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Primary 4 Mathematics Practice Paper 1

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Questions

TuitionGoWhere Practice Paper - Mathematics Primary 4

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

Name: _________________________
Class: Primary 4 _______
Date: _________________________

INSTRUCTIONS TO CANDIDATES

Do not turn over this page until you are told to do so.
Follow all instructions carefully.
Answer all questions.
Write your answers in this booklet.
The number of marks is given in brackets [ ] at the end of each question or part question.
The total number of marks for this paper is 100.
You may use a calculator for this paper.
Show all working clearly in the space provided.

SECTION 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 68,429, which digit is in the ten thousands place? [2]

(1) 6
(2) 8
(3) 4
(4) 2
Answer: (_____)

2. What does the digit 7 stand for in 57,381? [2]

(1) 7
(2) 70
(3) 700
(4) 7000
Answer: (_____)

3. Round 42,673 to the nearest hundred. [2]

(1) 42,600
(2) 42,700
(3) 43,000
(4) 42,670
Answer: (_____)

4. Which of the following numbers when rounded to the nearest thousand gives 35,000? [2]

(1) 34,499
(2) 34,500
(3) 35,500
(4) 35,501
Answer: (_____)

5. 84,000 + 3,000 + 600 + 40 + 9 = __________ [2]

(1) 87,649
(2) 87,659
(3) 87,749
(4) 87,759
Answer: (_____)

6. The difference between 62,000 and 28,475 is __________ [2]

(1) 33,525
(2) 33,535
(3) 34,525
(4) 34,535
Answer: (_____)

7. 345 × 28 = __________ [2]

(1) 9,660
(2) 9,660
(3) 9,660
(4) 9,660
Answer: (_____)

8. When a number is divided by 8, the quotient is 4,321 and the remainder is 5. What is the number? [2]

(1) 34,568
(2) 34,573
(3) 34,563
(4) 34,578
Answer: (_____)

9. Which of the following is a factor of 84? [2]

(1) 5
(2) 6
(3) 8
(4) 9
Answer: (_____)

10. The first four multiples of 12 are __________ [2]

(1) 12, 24, 36, 48
(2) 12, 24, 36, 46
(3) 12, 24, 34, 48
(4) 12, 22, 36, 48
Answer: (_____)

SECTION B: Short-Answer Questions (40 marks)

Questions 11 to 25 carry 2 to 4 marks each. Write your answers in the spaces provided. Show your working clearly.

11. Write 73,045 in words. [2]

12. In 92,507, the digit 5 is in the place and its value is . [2]

13. Arrange the following numbers in order, starting from the smallest. [2]

58,302 ; 58,032 ; 58,230 ; 58,320

14. Complete the number pattern. [2]

42,000 ; 41,500 ; 41,000 ; __________ ; 40,000

15. Round 67,849 to the nearest thousand. [2]

16. Find the sum of 38,427 and 25,684. [2]

17. Subtract 19,876 from 50,000. [2]

18. Multiply 4,326 by 7. [2]

19. Divide 36,456 by 6. [2]

20. Find all the factors of 36. [2]

21. List the first five multiples of 9. [2]

22. Is 7 a factor of 91? Explain your answer. [2]

23. Find the common factors of 24 and 36. [3]

24. Find the first two common multiples of 4 and 6. [3]

25. A number is between 50 and 100. It is a multiple of 8. When divided by 9, the remainder is 7. What is the number? [4]

SECTION C: Long-Answer / Word Problems (40 marks)

Questions 26 to 30 carry 8 marks each. Show your working clearly and write your final answer in the space provided.

26. Singapore's population density is about 8,358 people per square kilometre. [8]

(a) Round this number to the nearest hundred.
(b) The area of Bukit Panjang is about 9 square kilometres. Estimate the population of Bukit Panjang using your rounded answer from (a).
(c) The actual population of Bukit Panjang is 75,222. Find the difference between your estimated population and the actual population.

Working:

(a) ________________________________________________________________________

(b) ________________________________________________________________________

27. A factory produced 48,650 toys in January. [8]

In February, it produced 5,340 fewer toys than in January. In March, it produced twice as many toys as in February. (a) How many toys were produced in February?
(b) How many toys were produced in March?
(c) What was the total number of toys produced in the three months?

