Primary 5 Mathematics Practice Paper 2

TuitionGoWhere Practice Paper - Mathematics Primary 5

TuitionGoWhere Practice Paper (AI)

Answer Key and Marking Scheme - Whole Numbers Practice Paper, Version 2 of 5

Total Marks: 60

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Section A (Questions 1-5) — 10 marks

Question 1 (2 marks) Answer: 6,308,020

• Teaching note: Read each part by place value. Six million = 6,000,000; three hundred and eight thousand = 308,000; twenty = 20. Add: $6{,}000{,}000 + 308{,}000 + 20 = 6{,}308{,}020$.
• Marking: 2 marks for correct numeral. 1 mark if digits are mostly correct but a zero placeholder is missing (e.g., 6,3820 or 6,038,020).
• Common mistake: forgetting the zero in the thousands place (writing 6,38,020 patterns) or writing 6,308,200 (swapping tens and hundreds).

Question 2 (2 marks) Answer: 200,000

• Teaching note: In 7,258,304, count places from the right: ones, tens, hundreds, thousands, ten thousands, hundred thousands. The digit 2 sits in the hundred thousands place, so its value is $2 \times 100{,}000 = 200{,}000$.
• Marking: 2 marks for 200,000. 1 mark for answering "hundred thousands" (correct place named but value not given).

Question 3 (2 marks) Answer: 4,763,000

• Teaching note: To round to the nearest thousand, look at the hundreds digit. In 4,762,589 the hundreds digit is 5, so round up: 4,762 thousands becomes 4,763 thousands → 4,763,000.
• Marking: 2 marks for 4,763,000. 1 mark for correct method with one slip (e.g., 4,762,000 shows rounding-down error).

Question 4 (2 marks) Answer: 13,800

• Teaching note: $46 \times 300 = 46 \times 3 \times 100$. First $46 \times 3 = 138$, then $\times 100$ shifts the digits two places: 13,800.
• Marking: 2 marks for 13,800. 1 mark for 1,380 (place-value shift error).

Question 5 (2 marks) Answer: 80

• Teaching note: Cancel zeros first: $72{,}000 \div 900 = 720 \div 9 = 80$. Removing one zero from each number keeps the answer the same because both are divided by 10.
• Marking: 2 marks for 80. 1 mark for 8 (missing a zero) or 800 (extra zero).

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Section B (Questions 6-15) — 30 marks

Question 6 (3 marks) Answer: 5,049,213 < 5,094,312 < 5,401,932 < 5,409,123

• Teaching note: Compare digits from the left. All begin with 5, then split into the 50-group and the 54-group. Within 50-group: 49 < 94, so 5,049,213 comes before 5,094,312. Within 54-group: 401 < 409, so 5,401,932 before 5,409,123.
• Marking: 3 marks for fully correct order; deduct 1 mark per misplaced number (maximum deduction 3).
• Common mistake: comparing only the first three digits and treating 5,409,123 as smallest because "4" appears early.

Question 7 (3 marks) Answer: Three million, seventy thousand, eight hundred and fifty

• Teaching note: Split into periods: 3 million | 070 thousand | 850. Say each period with its label; the 0 in the hundred thousands place means nothing is said before "seventy thousand".
• Marking: 3 marks fully correct in words. Deduct 1 mark for writing a digit instead of a word anywhere, or for "seven hundred thousand" misreading of 070.
• Common mistake: writing "seven hundred thousand" instead of "seventy thousand".

Question 8 (3 marks) Answer: 42

• Working:
  1. Brackets first: $27 - 18 = 9$
  2. Multiplication before division/addition, left to right: $4 \times 9 = 36$
  3. Division: $36 \div 6 = 6$
  4. Addition last: $36 + 6 = 42$
• Marking: 1 mark for evaluating the bracket correctly; 1 mark for correct order of × and ÷ before +; 1 mark for final answer 42.
• Common mistake: doing $36 + 4$ first (ignoring order of operations), giving 41 or similar.

