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Primary 6 PSLE Mathematics Practice Paper 5

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TuitionGoWhere Practice Paper - Mathematics Primary 6 PSLE

TuitionGoWhere Practice Paper (AI)

Subject: Mathematics Level: Primary 6 (PSLE) Paper: Practice Paper — Whole Numbers Duration: 50 minutes Total Marks: 40 Name: ____________________ Class: ____________________ Date: ____________________

Instructions

Answer all questions.
Show your working clearly in the space provided.
Write your answers in the answer spaces.
Do not use a calculator.
You are allowed to use a ruler and other geometrical instruments.

Section A: Short Answer Questions (20 marks)

Questions 1–10 carry 2 marks each.

1. Write the following number in words. 7,083,506

Answer: _______________________________________________

2. Arrange the following numbers in order from smallest to largest. 4,502,100 4,520,010 4,502,010 4,520,100

Answer: _______ , _______ , _______ , _______

3. Round 3,847,265 to the nearest hundred thousand.

Answer: ____________________

4. Find the value of 5 × (12,000 + 3,400).

Answer: ____________________

5. List all the factors of 84.

Answer: _______________________________________________

6. Find the highest common factor (HCF) of 36 and 60.

Answer: ____________________

7. Find the lowest common multiple (LCM) of 8 and 14.

Answer: ____________________

8. What is the smallest number that is exactly divisible by 6, 9, and 15?

Answer: ____________________

9. Express 50,400 as a product of its prime factors using index notation.

Answer: ____________________

10. A number is divisible by both 4 and 6. It lies between 200 and 250. What are all the possible values of this number?

Answer: _______________________________________________

Section B: Structured Questions (12 marks)

Questions 11–13 carry 4 marks each.

11. The table below shows the population of four towns.

Town	Population
A	2,450,380
B	2,540,038
C	2,405,830
D	2,450,830

(a) Which town has the greatest population?

Answer: ____________________

(b) Round each population to the nearest hundred thousand. Which two towns have the same rounded population?

Answer: ____________________ and ____________________

Answer: ____________________

12. A factory produces 2,450 toys per day. The toys are packed into boxes of 12.

(a) How many full boxes can be packed in one day?

Answer: ____________________

(b) How many toys are left over?

Answer: ____________________

13. Three traffic lights at a junction change their signals at regular intervals. Light A changes every 40 seconds, Light B every 60 seconds, and Light C every 90 seconds. They all change together at 8:00 a.m.

(a) After how many seconds will all three lights change together again?

Answer: ____________________

(b) How many times will all three lights change together between 8:00 a.m. and 8:30 a.m. (inclusive of 8:00 a.m.)?

Answer: ____________________

Section C: Problem-Solving Questions (8 marks)

Questions 14–15 carry 4 marks each.

14. A school organised a charity walk. 2,400 students were divided into teams. Each team had the same number of students.

(a) If there are between 15 and 30 teams, list all the possible numbers of teams.

Answer: _______________________________________________

(b) The organisers want each team to have between 60 and 100 students. How many teams should be formed?

Answer: ____________________

15. During a fundraising event, three classes collected a total of $5,040.

Class 6A collected twice as much as Class 6B.
Class 6C collected $360 more than Class 6B.

How much did each class collect?

Answer:

Class 6A: $____________________

Class 6B: $____________________

Class 6C: $____________________

End of Paper

Answers

TuitionGoWhere Practice Paper — Mathematics Primary 6 PSLE

Answer Key — Whole Numbers (Version 5)

Section A: Short Answer Questions (20 marks)

1. (2 marks) Answer: Seven million, eighty-three thousand, five hundred and six.

Working: 7,083,506 = 7 millions + 83 thousands + 5 hundreds + 6 ones.

Marking notes: Award 2 marks for the correct word form. Accept "seven million eighty-three thousand five hundred six" (without "and"). Award 1 mark if the student writes the correct number in words but makes a minor error in one place value group (e.g., "eighty-three thousand" written incorrectly). Award 0 marks for a completely incorrect word form.

2. (2 marks) Answer: 4,502,010 , 4,502,100 , 4,520,010 , 4,520,100

Working: Compare digit by digit from the left. All start with 4,5. At the thousands place: 0 < 2, so 4,502,___ come first. Between 4,502,010 and 4,502,100: 0 hundred < 1 hundred, so 4,502,010 < 4,502,100. Similarly 4,520,010 < 4,520,100.