Working:

(a) ________________________________________________________________________

(b) ________________________________________________________________________

28. Mrs Tan had $85,000. [8]

She spent $28,450 on a renovation. She spent$ 12,800 on furniture. She divided the remaining money equally among her 4 children. (a) How much money did she spend altogether on renovation and furniture?
(b) How much money did she have left?
(c) How much did each child receive?

Working:

(a) ________________________________________________________________________

(b) ________________________________________________________________________

29. There are 3,456 students in a school. [8]

The students are divided equally into 8 levels (Primary 1 to Primary 6, plus two kindergarten levels). Each level has the same number of classes. There are 4 classes in each level. (a) How many students are there in each level?
(b) How many students are there in each class?
(c) If 3 students from each class are chosen for a competition, how many students are chosen in total?

Working:

(a) ________________________________________________________________________

(b) ________________________________________________________________________

30. A number when rounded to the nearest thousand is 40,000. [8]

When rounded to the nearest hundred, it is 39,800. The sum of its digits is 25. The digit in the tens place is twice the digit in the ones place. What is the number?

Working:

END OF PAPER
Total Marks: 100

Answers

TuitionGoWhere Practice Paper - Mathematics Primary 4 (Answer Key)

Subject: Mathematics
Level: Primary 4
Paper: Practice Paper 1 (Version 1)
Total Marks: 100

SECTION A: Multiple-Choice Questions (20 marks)

1. Answer: (1) 6 [2]

Explanation: In the number 68,429, the digits from left to right are: 6 (ten thousands), 8 (thousands), 4 (hundreds), 2 (tens), 9 (ones). The digit in the ten thousands place is 6.

2. Answer: (4) 7000 [2]

Explanation: In 57,381, the digit 7 is in the thousands place. Its value is 7 × 1,000 = 7,000.

3. Answer: (2) 42,700 [2]

Explanation: To round 42,673 to the nearest hundred, look at the tens digit (7). Since 7 ≥ 5, round up the hundreds digit from 6 to 7. The number becomes 42,700.

4. Answer: (2) 34,500 [2]

Explanation: When rounding to the nearest thousand, numbers from 34,500 to 35,499 round to 35,000. 34,499 rounds to 34,000. 35,500 and 35,501 round to 36,000.

5. Answer: (1) 87,649 [2]

Explanation: 84,000 + 3,000 = 87,000; 87,000 + 600 = 87,600; 87,600 + 40 = 87,640; 87,640 + 9 = 87,649.

6. Answer: (1) 33,525 [2]

Explanation: 62,000 − 28,475 = 33,525. Check: 33,525 + 28,475 = 62,000 ✓

7. Answer: (1) 9,660 [2]

Explanation: 345 × 28 = 345 × (20 + 8) = 345 × 20 + 345 × 8 = 6,900 + 2,760 = 9,660.

8. Answer: (2) 34,573 [2]

Explanation: Number = (Divisor × Quotient) + Remainder = (8 × 4,321) + 5 = 34,568 + 5 = 34,573.

9. Answer: (2) 6 [2]

Explanation: Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84. 6 is a factor (84 ÷ 6 = 14). 5, 8, and 9 are not factors of 84.

10. Answer: (1) 12, 24, 36, 48 [2]

Explanation: Multiples of 12: 12×1=12, 12×2=24, 12×3=36, 12×4=48. The first four multiples are 12, 24, 36, 48.

SECTION B: Short-Answer Questions (40 marks)

11. Seventy-three thousand and forty-five [2]

Marking: 1 mark for "seventy-three thousand", 1 mark for "forty-five" (accept "and" or without).

12. hundreds place; 500 [2]

Explanation: In 92,507, the digits are: 9 (ten thousands), 2 (thousands), 5 (hundreds), 0 (tens), 7 (ones). The digit 5 is in the hundreds place, so its value is 5 × 100 = 500.

13. 58,032 ; 58,230 ; 58,302 ; 58,320 [2]

Explanation: Compare from the leftmost digit. All have 58,___. Compare hundreds: 0 < 2 < 3. For 58,302 and 58,320, compare tens: 0 < 2.

14. 40,500 [2]

Explanation: The pattern decreases by 500 each time: 42,000 − 500 = 41,500; 41,500 − 500 = 41,000; 41,000 − 500 = 40,500; 40,500 − 500 = 40,000.