Question 9 (3 marks) Answer: (a) 8,550,000 (b) 8,500,000

• Teaching note: (a) Nearest ten thousand: check the thousands digit (9), which is 5 or more, so round up: 8,549,607 → 8,550,000. (b) Nearest hundred thousand: check the ten thousands digit (4), which is less than 5, so round down: 8,500,000.
• Marking: (a) 1 mark. (b) 2 marks: 1 for identifying the correct checking digit, 1 for 8,500,000.
• Common mistake: rounding twice (rounding the already-rounded answer again).

Question 10 (3 marks) Expected visual: a seven-column place-value chart (Millions to Ones) showing digits 4 | 2 | 7 | 0 | 9 | 6 | 3, i.e., the number 4,270,963. Answer: (a) 4,270,963 (b) 70,000

• Teaching note: (a) Read one digit per column, using commas every three places from the right. (b) The ten thousands column holds 7, so its value is $7 \times 10{,}000 = 70{,}000$.
• Marking: (a) 1 mark. (b) 2 marks: 1 for locating the ten thousands digit, 1 for 70,000 (not just "7").
• Common mistake: giving the place name instead of the value, or reading the chart as 427,0963 without grouping.

Question 11 (3 marks) Answer: 90,000 seats

• Working: Total seats $= 250 \times 360 = 25 \times 36 \times 100 = 900 \times 100 = 90{,}000$.
• Marking: 1 mark for setting up $250 \times 360$; 1 mark for correct multiplication method; 1 mark for 90,000 with unit "seats".
• Common mistake: multiplying 250 × 36 and stopping at 9,000.

Question 12 (3 marks) Answer: 29 buses

• Working: $1{,}275 \div 45 = 28$ remainder 15, since $45 \times 28 = 1{,}260$ and $1{,}275 - 1{,}260 = 15$.
• Interpretation: The remaining 15 students still need a bus, so round up: $28 + 1 = 29$ buses.
• Marking: 1 mark for division set up; 1 mark for quotient 28 remainder 15; 1 mark for concluding 29 buses.
• Common mistake: answering 28 by ignoring the remainder. The remainder forces one more bus.

Question 13 (3 marks) Answer: 34,567

• Working: Number $=$ quotient $\times$ divisor $+$ remainder $= 34 \times 1{,}000 + 567 = 34{,}000 + 567 = 34{,}567$.
• Check: $34{,}567 \div 1{,}000 = 34$ remainder 567. ✓
• Marking: 1 mark for knowing the relationship (quotient × divisor + remainder); 1 mark for 34,000 + 567; 1 mark for 34,567.
• Common mistake: writing 34.567 (treating the remainder as decimals) instead of appending it as a whole-number remainder.

Question 14 (3 marks) Answer: 2,115,000 badges

• Working:
  1. Factory B $= 1{,}250{,}000 - 385{,}000 = 865{,}000$
  2. Total $= 1{,}250{,}000 + 865{,}000 = 2{,}115{,}000$
• Marking: 1 mark for finding Factory B's production; 1 mark for adding the two amounts; 1 mark for 2,115,000 with unit.
• Common mistake: adding 385,000 instead of subtracting to find Factory B.

Question 15 (3 marks) Answer: 97,530

• Working: An even number must end in an even digit. The only even digit available is 0, so 0 goes in the ones place. To make the number greatest, arrange the remaining digits from largest to smallest in the highest places: 9, 7, 5, 3, then 0 → 97,530.
• Marking: 1 mark for recognising the number must end in 0; 1 mark for ordering remaining digits in descending order; 1 mark for 97,530.
• Common mistake: forming 97,530 ending in 0 but placing digits randomly, or forming 97,531/97,535 (odd numbers).

