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Primary 6 PSLE Mathematics Semestral Assessment 2 (End of Year) Paper 4
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Questions
TuitionGoWhere Practice Paper - Mathematics Primary 6 PSLE
School: TuitionGoWhere Secondary School (AI) Subject: Mathematics Level: Primary 6 (PSLE) Paper: SA2 Practice Paper — Version 4 of 5 Duration: 1 hour 30 minutes (90 minutes) Total Marks: 60
Name: ___________________________ Class: ___________________________ Date: ___________________________
Instructions
- Write your name, class, and date clearly on this paper.
- Answer ALL questions in the spaces provided.
- Show your working clearly. Marks are awarded for correct method even if the final answer is wrong.
- Do not use a calculator.
- The number of marks for each question is shown in brackets [ ].
- You are advised to spend about 1 hour 20 minutes on this paper and use the remaining 10 minutes to check your answers.
Section A: Short Answer Questions (20 marks)
Answer each question in the space provided. Each question carries 2 marks.
1. Write the number seven million, three hundred five thousand, two hundred and eight in numerals.
Answer: ___________________________
2. Round 4,856,312 to the nearest hundred thousand.
Answer: ___________________________
3. Find the value of 3 × 10⁴ + 5 × 10² + 7 × 10⁰.
Answer: ___________________________
4. List all the factors of 72.
Answer: ___________________________
5. Find the highest common factor (HCF) of 24 and 60.
Answer: ___________________________
6. Find the lowest common multiple (LCM) of 8 and 12.
Answer: ___________________________
7. Express 360 as a product of its prime factors using index notation.
Answer: ___________________________
8. What is the smallest number that must be added to 9,999 to make it divisible by 17?
Answer: ___________________________
9. Find the value of 2⁵ − 3³.
Answer: ___________________________
10. The product of two numbers is 1,260. One number is 35. Find the other number.
Answer: ___________________________
Section B: Structured Questions (20 marks)
Answer all questions. Show your working clearly. Each question carries 4 marks.
11. A factory produced 2,450,000 toys in January and 3,175,000 toys in February. (a) How many toys were produced in the two months altogether?
Answer: ___________________________
(b) In March, the factory produced 587,000 fewer toys than in February. How many toys were produced in March?
Answer: ___________________________
12. A school library has 12,480 books. The books are to be arranged equally on 32 shelves. (a) How many books will be on each shelf?
Answer: ___________________________
(b) If each shelf can hold a maximum of 400 books, will there be enough space on the 32 shelves for all the books? Show your working.
Answer: ___________________________
13. The HCF of two numbers is 8 and their LCM is 96. If one of the numbers is 24, find the other number.
Answer: ___________________________
14. A number is divisible by both 6 and 8. What is the smallest such number that is greater than 200?
Answer: ___________________________
15. Find the value of:
(a) 144 ÷ 12 × 5 − 28
Answer: ___________________________
(b) 7 × (15 − 8) + 42 ÷ 6
Answer: ___________________________
Section C: Problem-Solving Questions (20 marks)
Answer all questions. Show your working clearly. Each question carries 5 marks.
16. At a concert, 4,850 adults and 3,120 children attended. The total ticket revenue was 10. How much did each child ticket cost?
Answer: ___________________________
17. A farmer has 1,260 chickens and ducks. The number of chickens is 4 times the number of ducks. (a) How many ducks does the farmer have?
Answer: ___________________________
(b) He sells 180 chickens. How many chickens does he have left?
Answer: ___________________________
(c) He then buys 90 more ducks. What is the new ratio of chickens to ducks?
Answer: ___________________________
18. Three friends — Ali, Bala, and Carol — shared a sum of money. Ali received 2/5 of the total. Bala received 1/3 of the remainder. Carol received the rest, which was $240. (a) What fraction of the total did Carol receive?
Answer: ___________________________
(b) What was the total sum of money shared?
Answer: ___________________________
19. A rectangular hall has a length of 48 m and a width of 36 m. Square tiles of the largest possible size (whole number of metres) are used to cover the floor without cutting. (a) What is the side length of each square tile?
Answer: ___________________________
(b) How many tiles are needed to cover the floor?
Answer: ___________________________
20. The numbers A, B, and C are three different whole numbers between 1 and 100.
- A is a multiple of 6.
- B is a multiple of 8.
- C is a multiple of 9.
- The sum A + B + C = 150.
Find one possible set of values for A, B, and C.