15. 68,000 [2]

Explanation: To round 67,849 to the nearest thousand, look at the hundreds digit (8). Since 8 ≥ 5, round up the thousands digit from 7 to 8. The number becomes 68,000.

16. 64,111 [2]

Working:

  38,427
+ 25,687
--------
  64,111

Check: 64,111 − 25,687 = 38,424 (close, recheck: 38,427 + 25,684 = 64,111) ✓

17. 30,124 [2]

Working:

  50,000
- 19,876
--------
  30,124

Check: 30,124 + 19,876 = 50,000 ✓

18. 30,282 [2]

Working: 4,326 × 7 = (4,000 × 7) + (300 × 7) + (20 × 7) + (6 × 7) = 28,000 + 2,100 + 140 + 42 = 30,282.

19. 6,076 [2]

Working: 36,456 ÷ 6 = 6,076. Check: 6,076 × 6 = 36,456 ✓

20. 1, 2, 3, 4, 6, 9, 12, 18, 36 [2]

Explanation: Factors of 36 come in pairs: 1×36, 2×18, 3×12, 4×9, 6×6. List in order: 1, 2, 3, 4, 6, 9, 12, 18, 36.

21. 9, 18, 27, 36, 45 [2]

Explanation: Multiples of 9: 9×1=9, 9×2=18, 9×3=27, 9×4=36, 9×5=45.

22. Yes, 7 is a factor of 91 because 91 ÷ 7 = 13 with no remainder. [2]

Marking: 1 mark for "Yes", 1 mark for correct explanation (91 ÷ 7 = 13 exactly / 7 × 13 = 91).

23. 1, 2, 3, 4, 6, 12 [3]

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 Marking: 1 mark for correct factors of 24, 1 mark for correct factors of 36, 1 mark for correct common factors.

24. 12, 24 [3]

Working:

Multiples of 4: 4, 8, 12, 16, 20, 24, 28, ...
Multiples of 6: 6, 12, 18, 24, 30, ...
Common multiples: 12, 24, 36, ...
First two: 12, 24 Marking: 1 mark for listing multiples of 4, 1 mark for listing multiples of 6, 1 mark for correct first two common multiples.

25. 88 [4]

Working:

Multiples of 8 between 50 and 100: 56, 64, 72, 80, 88, 96
Check each for remainder 7 when divided by 9:
- 56 ÷ 9 = 6 R 2 ✗
- 64 ÷ 9 = 7 R 1 ✗
- 72 ÷ 9 = 8 R 0 ✗
- 80 ÷ 9 = 8 R 8 ✗
- 88 ÷ 9 = 9 R 7 ✓
- 96 ÷ 9 = 10 R 6 ✗ Answer: 88 Marking: 1 mark for listing multiples of 8, 1 mark for checking division by 9, 1 mark for identifying 88, 1 mark for final answer.

SECTION C: Long-Answer / Word Problems (40 marks)

26. [8]

(a) 8,400 [2] Working: 8,358 rounded to nearest hundred → look at tens digit (5). Since 5 ≥ 5, round up hundreds digit from 3 to 4. Answer: 8,400.

(b) 75,600 [3] Working: Estimated population = 8,400 × 9 = 75,600. Marking: 1 mark for using rounded value from (a), 1 mark for multiplication, 1 mark for correct answer.

(c) 378 [3] Working: Difference = 75,600 − 75,222 = 378. Marking: 1 mark for subtraction setup, 1 mark for correct calculation, 1 mark for answer with unit (people).

27. [8]

(a) 43,310 [2] Working: February = 48,650 − 5,340 = 43,310.

(b) 86,620 [3] Working: March = 43,310 × 2 = 86,620. Marking: 1 mark for using February's answer, 1 mark for multiplication, 1 mark for correct answer.

(c) 178,580 [3] Working: Total = 48,650 + 43,310 + 86,620 = 178,580. Marking: 1 mark for adding all three months, 1 mark for correct addition, 1 mark for final answer.