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Section C (Questions 16-20) — 20 marks

Question 16 (4 marks) Answer: (a) One million, nine hundred and sixty-four thousand, three hundred and twenty (b) 2,000,000

• Teaching note: (a) Group as 1 million | 964 thousand | 320 and read each group with its label. (b) To round to the nearest hundred thousand, check the ten thousands digit: it is 6 (5 or more), so round the 9 up. This carries over: 1,964,320 → 2,000,000.
• Marking: (a) 2 marks: 1 for correct millions/thousands wording, 1 for the final "three hundred and twenty"; deduct 1 mark for any digit written as a numeral. (b) 2 marks: 1 for checking the ten thousands digit, 1 for 2,000,000.
• Common mistake: writing 1,900,000 (rounding down despite the 6) or 1,960,000 (wrong place value).

Question 17 (4 marks) Answer: 127

• Working in order:
  1. Brackets: $5 + 7 = 12$
  2. Multiplication: $8 \times 12 = 96$
  3. Division: $96 \div 12 = 8$
  4. Subtraction and addition, left to right: $120 - 8 = 112$, then $112 + 15 = 127$
• Marking: 1 mark for bracket step; 1 mark for × before ÷/+ order; 1 mark for handling − then + left to right; 1 mark for final answer 127.
• Common mistake: computing $120 - 8 \times 12$ as $(120-8) \times 12$, or adding 15 before subtracting 8 (which coincidentally also gives 127 here — require the ordered working to be shown for full marks).

Question 18 (4 marks) Answer: $13,750

• Working:
  1. Money after buying the car: \95{,}000 - $68{,}500 = $26{,}500$
  2. Money after repairs: \26{,}500 - $12{,}750 = $13{,}750$
• Alternative: Total spent = \68{,}500 + $12{,}750 = $81{,}250$; then$$95{,}000 - $81{,}250 = $13{,}750$.
• Marking: 1 mark for a correct first subtraction (or total spending); 1 mark for the second subtraction; 1 mark for accurate arithmetic; 1 mark for final answer with the dollar sign/$ unit.
• Common mistake: subtracting only one expense, giving $26,500.

Question 19 (4 marks) Answer: 300

• Working (work backwards, reversing each step):
  1. Reverse "subtract 4,500": $25{,}500 + 4{,}500 = 30{,}000$
  2. Reverse "multiply by 100": $30{,}000 \div 100 = 300$
• Check forwards: $300 \times 100 = 30{,}000$; $30{,}000 - 4{,}500 = 25{,}500$. ✓
• Marking: 1 mark for reversing the subtraction (adding); 1 mark for reversing the multiplication (dividing); 1 mark for 300; 1 mark for a verification check or clearly labelled reverse steps.
• Common mistake: repeating the forward operations (subtracting 4,500 and dividing) instead of reversing them.

Question 20 (4 marks) Answer: (a) 611,205 (b) 610,000

• Working:
  1. Larger number $=$ smaller $+$ difference $= 486{,}205 + 125{,}000 = 611{,}205$
  2. Nearest ten thousand: check the thousands digit of 611,205, which is 1 (less than 5), so round down: $611{,}205 \rightarrow 610{,}000$
• Marking: (a) 2 marks: 1 for recognising addition is needed, 1 for 611,205. (b) 2 marks: 1 for checking the thousands digit, 1 for 610,000.
• Common mistake: subtracting 125,000 (confusing which number is larger), or rounding to

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TuitionGoWhere Practice Paper - Mathematics Primary 5

TuitionGoWhere Practice Paper (AI)

Answer Key and Marking Scheme - Whole Numbers Practice Paper, Version 2 of 5

Total Marks: 60

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Section A (Questions 1-5) — 10 marks

Question 1 (2 marks) Answer: 6,308,020

• Teaching note: Read each part by place value. Six million = 6,000,000; three hundred and eight thousand = 308,000; twenty = 20. Add: $6{,}000{,}000 + 308{,}000 + 20 = 6{,}308{,}020$.
• Marking: 2 marks for correct numeral. 1 mark if digits are mostly correct but a zero placeholder is missing (e.g., 6,3820 or 6,038,020).
• Common mistake: forgetting the zero in the thousands place or writing 6,308,200 (swapping tens and hundreds).