Answer: A = _______, B = _______, C = _______
End of Paper
Answers
TuitionGoWhere Practice Paper — Mathematics Primary 6 SA2 (Version 4 of 5)
Answer Key and Marking Scheme
Section A: Short Answer Questions (20 marks)
1. Write the number seven million, three hundred five thousand, two hundred and eight in numerals.
Answer: 7,305,208
Working:
- 7,000,000 + 305,000 + 208 = 7,305,208
Marks: 2 — Award 2 marks for correct numeral. Award 1 mark if the student writes 7305208 (without commas) but the value is correct.
2. Round 4,856,312 to the nearest hundred thousand.
Answer: 4,900,000
Working:
- The hundred-thousands digit is 8 (in 4,856,312).
- The ten-thousands digit is 5, so we round up.
- 4,800,000 → round up → 4,900,000
Marks: 2 — Award 2 marks for correct answer. Award 1 mark if the student writes 4,860,000 (rounded to nearest ten thousand instead — partial understanding shown).
3. Find the value of 3 × 10⁴ + 5 × 10² + 7 × 10⁰.
Answer: 30,507
Working:
- 3 × 10⁴ = 3 × 10,000 = 30,000
- 5 × 10² = 5 × 100 = 500
- 7 × 10⁰ = 7 × 1 = 7
- 30,000 + 500 + 7 = 30,507
Marks: 2 — Award 2 marks for correct answer. Award 1 mark for correct expansion but arithmetic error.
4. List all the factors of 72.
Answer: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Working:
- 1 × 72 = 72
- 2 × 36 = 72
- 3 × 24 = 72
- 4 × 18 = 72
- 6 × 12 = 72
- 8 × 9 = 72
Marks: 2 — Award 2 marks for all 12 factors listed correctly. Award 1 mark if at least 8 factors are correct and no incorrect factors are listed.
5. Find the highest common factor (HCF) of 24 and 60.
Answer: 12
Working:
- Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
- 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
Marks: 2 — Award 2 marks for correct answer. Award 1 mark for correct method with minor error.
6. Find the lowest common multiple (LCM) of 8 and 12.
Answer: 24
Working:
- Multiples of 8: 8, 16, 24, 32, ...
- Multiples of 12: 12, 24, 36, ...
- LCM = 24
Marks: 2 — Award 2 marks for correct answer. Award 1 mark for correct listing but incorrect LCM.
7. Express 360 as a product of its prime factors using index notation.
Answer: 2³ × 3² × 5
Working:
- 360 ÷ 2 = 180
- 180 ÷ 2 = 90
- 90 ÷ 2 = 45
- 45 ÷ 3 = 15
- 15 ÷ 3 = 5
- 5 ÷ 5 = 1
- 360 = 2 × 2 × 2 × 3 × 3 × 5 = 2³ × 3² × 5
Marks: 2 — Award 2 marks for correct answer. Award 1 mark for correct prime factorisation without index notation (e.g., 2 × 2 × 2 × 3 × 3 × 5).
8. What is the smallest number that must be added to 9,999 to make it divisible by 17?
Answer: 15
Working:
- 9,999 ÷ 17 = 588 remainder 3 (since 17 × 588 = 9,996)
- Remainder = 9,999 − 9,996 = 3
- Number to add = 17 − 3 = 14
Correction: 17 × 588 = 9,996. 9,999 − 9,996 = 3. So 17 − 3 = 14.
Answer: 14
Marks: 2 — Award 2 marks for correct answer. Award 1 mark for correct division but arithmetic error in final step.
9. Find the value of 2⁵ − 3³.
Answer: 5
Working:
- 2⁵ = 2 × 2 × 2 × 2 × 2 = 32
- 3³ = 3 × 3 × 3 = 27
- 32 − 27 = 5
Marks: 2 — Award 2 marks for correct answer. Award 1 mark for correct evaluation of powers but subtraction error.
10. The product of two numbers is 1,260. One number is 35. Find the other number.
Answer: 36
Working:
- Other number = 1,260 ÷ 35
- 1,260 ÷ 35 = 36
Marks: 2 — Award 2 marks for correct answer. Award 1 mark for setting up 1,260 ÷ 35 but incorrect division.
Section B: Structured Questions (20 marks)
11. A factory produced 2,450,000 toys in January and 3,175,000 toys in February.
(a) How many toys were produced in the two months altogether?
Answer: 5,625,000
Working:
- 2,450,000 + 3,175,000 = 5,625,000
Marks: 2 — Award 2 marks for correct answer. Award 1 mark for correct setup but addition error.
(b) In March, the factory produced 587,000 fewer toys than in February. How many toys were produced in March?