28. [8]

**(a) $41,250** [2] **Working:** Total spent =$ 28,450 + $12,800 =$ 41,250.

**(b) $43,750** [2] **Working:** Remaining =$ 85,000 − $41,250 =$ 43,750.

**(c) $10,937.50** [4] **Working:** Each child =$ 43,750 ÷ 4 = $10,937.50. **Marking:** 1 mark for using remaining amount from (b), 1 mark for division by 4, 1 mark for correct calculation, 1 mark for answer with$ sign and 2 decimal places.

29. [8]

(a) 432 [2] Working: Students per level = 3,456 ÷ 8 = 432.

(b) 108 [3] Working: Students per class = 432 ÷ 4 = 108. Marking: 1 mark for using (a)'s answer, 1 mark for division by 4, 1 mark for correct answer.

(c) 96 [3] Working: Total classes = 8 levels × 4 classes = 32 classes. Students chosen = 32 × 3 = 96. Marking: 1 mark for finding total classes, 1 mark for multiplication by 3, 1 mark for correct answer.

30. 39,842 [8]

Working: Let the number be 39,abc (since it rounds to 40,000 to nearest thousand, it must be between 39,500 and 40,499; and rounds to 39,800 to nearest hundred, so it must be between 39,750 and 39,849).

So the number is 39,8xy where x is tens digit, y is ones digit. Given: x = 2y (tens digit is twice ones digit) Sum of digits = 3 + 9 + 8 + x + y = 25 → 20 + x + y = 25 → x + y = 5

Substitute x = 2y: 2y + y = 5 3y = 5 y = 5/3 (not an integer) → Wait, recheck.

Actually, the number rounds to 39,800 to nearest hundred, so it's between 39,750 and 39,849. The thousands digit is 9, hundreds digit is 8. Number = 39,8xy where x = tens, y = ones. Range: 39,750 ≤ 39,8xy ≤ 39,849 → so x can be 0,1,2,3,4 (but 39,850 would round to 39,900).

Sum of digits: 3 + 9 + 8 + x + y = 25 → x + y = 5. Given: x = 2y. So 2y + y = 5 → 3y = 5 → y = 5/3. Not possible.

Wait, maybe the number is 39,7xy? No, rounds to 39,800 means hundreds digit is 8. Let me re-read: "When rounded to the nearest hundred, it is 39,800." So the number is between 39,750 and 39,849 inclusive. Hundreds digit is 8. Tens digit x, ones digit y. 3 + 9 + 8 + x + y = 25 → x + y = 5. x = 2y. 2y + y = 5 → 3y = 5 → y = 1.67. Not integer.

Is there an error? Let me check the rounding range again. 39,800 to nearest hundred: numbers from 39,750 to 39,849. If the number is 39,842: digits sum = 3+9+8+4+2 = 26. Not 25. 39,831: sum = 3+9+8+3+1 = 24. 39,820: sum = 3+9+8+2+0 = 22. 39,814: sum = 3+9+8+1+4 = 25. Tens=1, ones=4. Is tens twice ones? 1 ≠ 2×4. No. 39,805: sum = 3+9+8+0+5 = 25. Tens=0, ones=5. 0 ≠ 10. No.

What if the number is 39,7xy? Rounds to 39,800? 39,750 rounds to 39,800. So 39,750 to 39,799 also round to 39,800. Then hundreds digit is 7. Sum: 3+9+7+x+y = 25 → x+y = 6. x = 2y → 3y = 6 → y = 2, x = 4. Number = 39,742. Check: 39,742 rounded to nearest thousand → 40,000? 39,742 is between 39,500 and 40,499, so yes, rounds to 40,000. Rounded to nearest hundred: 39,742 → look at tens (4), <5, so rounds to 39,700. Not 39,800. ✗

What about 39,750 to 39,799? 39,750: sum = 3+9+7+5+0 = 24. 39,762: sum = 3+9+7+6+2 = 27. 39,741: sum = 24. 39,732: sum = 24.

Let me try: number rounds to 40,000 (nearest thousand) → 39,500 to 40,499. Rounds to 39,800 (nearest hundred) → 39,750 to 39,849. Intersection: 39,750 to 39,849.

Let number = 39,8xy (since 39,750-39,799 have hundreds=7, but round to 39,800? Wait: 39,750 rounded to nearest hundred: tens=5, so round up hundreds from 7 to 8 → 39,800. Yes! So 39,750 to 39,799 also round to 39,800. And 39,800 to 39,849 round to 39,800.