Question 2 (2 marks) Answer: 200,000

• Teaching note: In 7,258,304, count places from the right: ones, tens, hundreds, thousands, ten thousands, hundred thousands. The digit 2 sits in the hundred thousands place, so its value is $2 \times 100{,}000 = 200{,}000$.
• Marking: 2 marks for 200,000. 1 mark for answering "hundred thousands" (correct place named but value not given).

Question 3 (2 marks) Answer: 4,763,000

• Teaching note: To round to the nearest thousand, look at the hundreds digit. In 4,762,589 the hundreds digit is 5, so round up: 4,762 thousands becomes 4,763 thousands → 4,763,000.
• Marking: 2 marks for 4,763,000. 1 mark for correct method with one slip (e.g., 4,762,000 shows rounding-down error).

Question 4 (2 marks) Answer: 13,800

• Teaching note: $46 \times 300 = 46 \times 3 \times 100$. First $46 \times 3 = 138$, then $\times 100$ shifts the digits two places: 13,800.
• Marking: 2 marks for 13,800. 1 mark for 1,380 (place-value shift error).

Question 5 (2 marks) Answer: 80

• Teaching note: Cancel zeros first: $72{,}000 \div 900 = 720 \div 9 = 80$. Removing one zero from each number keeps the answer the same because both are divided by 10.
• Marking: 2 marks for 80. 1 mark for 8 (missing a zero) or 800 (extra zero).

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Section B (Questions 6-15) — 30 marks

Question 6 (3 marks) Answer: 5,049,213 < 5,094,312 < 5,401,932 < 5,409,123

• Teaching note: Compare digits from the left. All begin with 5, then split into the 50-group and the 54-group. Within 50-group: 49 < 94, so 5,049,213 comes before 5,094,312. Within 54-group: 401 < 409, so 5,401,932 before 5,409,123.
• Marking: 3 marks for fully correct order; deduct 1 mark per misplaced number (maximum deduction 3).
• Common mistake: comparing only the first three digits and treating 5,409,123 as smallest because "4" appears early.

Question 7 (3 marks) Answer: Three million, seventy thousand, eight hundred and fifty

• Teaching note: Split into periods: 3 million | 070 thousand | 850. Say each period with its label; the 0 in the hundred thousands place means nothing is said before "seventy thousand".
• Marking: 3 marks fully correct in words. Deduct 1 mark for writing a digit instead of a word anywhere, or for a "seven hundred thousand" misreading of 070.
• Common mistake: writing "seven hundred thousand" instead of "seventy thousand".

Question 8 (3 marks) Answer: 42

• Working:
  1. Brackets first: $27 - 18 = 9$
  2. Multiplication before division/addition, left to right: $4 \times 9 = 36$
  3. Division: $36 \div 6 = 6$
  4. Addition last: $36 + 6 = 42$
• Marking: 1 mark for evaluating the bracket correctly; 1 mark for correct order of × and ÷ before +; 1 mark for final answer 42.
• Common mistake: doing $36 + 4$ first (ignoring order of operations), giving 41 or similar.

Question 9 (3 marks) Answer: (a) 8,550,000 (b) 8,500,000

• Teaching note: (a) Nearest ten thousand: check the thousands digit (9), which is 5 or more, so round up: 8,549,607 → 8,550,000. (b) Nearest hundred thousand: check the ten thousands digit (4), which is less than 5, so round down: 8,500,000.
• Marking: (a) 1 mark. (b) 2 marks: 1 for identifying the correct checking digit, 1 for 8,500,000.
• Common mistake: rounding twice (rounding the already-rounded answer again).

Question 10 (3 marks) Expected visual: a seven-column place-value chart (Millions to Ones) showing digits 4 | 2 | 7 | 0 | 9 | 6 | 3, i.e., the number 4,270,963. Answer: (a) 4,270,963 (b) 70,000

• Teaching note: (a) Read one digit per column, using commas every three places from the right. (b) The ten thousands column holds 7, so its value is $7 \times 10{,}000 = 70{,}000$.
• Marking: (a) 1 mark. (b) 2 marks: 1 for locating the ten thousands digit, 1 for 70,000 (not just "7").
• Common mistake: giving the place name instead of the value, or reading the chart as 427,0963 without grouping.