Marking notes: Award 2 marks for the correct order. Award 1 mark if two adjacent numbers are swapped but the rest are correct. Award 0 marks for a completely incorrect order.

3. (2 marks) Answer: 3,800,000

Working: The hundred-thousands digit is 8 (in 3,847,265). The ten-thousands digit is 4. Since 4 < 5, we round down. 3,847,265 rounded to the nearest hundred thousand = 3,800,000.

Marking notes: Award 2 marks for the correct answer. Award 1 mark if the student identifies the correct place value but rounds incorrectly (e.g., 3,900,000). Award 0 marks for an incorrect answer with no working.

4. (2 marks) Answer: 87,000

Working: 5 × (12,000 + 3,400) = 5 × 15,400 = 77,000.

Wait — let me recalculate: 12,000 + 3,400 = 15,400. Then 5 × 15,400 = 77,000.

Answer: 77,000

Working: 12,000 + 3,400 = 15,400. 5 × 15,400 = 77,000.

Marking notes: Award 2 marks for the correct answer. Award 1 mark for correct addition but incorrect multiplication, or vice versa. Award 0 marks for an incorrect answer with no working.

5. (2 marks) Answer: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84

Working: Find factor pairs of 84:

1 × 84 = 84
2 × 42 = 84
3 × 28 = 84
4 × 21 = 84
6 × 14 = 84
7 × 12 = 84

Marking notes: Award 2 marks for all 12 factors listed correctly. Award 1 mark if at least 8 factors are listed correctly. Award 0 marks for fewer than 8 correct factors or no answer.

6. (2 marks) Answer: 12

Working: Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60. Common factors: 1, 2, 3, 4, 6, 12. HCF = 12.

Alternatively, using prime factorisation: 36 = 2² × 3² 60 = 2² × 3 × 5 HCF = 2² × 3 = 12.

Marking notes: Award 2 marks for the correct answer. Award 1 mark for a correct method with a minor arithmetic error. Award 0 marks for an incorrect answer with no working.

7. (2 marks) Answer: 56

Working: Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, … Multiples of 14: 14, 28, 42, 56, 70, … LCM = 56.

Alternatively: 8 = 2³ 14 = 2 × 7 LCM = 2³ × 7 = 56.

Marking notes: Award 2 marks for the correct answer. Award 1 mark for a correct method with a minor error. Award 0 marks for an incorrect answer with no working.

8. (2 marks) Answer: 90

Working: Find the LCM of 6, 9, and 15. 6 = 2 × 3 9 = 3² 15 = 3 × 5 LCM = 2 × 3² × 5 = 2 × 9 × 5 = 90.

Marking notes: Award 2 marks for the correct answer. Award 1 mark for a correct method with a minor error. Award 0 marks for an incorrect answer with no working.

9. (2 marks) Answer: 2⁴ × 3² × 5² × 7

Working: 50,400 ÷ 2 = 25,200 25,200 ÷ 2 = 12,600 12,600 ÷ 2 = 6,300 6,300 ÷ 2 = 3,150 3,150 ÷ 3 = 1,050 1,050 ÷ 3 = 350 350 ÷ 2 = 175 — wait, let me redo this.

50,400 ÷ 2 = 25,200 25,200 ÷ 2 = 12,600 12,600 ÷ 2 = 6,300 6,300 ÷ 2 = 3,150 3,150 ÷ 3 = 1,050 1,050 ÷ 3 = 350 350 ÷ 2 = 175 — but 350 ÷ 2 = 175, so that's another 2. Let me recount.

Actually: 50,400 = 504 × 100 = (8 × 63) × (4 × 25) = (2³ × 7 × 9) × (2² × 5²) = 2³ × 3² × 7 × 2² × 5² = 2⁵ × 3² × 5² × 7.

Let me verify: 2⁵ = 32, 3² = 9, 5² = 25, 7 = 7. 32 × 9 = 288; 288 × 25 = 7,200; 7,200 × 7 = 50,400. ✓

Answer: 2⁵ × 3² × 5² × 7

Marking notes: Award 2 marks for the correct answer. Award 1 mark if the student shows a correct factor tree or division method but makes one error. Award 0 marks for an incorrect answer with no working.

10. (2 marks) Answer: 204, 216, 228, 240

Working: A number divisible by both 4 and 6 must be divisible by LCM(4, 6) = 12. Multiples of 12 between 200 and 250: 12 × 17 = 204 12 × 18 = 216 12 × 19 = 228 12 × 20 = 240 12 × 21 = 252 (too large)

Marking notes: Award 2 marks for all four correct values. Award 1 mark for finding the LCM correctly and listing at least two correct multiples. Award 0 marks for an incorrect answer with no working.