So two cases: Case 1: 39,7xy where 50 ≤ xy ≤ 99 (i.e., 39,750 to 39,799) Case 2: 39,8xy where 00 ≤ xy ≤ 49 (i.e., 39,800 to 39,849)

Case 1: Digits: 3,9,7,x,y. Sum = 19 + x + y = 25 → x + y = 6. x = 2y → 3y = 6 → y = 2, x = 4. Number = 39,742. But 39,742 is not in 39,750-39,799. ✗

Case 2: Digits: 3,9,8,x,y. Sum = 20 + x + y = 25 → x + y = 5. x = 2y → 3y = 5 → y = 5/3. Not integer. ✗

Hmm. Let me re-read the question: "The digit in the tens place is twice the digit in the ones place." Maybe the number is 40,xxx? Rounds to 40,000 to nearest thousand: 39,500 to 40,499. If number is 40,0xy: sum = 4+0+0+x+y = 4+x+y=25 → x+y=21. Impossible (max 9+9=18). 40,1xy: 4+0+1+x+y=25 → x+y=20. Impossible. 40,2xy: x+y=19. Impossible. 40,3xy: x+y=18 → x=9,y=9. Tens=9, ones=9. 9 ≠ 2×9. No. 40,4xy: x+y=17. x=2y → 3y=17. No.

What if "rounded to the nearest thousand is 40,000" means the number is 40,000 exactly? No, "a number when rounded..."

Let me check the problem statement again. Maybe I made an error in the question design. The question asks for a number that satisfies all conditions. Let me construct one that works.

We need:

Rounds to 40,000 (nearest 1000) → range [39500, 40499]
Rounds to 39,800 (nearest 100) → range [39750, 39849]
Sum of digits = 25
Tens digit = 2 × Ones digit

Intersection of ranges: [39750, 39849]

Let number = 39,8ab where a=tens, b=ones, and 00 ≤ ab ≤ 49 (since max 39849) Or 39,7ab where 50 ≤ ab ≤ 99

For 39,8ab: digits 3,9,8,a,b. Sum = 20+a+b=25 → a+b=5. a=2b → 3b=5 → no integer solution.

For 39,7ab: digits 3,9,7,a,b. Sum = 19+a+b=25 → a+b=6. a=2b → 3b=6 → b=2, a=4. Number = 39,742. But 39,742 is not in [39750, 39799]. It's 39,742 < 39,750.

So no solution exists with these constraints. I need to fix the question or the answer.

Let me adjust the question to make it work. Change "sum of digits is 25" to "sum of digits is 24"? For 39,742: sum = 3+9+7+4+2 = 25. Wait, 3+9+7+4+2 = 25. Yes! 39,742 has sum 25. But 39,742 rounds to nearest hundred: tens=4 <5, so rounds to 39,700. Not 39,800.

What about 39,753? Sum = 3+9+7+5+3 = 27. 39,762: sum = 27. 39,771: sum = 27. 39,780: sum = 27. 39,792: sum = 30.

What about 39,831? Sum = 24. Tens=3, ones=1. 3 ≠ 2. 39,842? Sum = 26. Tens=4, ones=2. 4 = 2×2 ✓. But sum is 26, not 25. 39,820? Sum = 22. Tens=2, ones=0. 2 ≠ 0. 39,814? Sum = 25. Tens=1, ones=4. 1 ≠ 8. 39,805? Sum = 25. Tens=0, ones=5. 0 ≠ 10.

39,764? Sum = 29. 39,752? Sum = 26. Tens=5, ones=2. 5 ≠ 4. 39,741? Sum = 24. Tens=4, ones=1. 4 ≠ 2. 39,730? Sum = 19.

Let me try: 39,8ab with a=2b, a+b=5. No solution. 39,7ab with a=2b, a+b=6 → b=2, a=4 → 39,742. But rounds to 39,700.

What if the rounding to nearest hundred is 39,700? Then the question would work for 39,742. But the question says 39,800.

Let me change the question slightly: "When rounded to the nearest hundred, it is 39,700." Then answer is 39,742. But the paper is already generated. I must provide an answer key for the question as written.

As written, there is NO number satisfying all conditions. This is a flawed question. But as an answer key, I should either:

Point out the error and give the closest number.
Assume a typo in the question and solve for the intended version.

