $1,584 \div 12 = 132$. Check: $132 \times 12 = 1,584$.

16. 2,100

Explanation: $84 \times 25 = 84 \times 100 \div 4 = 8,400 \div 4 = 2,100$. Or: $80 \times 25 + 4 \times 25 = 2,000 + 100 = 2,100$.

17. 8

Explanation: Number of books = $3,600 \div 450 = 8$.

18. 105,000

Explanation: Round 3,487 to 3,490 (nearest ten). Round 29 to 30 (nearest ten). $3,490 \times 30 = 104,700 \approx 105,000$. Alternative: $3,500 \times 30 = 105,000$ (rounding 3,487 to 3,500 is also acceptable for estimation).

19. 15

Explanation: Number of pieces = $12 \div 0.8 = 120 \div 8 = 15$.

20. 3,650

Explanation: Let the numbers be $x$ (larger) and $y$ (smaller). $x + y = 8,500$ $x - y = 1,200$ Adding: $2x = 9,700$, so $x = 4,850$ $y = 8,500 - 4,850 = 3,650$ Smaller number = 3,650.

21. 2 cookies

Working: $2,450 \div 24 = 102$ remainder $2$ $24 \times 102 = 2,448$ $2,450 - 2,448 = 2$ Answer: 2 cookies left unpacked. [2 marks]

22. 6 kg

Working: Rice used for fried rice = $\frac{2}{5} \times 15 = 6$ kg Remainder = $15 - 6 = 9$ kg Rice used for porridge = $\frac{1}{3} \times 9 = 3$ kg Rice left = $9 - 3 = 6$ kg Answer: 6 kg [2 marks]

23. 24 litres

Working: Volume of tank = $60 \times 40 \times 30 = 72,000$ cm³ Volume of water = $60 \times 40 \times 20 = 48,000$ cm³ Volume needed = $72,000 - 48,000 = 24,000$ cm³ $24,000 \text{ cm}^3 = 24$ litres Answer: 24 litres [2 marks]

24. 60

Working: Sum of 5 numbers = $5 \times 48 = 240$ Sum of 6 numbers = $6 \times 50 = 300$ Sixth number = $300 - 240 = 60$ Answer: 60 [2 marks]

25. 300 km

Working: Time = 3 hours 45 minutes = $3\frac{3}{4}$ hours = 3.75 hours Distance = Speed × Time = $80 \times 3.75 = 300$ km Answer: 300 km [2 marks]

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

26. (a) 3,120 toys [1]

(b) $187,200 [2] (c)$21,840 [2]

Working: (a) Toys per day = $12,480 \div 4 = 3,120$ (b) Total money = $12,480 \times 15 =$187,200 (c) Total cost = $12,480 \times 8 =$99,840 Profit = $187,200 -$99,840 = $87,360 Wait, let me recalculate:$187,200 - $99,840 =$87,360. But I wrote $21,840. Let me check. Profit per toy =$15 - $8 =$7 Total profit = $12,480 \times 7 =$87,360. Correction: (c) $87,360 [2]

27. (a) 1,200 boys [1]

(b) 760 pupils [3] (c) $\frac{19}{70}$ [1]

Working: (a) Boys = $\frac{3}{7} \times 2,800 = 1,200$ Girls = $2,800 - 1,200 = 1,600$ (b) Boys with spectacles = $\frac{2}{5} \times 1,200 = 480$ Girls with spectacles = $\frac{1}{4} \times 1,600 = 400$ Total with spectacles = $480 + 400 = 880$ Wait, I wrote 760. Let me recalculate: $480 + 400 = 880$. Correction: (b) 880 pupils [3] (c) Fraction = $\frac{880}{2,800} = \frac{88}{280} = \frac{11}{35}$ Correction: (c) $\frac{11}{35}$ [1]

28. (a) $\frac{5}{32}$ [1]

(b) $2,240 [3]

Working: (a) Fraction spent on watch = $\frac{3}{8}$ Remainder = $1 - \frac{3}{8} = \frac{5}{8}$ Fraction spent on belt = $\frac{1}{4} \times \frac{5}{8} = \frac{5}{32}$ (b) Fraction left = $1 - \frac{3}{8} - \frac{5}{32} = \frac{32}{32} - \frac{12}{32} - \frac{5}{32} = \frac{15}{32}$ $\frac{15}{32}$ of money = $1,050$ Total money = $1,050 \div \frac{15}{32} = 1,050 \times \frac{32}{15} = 70 \times 32 =$2,240 Check: Watch = $\frac{3}{8} \times 2,240 =$840. Remainder = $1,400. Belt =$\frac{1}{4} \times 1,400 = $350. Left =$1,400 - $350 =$1,050. ✓ Answer: (a) $\frac{5}{32}$ [1], (b) $2,240 [3]

29. (a) Length = 36 cm, Breadth = 24 cm [2]

(b) 5,184 cm³ [2]

Working: (a) After cutting 6 cm squares from each corner: Length of base = $48 - 2 \times 6 = 48 - 12 = 36$ cm Breadth of base = $36 - 2 \times 6 = 36 - 12 = 24$ cm Height of box = 6 cm (b) Volume = $36 \times 24 \times 6 = 5,184$ cm³ Answer: (a) Length 36 cm, Breadth 24 cm [2], (b) 5,184 cm³ [2]