Section B: Structured Questions (12 marks)

11. (4 marks)

(a) (1 mark) Answer: Town B

Working: Compare populations. 2,540,038 is the largest (5 in the hundred-thousands place vs. 4 for the others).

Marking notes: Award 1 mark for the correct answer.

(b) (2 marks) Answer: Town A and Town D

Working:

Town A: 2,450,380 → nearest hundred thousand = 2,500,000 (ten-thousands digit is 5, so round up)
Town B: 2,540,038 → nearest hundred thousand = 2,500,000 (ten-thousands digit is 4, so round down)
Town C: 2,405,830 → nearest hundred thousand = 2,400,000 (ten-thousands digit is 0, so round down)
Town D: 2,450,830 → nearest hundred thousand = 2,500,000 (ten-thousands digit is 5, so round up)

Wait — let me recheck:

Town A: 2,450,380 — the hundred-thousands digit is 4, the ten-thousands digit is 5. Since 5 ≥ 5, round up: 2,500,000.
Town B: 2,540,038 — the hundred-thousands digit is 5, the ten-thousands digit is 4. Since 4 < 5, round down: 2,500,000.
Town C: 2,405,830 — the hundred-thousands digit is 4, the ten-thousands digit is 0. Since 0 < 5, round down: 2,400,000.
Town D: 2,450,830 — the hundred-thousands digit is 4, the ten-thousands digit is 5. Since 5 ≥ 5, round up: 2,500,000.

Towns A, B, and D all round to 2,500,000. But the question asks for "two towns." Let me re-read: "Which two towns have the same rounded population?"

Actually, three towns (A, B, D) round to 2,500,000. The question says "two towns" which is ambiguous. Let me adjust the question to avoid this issue.

Actually, looking more carefully: Town A = 2,450,380 and Town D = 2,450,830 both round to 2,500,000. Town B = 2,540,038 also rounds to 2,500,000. So three towns share the same rounded value. The question asks for "two towns" — any two of A, B, D would be acceptable.

Marking notes: Award 2 marks for identifying any two of Towns A, B, and D (all round to 2,500,000). Award 1 mark if the student correctly rounds at least three populations but identifies only one pair. Award 0 marks for incorrect rounding.

Working: Largest = 2,540,038 (Town B). Smallest = 2,405,830 (Town C). Difference = 2,540,038 − 2,405,830 = 134,208.

Marking notes: Award 1 mark for the correct answer.

12. (4 marks)

(a) (1 mark) Answer: 204

Working: 2,450 ÷ 12 = 204 remainder 2. So 204 full boxes.

Marking notes: Award 1 mark for the correct answer.

(b) (1 mark) Answer: 2

Working: 2,450 − (204 × 12) = 2,450 − 2,448 = 2 toys left over.

Marking notes: Award 1 mark for the correct answer.

Working: Full boxes per day = 204. Days in 3 weeks = 6 × 3 = 18 days. Total full boxes = 204 × 18 = 3,672.

Marking notes: Award 2 marks for the correct answer. Award 1 mark for finding the correct number of days (18) but making a multiplication error, or for multiplying 204 × 6 = 1,224 (one week only). Award 0 marks for an incorrect answer with no working.

13. (4 marks)

(a) (2 marks) Answer: 360 seconds

Working: Find LCM of 40, 60, and 90. 40 = 2³ × 5 60 = 2² × 3 × 5 90 = 2 × 3² × 5 LCM = 2³ × 3² × 5 = 8 × 9 × 5 = 360.

Marking notes: Award 2 marks for the correct answer. Award 1 mark for a correct method (prime factorisation) with a minor error. Award 0 marks for an incorrect answer with no working.

(b) (2 marks) Answer: 6

Working: 8:00 a.m. to 8:30 a.m. = 30 minutes = 1,800 seconds. The lights change together every 360 seconds. Number of times = 1,800 ÷ 360 = 5 intervals, plus the initial time at 8:00 a.m. So total = 5 + 1 = 6 times.

The times are: 8:00, 8:06, 8:12, 8:18, 8:24, 8:30.

Marking notes: Award 2 marks for the correct answer. Award 1 mark for finding 5 (forgetting to include the initial time) or for a correct method with a minor error. Award 0 marks for an incorrect answer with no working.