Given this is an answer key for a generated paper, I'll note the issue and provide the intended solution assuming "39,700" for the hundred rounding, or adjust the sum.

Actually, looking at 39,842: rounds to 40,000 (nearest 1000)? 39,842 is in [39500,40499] yes. Rounds to 39,800 (nearest 100)? 39,842 → tens=4<5 → 39,800 yes. Sum=3+9+8+4+2=26. Tens=4, ones=2 → 4=2×2 yes. Only sum is off by 1.

39,831: sum=24, tens=3, ones=1 (3≠2). 39,820: sum=22, tens=2, ones=0 (2≠0). 39,814: sum=25, tens=1, ones=4 (1≠8). 39,805: sum=25, tens=0, ones=5 (0≠10).

39,764: rounds to 39,800? 39,764 → tens=6≥5 → 39,800 yes. Rounds to 40,000? yes. Sum=29. Tens=6, ones=4 (6≠8). 39,752: rounds to 39,800? tens=5≥5 → 39,800 yes. Sum=26. Tens=5, ones=2 (5≠4). 39,741: rounds to 39,700. No.

What about 39,786? Sum=33. 39,792? Sum=30.

Okay, the only number that satisfies rounding to 40,000 and 39

<stage5_exam_answers_md>

TuitionGoWhere Practice Paper - Mathematics Primary 4 (Answer Key)

Subject: Mathematics
Level: Primary 4
Paper: Practice Paper 1 (Version 1)
Total Marks: 100

SECTION A: Multiple-Choice Questions (20 marks)

1. Answer: (1) 6 [2]

Explanation: In the number 68,429, the digits from left to right are: 6 (ten thousands), 8 (thousands), 4 (hundreds), 2 (tens), 9 (ones). The digit in the ten thousands place is 6.

2. Answer: (4) 7000 [2]

Explanation: In 57,381, the digit 7 is in the thousands place. Its value is 7 × 1,000 = 7,000.

3. Answer: (2) 42,700 [2]

Explanation: To round 42,673 to the nearest hundred, look at the tens digit (7). Since 7 ≥ 5, round up the hundreds digit from 6 to 7. The number becomes 42,700.

4. Answer: (2) 34,500 [2]

Explanation: When rounding to the nearest thousand, numbers from 34,500 to 35,499 round to 35,000. 34,499 rounds to 34,000. 35,500 and 35,501 round to 36,000.

5. Answer: (1) 87,649 [2]

Explanation: 84,000 + 3,000 = 87,000; 87,000 + 600 = 87,600; 87,600 + 40 = 87,640; 87,640 + 9 = 87,649.

6. Answer: (1) 33,525 [2]

Explanation: 62,000 − 28,475 = 33,525. Check: 33,525 + 28,475 = 62,000 ✓

7. Answer: (1) 9,660 [2]

Explanation: 345 × 28 = 345 × (20 + 8) = 345 × 20 + 345 × 8 = 6,900 + 2,760 = 9,660.

8. Answer: (2) 34,573 [2]

Explanation: Number = (Divisor × Quotient) + Remainder = (8 × 4,321) + 5 = 34,568 + 5 = 34,573.

9. Answer: (2) 6 [2]

Explanation: Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84. 6 is a factor (84 ÷ 6 = 14). 5, 8, and 9 are not factors of 84.

10. Answer: (1) 12, 24, 36, 48 [2]

Explanation: Multiples of 12: 12×1=12, 12×2=24, 12×3=36, 12×4=48. The first four multiples are 12, 24, 36, 48.

SECTION B: Short-Answer Questions (40 marks)

11. Seventy-three thousand and forty-five [2]

Marking: 1 mark for "seventy-three thousand", 1 mark for "forty-five" (accept "and" or without).

12. hundreds place; 500 [2]

Explanation: In 92,507, the digits are: 9 (ten thousands), 2 (thousands), 5 (hundreds), 0 (tens), 7 (ones). The digit 5 is in the hundreds place, so its value is 5 × 100 = 500.

13. 58,032 ; 58,230 ; 58,302 ; 58,320 [2]

Explanation: Compare from the leftmost digit. All have 58,___. Compare hundreds: 0 < 2 < 3. For 58,302 and 58,320, compare tens: 0 < 2.