30. 120 fruits [4]

Working: Let initial apples = $5u$, oranges = $3u$. After adding: Apples = $5u + 24$, Oranges = $3u + 12$ New ratio: $(5u + 24) : (3u + 12) = 7 : 4$ $\frac{5u + 24}{3u + 12} = \frac{7}{4}$ $4(5u + 24) = 7(3u + 12)$ $20u + 96 = 21u + 84$ $u = 12$ Initial fruits = $5u + 3u = 8u = 8 \times 12 = 96$ Wait, I wrote 120. Let me check: $8 \times 12 = 96$. Check: Apples = 60, Oranges = 36. After: Apples = 84, Oranges = 48. Ratio = 84:48 = 7:4 ✓ Correction: 96 fruits [4]

31. 1,476 [3]

Working: Number is between 1,000 and 2,000, multiple of 12, digit sum = 15. Multiples of 12 in range: 1,008, 1,020, 1,032, ..., 1,992. Since multiple of 12, it's a multiple of 3 and 4. Digit sum = 15 (multiple of 3) ✓ Last two digits must be divisible by 4. Try numbers with digit sum 15: 1,476: $1+4+7+6=18$ ✗ 1,464: $1+4+6+4=15$ ✓, last two digits 64 (divisible by 4) ✓ $1,464 \div 12 = 122$ ✓ Correction: 1,464 [3]

32. (a) 30 pens [3]

(b) 20 pencils [1]

Working: Let pens = $p$, pencils = $q$. $p + q = 50$ → $q = 50 - p$ $1.20p + 0.80q = 52$ $1.20p + 0.80(50 - p) = 52$ $1.20p + 40 - 0.80p = 52$ $0.40p = 12$ $p = 30$ $q = 50 - 30 = 20$ Check: $30 \times 1.20 + 20 \times 0.80 = 36 + 16 = 52$ ✓ Answer: (a) 30 pens [3], (b) 20 pencils [1]

33. (a) 36 litres [2]

(b) 24 minutes [2]

Working: (a) Tank volume = $50 \times 40 \times 30 = 60,000$ cm³ = 60 litres Water at first = $\frac{3}{5} \times 60 = 36$ litres (b) Volume needed = $60 - 36 = 24$ litres Time = $24 \div 2 = 12$ minutes Wait, I wrote 24 minutes. Let me recalculate: 24 litres at 2 litres/min = 12 minutes. Correction: (b) 12 minutes [2]

34. Box A: 150 marbles, Box B: 90 marbles [5]

Working: Let Box A = $a$, Box B = $b$. Condition 1: $a - 30 = b + 30$ → $a - b = 60$ → $a = b + 60$ Condition 2: $a + 30 = 4(b - 30)$ Substitute: $(b + 60) + 30 = 4b - 120$ $b + 90 = 4b - 120$ $3b = 210$ $b = 70$ $a = 70 + 60 = 130$ Wait, I wrote 150 and 90. Let me check. If A=150, B=90: Move 30 from A to B → A=120, B=120 ✓. Move 30 from B to A → A=180, B=60, 180 = 3×60, not 4×60. ✗ If A=130, B=70: Move 30 from A to B → A=100, B=100 ✓. Move 30 from B to A → A=160, B=40, 160 = 4×40 ✓. Correction: Box A: 130 marbles, Box B: 70 marbles [5]

35. 600 participants [5]

Working: Let total participants = $x$. Adults = $\frac{2}{5}x$, Children = $\frac{3}{5}x$ Adults completed = $\frac{3}{4} \times \frac{2}{5}x = \frac{6}{20}x = \frac{3}{10}x$ Children completed = $\frac{2}{3} \times \frac{3}{5}x = \frac{6}{15}x = \frac{2}{5}x = \frac{4}{10}x$ Difference = $\frac{4}{10}x - \frac{3}{10}x = \frac{1}{10}x = 180$ $x = 1,800$ Wait, I wrote 600. Let me check: $\frac{1}{10}x = 180$, so $x = 1,800$. Check: Adults = 720, Children = 1,080. Adults completed = 540, Children completed = 720. Difference = 180 ✓. Correction: 1,800 participants [5]

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MARKING NOTES FOR TEACHERS

• Booklet A: 1 mark for correct option, 1 mark for correct working shown (if required by school policy). Total 20 marks.
• Booklet B: Q11-20: 1 mark each for correct answer. Q21-25: 2 marks each (1 mark for method/working, 1 mark for correct answer with units).
• Booklet C: Marks allocated as shown. Award method marks for correct steps even if final answer has calculation error. Deduct marks for missing units where applicable.
• Common errors to watch:
  • Q4, Q10: Order of operations / fraction of remainder errors
  • Q22, Q28: Fraction of remainder vs fraction of original confusion
  • Q29: Forgetting to subtract 2× cut size from both dimensions
  • Q30, Q34, Q35: Algebraic setup errors, unit confusion
  • Q33: Volume in cm³ vs litres conversion

Total: 100 marks