Section C: Problem-Solving Questions (8 marks)

14. (4 marks)

(a) (2 marks) Answer: 16, 20, 24, 25, 30

Working: We need factors of 2,400 that are between 15 and 30. 2,400 = 2⁵ × 3 × 5². Factors between 15 and 30:

16 = 2⁴ → 2,400 ÷ 16 = 150 ✓
20 = 2² × 5 → 2,400 ÷ 20 = 120 ✓
24 = 2³ × 3 → 2,400 ÷ 24 = 100 ✓
25 = 5² → 2,400 ÷ 25 = 96 ✓
30 = 2 × 3 × 5 → 2,400 ÷ 30 = 80 ✓

Also check: 15 = 3 × 5 → 2,400 ÷ 15 = 160 ✓ (15 is between 15 and 30, inclusive? The question says "between 15 and 30" — I'll assume inclusive.)

Wait, 15 is between 15 and 30 (inclusive). Let me include it. 15: 2,400 ÷ 15 = 160 ✓

So the possible numbers of teams are: 15, 16, 20, 24, 25, 30.

Hmm, but I should check if the question means strictly between or inclusive. In PSLE context, "between 15 and 30" typically means 15 < n < 30 (exclusive). Let me assume exclusive.

Factors strictly between 15 and 30: 16, 20, 24, 25.

Actually, let me reconsider. In common PSLE usage, "between 15 and 30" can be ambiguous. To be safe, I'll list all factors from 16 to 29: 16, 20, 24, 25.

Answer: 16, 20, 24, 25

Marking notes: Award 2 marks for all four correct values. Award 1 mark for at least two correct values. Award 0 marks for an incorrect answer with no working.

(b) (2 marks) Answer: 24, 25, or 30 teams (any one acceptable, or list all)

Working: If each team has between 60 and 100 students:

2,400 ÷ 60 = 40 teams (but 40 > 30, so not in range from part (a))
2,400 ÷ 100 = 24 teams

So the number of teams must be between 24 and 40. But from part (a), the number of teams must be between 15 and 30. Combining: 24, 25, or 30 teams.

Wait — part (a) and part (b) are independent. Part (b) says "The organisers want each team to have between 60 and 100 students." This is a separate condition.

If each team has 60–100 students:

Minimum teams: 2,400 ÷ 100 = 24 teams
Maximum teams: 2,400 ÷ 60 = 40 teams

So the number of teams should be between 24 and 40. But we also need the number of teams to divide 2,400 exactly.

Factors of 2,400 between 24 and 40: 24, 25, 30, 40.

Answer: 24, 25, 30, or 40 teams

Hmm, but the question asks "How many teams should be formed?" — implying a single answer. This is ambiguous. Let me re-read the question.

Actually, looking at the question again: "The organisers want each team to have between 60 and 100 students. How many teams should be formed?"

This is asking for a specific number. But multiple answers are possible. In PSLE context, this type of question usually expects the student to find all possible values or to give one valid answer.

Let me adjust: the question could be interpreted as finding all possible values.

Answer: 24, 25, 30, or 40 teams

Marking notes: Award 2 marks for all four correct values (24, 25, 30, 40). Award 1 mark for at least two correct values. Award 0 marks for an incorrect answer with no working.

15. (4 marks) Answer: Class 6A: $2,340 Class 6B:$ 1,170 Class 6C: $1,530

Working: Let Class 6B collect $x. Then Class 6A collected$ 2x. Class 6C collected $(x + 360).

Total: x + 2x + (x + 360) = 5,040 4x + 360 = 5,040 4x = 5,040 − 360 = 4,680 x = 4,680 ÷ 4 = 1,170

Class 6B: $1,170 Class 6A:$ 1,170 × 2 = $2,340 Class 6C:$ 1,170 + $360 =$ 1,530

Check: $2,340 +$ 1,170 + $1,530 =$ 5,040 ✓

Marking notes: Award 4 marks for all three correct answers. Award 3 marks for a correct method with one arithmetic error. Award 2 marks for setting up the correct equation but making errors in solving. Award 1 mark for a correct first step (e.g., defining the variable). Award 0 marks for an incorrect answer with no working.

Summary of Marks

Question	Marks
1	2
2	2
3	2
4	2
5	2
6	2
7	2
8	2
9	2
10	2
11	4
12	4
13	4
14	4
15	4
Total	40

End of Answer Key