14. 40,500 [2]

Explanation: The pattern decreases by 500 each time: 42,000 − 500 = 41,500; 41,500 − 500 = 41,000; 41,000 − 500 = 40,500; 40,500 − 500 = 40,000.

15. 68,000 [2]

Explanation: To round 67,849 to the nearest thousand, look at the hundreds digit (8). Since 8 ≥ 5, round up the thousands digit from 7 to 8. The number becomes 68,000.

16. 64,111 [2]

Working:

  38,427
+ 25,684
--------
  64,111

Check: 64,111 − 25,684 = 38,427 ✓

17. 30,124 [2]

Working:

  50,000
- 19,876
--------
  30,124

Check: 30,124 + 19,876 = 50,000 ✓

18. 30,282 [2]

Working: 4,326 × 7 = (4,000 × 7) + (300 × 7) + (20 × 7) + (6 × 7) = 28,000 + 2,100 + 140 + 42 = 30,282.

19. 6,076 [2]

Working: 36,456 ÷ 6 = 6,076. Check: 6,076 × 6 = 36,456 ✓

20. 1, 2, 3, 4, 6, 9, 12, 18, 36 [2]

Explanation: Factors of 36 come in pairs: 1×36, 2×18, 3×12, 4×9, 6×6. List in order: 1, 2, 3, 4, 6, 9, 12, 18, 36.

21. 9, 18, 27, 36, 45 [2]

Explanation: Multiples of 9: 9×1=9, 9×2=18, 9×3=27, 9×4=36, 9×5=45.

22. Yes, 7 is a factor of 91 because 91 ÷ 7 = 13 with no remainder. [2]

Marking: 1 mark for "Yes", 1 mark for correct explanation (91 ÷ 7 = 13 exactly / 7 × 13 = 91).

23. 1, 2, 3, 4, 6, 12 [3]

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 Marking: 1 mark for correct factors of 24, 1 mark for correct factors of 36, 1 mark for correct common factors.

24. 12, 24 [3]

Working:

Multiples of 4: 4, 8, 12, 16, 20, 24, 28, ...
Multiples of 6: 6, 12, 18, 24, 30, ...
Common multiples: 12, 24, 36, ...
First two: 12, 24 Marking: 1 mark for listing multiples of 4, 1 mark for listing multiples of 6, 1 mark for correct first two common multiples.

25. 88 [4]

Working:

Multiples of 8 between 50 and 100: 56, 64, 72, 80, 88, 96
Check each for remainder 7 when divided by 9:
- 56 ÷ 9 = 6 R 2 ✗
- 64 ÷ 9 = 7 R 1 ✗
- 72 ÷ 9 = 8 R 0 ✗
- 80 ÷ 9 = 8 R 8 ✗
- 88 ÷ 9 = 9 R 7 ✓
- 96 ÷ 9 = 10 R 6 ✗ Answer: 88 Marking: 1 mark for listing multiples of 8, 1 mark for checking division by 9, 1 mark for identifying 88, 1 mark for final answer.

SECTION C: Long-Answer / Word Problems (40 marks)

26. [8]

(a) 8,400 [2] Working: 8,358 rounded to nearest hundred → look at tens digit (5). Since 5 ≥ 5, round up hundreds digit from 3 to 4. Answer: 8,400.

(b) 75,600 [3] Working: Estimated population = 8,400 × 9 = 75,600. Marking: 1 mark for using rounded value from (a), 1 mark for multiplication, 1 mark for correct answer.

(c) 378 [3] Working: Difference = 75,600 − 75,222 = 378. Marking: 1 mark for subtraction setup, 1 mark for correct calculation, 1 mark for answer with unit (people).

27. [8]

(a) 43,310 [2] Working: February = 48,650 − 5,340 = 43,310.

(b) 86,620 [3] Working: March = 43,310 × 2 = 86,620. Marking: 1 mark for using February's answer, 1 mark for multiplication, 1 mark for correct answer.

(c) 178,580 [3] Working: Total = 48,650 + 43,310 + 86,620 = 178,580. Marking: 1 mark for adding all three months, 1 mark for correct addition, 1 mark for final answer.