Answer: 2,588,000
Working:
- 3,175,000 − 587,000 = 2,588,000
Marks: 2 — Award 2 marks for correct answer. Award 1 mark for correct setup but subtraction error.
12. A school library has 12,480 books. The books are to be arranged equally on 32 shelves.
(a) How many books will be on each shelf?
Answer: 390
Working:
- 12,480 ÷ 32 = 390
Marks: 2 — Award 2 marks for correct answer. Award 1 mark for correct setup but division error.
(b) If each shelf can hold a maximum of 400 books, will there be enough space on the 32 shelves for all the books? Show your working.
Answer: Yes
Working:
- Total capacity = 32 × 400 = 12,800 books
- 12,800 > 12,480, so there is enough space.
Marks: 2 — Award 2 marks for correct answer with working. Award 1 mark for correct conclusion without working, or correct working with wrong conclusion.
13. The HCF of two numbers is 8 and their LCM is 96. If one of the numbers is 24, find the other number.
Answer: 32
Working:
- Product of two numbers = HCF × LCM
- Product = 8 × 96 = 768
- Other number = 768 ÷ 24 = 32
Marks: 4 — Award 4 marks for correct answer with full working. Award 2 marks for correct formula but arithmetic error. Award 1 mark for stating the formula HCF × LCM = product of two numbers.
14. A number is divisible by both 6 and 8. What is the smallest such number that is greater than 200?
Answer: 216
Working:
- LCM of 6 and 8:
- 6 = 2 × 3; 8 = 2³
- LCM = 2³ × 3 = 24
- Multiples of 24: 24, 48, ..., 192, 216, 240, ...
- 192 < 200, so the smallest multiple greater than 200 is 216
Marks: 4 — Award 4 marks for correct answer with full working. Award 2 marks for finding LCM = 24 but incorrect multiple. Award 1 mark for finding LCM of 6 and 8 = 24.
15. Find the value of:
(a) 144 ÷ 12 × 5 − 28
Answer: 32
Working:
- 144 ÷ 12 = 12
- 12 × 5 = 60
- 60 − 28 = 32
Marks: 2 — Award 2 marks for correct answer. Award 1 mark for correct first step but error in subsequent step.
(b) 7 × (15 − 8) + 42 ÷ 6
Answer: 56
Working:
- 15 − 8 = 7
- 7 × 7 = 49
- 42 ÷ 6 = 7
- 49 + 7 = 56
Marks: 2 — Award 2 marks for correct answer. Award 1 mark for correct bracket evaluation but error in subsequent steps.
Section C: Problem-Solving Questions (20 marks)
16. At a concert, 4,850 adults and 3,120 children attended. The total ticket revenue was 10. How much did each child ticket cost?
Answer: $5
Working:
- Revenue from adults = 4,850 × 48,500
- Revenue from children = 48,500 = $13,950
- Cost per child ticket = 4.47...**
Rechecking: 13,950 ÷ 3,120 = 4.471... This does not give a clean answer. Let me adjust the numbers in the question to give a clean answer.
Revised working (assuming intended answer is $5):
- Revenue from adults = 4,850 × 48,500
- Revenue from children = 48,500 = $13,950
- Cost per child ticket = $13,950 ÷ 3,120
Note: For a clean answer, if children = 2,790, then 5. However, as written with 3,120 children, the answer is not a whole number. For PSLE purposes, the numbers should yield a clean answer. The marking scheme below assumes the intended answer is $5 with adjusted context.
Working (corrected for marking):
- Revenue from adults = 4,850 × 48,500
- Revenue from children = 48,500 = $13,950
- Number of children = 3,120
- Cost per child ticket = 4.47 (not clean)
For a PSLE-appropriate answer, the question should use numbers that divide evenly. Accepting the question as written:
Answer: 4.50 to nearest 50¢) — However, this is not typical of PSLE. The question should be revised so that 62,450 − 48,500 = 13,950 divides evenly by the number of children.
Alternative clean version: If total revenue = $64,100:
- Revenue from children = 48,500 = $15,600
- 5**
Marks: 5 — Award 5 marks for correct answer with full working. Award 3 marks for correct method with one arithmetic error. Award 1 mark for finding revenue from adults correctly.
17. A farmer has 1,260 chickens and ducks. The number of chickens is 4 times the number of ducks.
(a) How many ducks does the farmer have?
Answer: 252
Working:
- Let ducks = 1 unit, chickens = 4 units
- Total = 5 units = 1,260
- 1 unit = 1,260 ÷ 5 = 252
- Ducks = 252
Marks: 2 — Award 2 marks for correct answer. Award 1 mark for correct model/unit setup.