28. [8]

**(a) $41,250** [2] **Working:** Total spent =$ 28,450 + $12,800 =$ 41,250.

**(b) $43,750** [2] **Working:** Remaining =$ 85,000 − $41,250 =$ 43,750.

29. [8]

(a) 432 [2] Working: Students per level = 3,456 ÷ 8 = 432.

(b) 108 [3] Working: Students per class = 432 ÷ 4 = 108. Marking: 1 mark for using (a)'s answer, 1 mark for division by 4, 1 mark for correct answer.

30. 39,782 [8]

Working:

The number rounds to 40,000 (nearest thousand) → between 39,500 and 40,499.
The number rounds to 39,800 (nearest hundred) → between 39,750 and 39,849.
So the number is in the range 39,750 to 39,849.
Let the number be 39,7xy or 39,8xy.
Sum of digits = 25.
Tens digit = 2 × ones digit.

Case 1: Number is 39,8xy (hundreds digit 8)

3 + 9 + 8 + x + y = 25 → x + y = 5
x = 2y → 2y + y = 5 → 3y = 5 → y = 5/3 (not an integer) → Impossible.

Case 2: Number is 39,7xy (hundreds digit 7, range 39,750–39,799)

3 + 9 + 7 + x + y = 25 → x + y = 6
x = 2y → 2y + y = 6 → 3y = 6 → y = 2
Then x = 2 × 2 = 4
Number = 39,742 → But this is less than 39,750, so it rounds to 39,700, not 39,800. → Invalid.

Re-evaluate range for rounding to 39,800:

Numbers from 39,750 to 39,849 round to 39,800.
This includes 39,750–39,799 (hundreds digit 7) and 39,800–39,849 (hundreds digit 8).

Check 39,750–39,799 (hundreds digit 7):

Sum: 3+9+7+x+y = 19+x+y = 25 → x+y = 6
x = 2y → 3y = 6 → y = 2, x = 4
Number = 39,742 (not in range 39,750–39,799) → No solution here.

Check 39,800–39,849 (hundreds digit 8):

Sum: 3+9+8+x+y = 20+x+y = 25 → x+y = 5
x = 2y → 3y = 5 → No integer solution.

Wait — re-read problem: "The digit in the tens place is twice the digit in the ones place."

Could the number be 39,8xy with x=4, y=2? Sum = 3+9+8+4+2 = 26 ≠ 25.
x=2, y=1? Sum = 3+9+8+2+1 = 23.
x=0, y=0? Sum = 20.

Alternative interpretation: The number rounds to 40,000 (nearest thousand) AND 39,800 (nearest hundred).

This means: 39,750 ≤ number ≤ 39,849.
Sum of digits = 25.
Tens = 2 × Ones.

List numbers in range with tens = 2×ones:

Ones=0, Tens=0: 39,700, 39,800 → sums 19, 20
Ones=1, Tens=2: 39,721, 39,821 → sums 22, 23
Ones=2, Tens=4: 39,742, 39,842 → sums 25, 26
Ones=3, Tens=6: 39,763, 39,863 (out of range) → 39,763 sum = 28
Ones=4, Tens=8: 39,784, 39,884 (out) → 39,784 sum = 31

Only 39,742 has digit sum 25.

But 39,742 rounds to 39,700 (nearest hundred), not 39,800.
39,742 rounds to 40,000 (nearest thousand) ✓
39,742 rounds to 39,700 (nearest hundred) ✗

Check 39,842:

Sum = 3+9+8+4+2 = 26 ≠ 25.
Rounds to 39,800 (nearest hundred) ✓
Rounds to 40,000 (nearest thousand) ✓
Tens (4) = 2 × Ones (2) ✓
Only fails sum of digits = 25 (is 26).

Conclusion: There is a typo in the problem. The sum of digits should be 26, not 25.

If sum = 26, answer is 39,842.
If sum = 25, no solution exists.

Assuming the intended answer is 39,842 (with sum of digits = 26), or accepting 39,742 with note about rounding discrepancy.

Most likely intended answer: 39,842 (satisfies all conditions except sum=25; sum=26 is very close, likely a typo). Marking: 2 marks for correct range identification, 2 marks for digit sum equation, 2 marks for tens/ones relationship, 2 marks for final answer (39,842) with working shown.

Final Answer: 39,842 (with note: sum of digits is 26; if sum must be 25, no solution exists).

END OF ANSWER KEY
Total Marks: 100

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