(b) He sells 180 chickens. How many chickens does he have left?
Answer: 1,008
Working:
- Chickens originally = 4 × 252 = 1,008
- Chickens left = 1,008 − 180 = 828
Correction: 4 × 252 = 1,008. Then 1,008 − 180 = 828.
Answer: 828
Marks: 1 — Award 1 mark for correct answer.
(c) He then buys 90 more ducks. What is the new ratio of chickens to ducks?
Answer: 828 : 342 = 46 : 19 (or 2.42 : 1, but simplest whole ratio preferred)
Working:
- New number of ducks = 252 + 90 = 342
- Chickens left = 828
- Ratio = 828 : 342
- Divide both by 6: 138 : 57
- Divide both by 3: 46 : 19
Marks: 2 — Award 2 marks for correct simplified ratio. Award 1 mark for correct unsimplified ratio (828 : 342).
18. Three friends — Ali, Bala, and Carol — shared a sum of money. Ali received 2/5 of the total. Bala received 1/3 of the remainder. Carol received the rest, which was $240.
(a) What fraction of the total did Carol receive?
Answer: 2/5
Working:
- Ali received 2/5, so remainder = 1 − 2/5 = 3/5
- Bala received 1/3 of 3/5 = 1/3 × 3/5 = 3/15 = 1/5
- Carol received = 3/5 − 1/5 = 2/5
Marks: 2 — Award 2 marks for correct answer with working. Award 1 mark for correct remainder after Ali but error in subsequent step.
(b) What was the total sum of money shared?
Answer: $600
Working:
- Carol received 2/5 of total = $240
- 2/5 of total = $240
- 1/5 of total = 120
- Total = 600**
Marks: 3 — Award 3 marks for correct answer with full working. Award 2 marks for correct fraction but arithmetic error. Award 1 mark for setting up 2/5 of total = $240.
19. A rectangular hall has a length of 48 m and a width of 36 m. Square tiles of the largest possible size (whole number of metres) are used to cover the floor without cutting.
(a) What is the side length of each square tile?
Answer: 12 m
Working:
- The largest square tile that fits exactly must have a side length equal to the HCF of 48 and 36.
- Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
- Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
- HCF = 12
Marks: 2 — Award 2 marks for correct answer. Award 1 mark for correct HCF method but wrong answer.
(b) How many tiles are needed to cover the floor?
Answer: 12
Working:
- Area of hall = 48 × 36 = 1,728 m²
- Area of one tile = 12 × 12 = 144 m²
- Number of tiles = 1,728 ÷ 144 = 12
Alternative method:
- Tiles along length = 48 ÷ 12 = 4
- Tiles along width = 36 ÷ 12 = 3
- Total tiles = 4 × 3 = 12
Marks: 3 — Award 3 marks for correct answer with working. Award 2 marks for correct method with arithmetic error. Award 1 mark for dividing length by tile side correctly.
20. The numbers A, B, and C are three different whole numbers between 1 and 100.
- A is a multiple of 6.
- B is a multiple of 8.
- C is a multiple of 9.
- The sum A + B + C = 150.
Find one possible set of values for A, B, and C.
Answer: A = 60, B = 24, C = 66 — Check: 66 is not a multiple of 9.
Working (finding a valid solution):
- Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96
- Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96
- Multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99
Try A = 60 (multiple of 6), B = 24 (multiple of 8):
- C = 150 − 60 − 24 = 66 → 66 is NOT a multiple of 9. ✗
Try A = 60, B = 48:
- C = 150 − 60 − 48 = 42 → NOT a multiple of 9. ✗
Try A = 60, B = 72:
- C = 150 − 60 − 72 = 18 → 18 IS a multiple of 9. ✓
- All different? 60, 72, 18 — yes. All between 1 and 100 — yes.
Answer: A = 60, B = 72, C = 18
Verification:
- 60 is a multiple of 6 ✓
- 72 is a multiple of 8 ✓
- 18 is a multiple of 9 ✓
- 60 + 72 + 18 = 150 ✓
- All different ✓
Marks: 5 — Award 5 marks for a correct set of values with verification. Award 3 marks for a correct set without verification. Award 1 mark for listing multiples of one of the numbers correctly.
Summary of Marks
| Section | Marks |
|---|---|
| Section A (Questions 1–10) | 20 |
| Section B (Questions 11–15) | 20 |
| Section C (Questions 16–20) | 20 |
| Total | 60 |
End of Answer Key