Question 11 (3 marks) Answer: 90,000 seats

• Working: Total seats $= 250 \times 360 = 25 \times 36 \times 100 = 900 \times 100 = 90{,}000$.
• Marking: 1 mark for setting up $250 \times 360$; 1 mark for correct multiplication method; 1 mark for 90,000 with unit "seats".
• Common mistake: multiplying 250 × 36 and stopping at 9,000.

Question 12 (3 marks) Answer: 29 buses

• Working: $1{,}275 \div 45 = 28$ remainder 15, since $45 \times 28 = 1{,}260$ and $1{,}275 - 1{,}260 = 15$.
• Interpretation: The remaining 15 students still need a bus, so round up: $28 + 1 = 29$ buses.
• Marking: 1 mark for division set up; 1 mark for quotient 28 remainder 15; 1 mark for concluding 29 buses.
• Common mistake: answering 28 by ignoring the remainder. The remainder forces one more bus.

Question 13 (3 marks) Answer: 34,567

• Working: Number $=$ quotient $\times$ divisor $+$ remainder $= 34 \times 1{,}000 + 567 = 34{,}000 + 567 = 34{,}567$.
• Check: $34{,}567 \div 1{,}000 = 34$ remainder 567. ✓
• Marking: 1 mark for knowing the relationship (quotient × divisor + remainder); 1 mark for 34,000 + 567; 1 mark for 34,567.
• Common mistake: writing 34.567 (treating the remainder as decimals) instead of appending it as a whole-number remainder.

Question 14 (3 marks) Answer: 2,115,000 badges

• Working:
  1. Factory B $= 1{,}250{,}000 - 385{,}000 = 865{,}000$
  2. Total $= 1{,}250{,}000 + 865{,}000 = 2{,}115{,}000$
• Marking: 1 mark for finding Factory B's production; 1 mark for adding the two amounts; 1 mark for 2,115,000 with unit.
• Common mistake: adding 385,000 instead of subtracting to find Factory B.

Question 15 (3 marks) Answer: 97,530

• Working: An even number must end in an even digit. The only even digit available is 0, so 0 goes in the ones place. To make the number greatest, arrange the remaining digits from largest to smallest in the highest places: 9, 7, 5, 3, then 0 → 97,530.
• Marking: 1 mark for recognising the number must end in 0; 1 mark for ordering remaining digits in descending order; 1 mark for 97,530.
• Common mistake: forming 97,530 ending in 0 but placing digits randomly, or forming 97,531/97,535 (odd numbers).

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Section C (Questions 16-20) — 20 marks

Question 16 (4 marks) Answer: (a) One million, nine hundred and sixty-four thousand, three hundred and twenty (b) 2,000,000

• Teaching note: (a) Group as 1 million | 964 thousand | 320 and read each group with its label. (b) To round to the nearest hundred thousand, check the ten thousands digit: it is 6 (5 or more), so round the 9 up. This carries over: 1,964,320 → 2,000,000.
• Marking: (a) 2 marks: 1 for correct millions/thousands wording, 1 for the final "three hundred and twenty"; deduct 1 mark for any digit written as a numeral. (b) 2 marks: 1 for checking the ten thousands digit, 1 for 2,000,000.
• Common mistake: writing 1,900,000 (rounding down despite the 6) or 1,960,000 (wrong place value).

Question 17 (4 marks) Answer: 127

• Working in order:
  1. Brackets: $5 + 7 = 12$
  2. Multiplication: $8 \times 12 = 96$
  3. Division: $96 \div 12 = 8$
  4. Subtraction and addition, left to right: $120 - 8 = 112$, then $112 + 15 = 127$
• Marking: 1 mark for bracket step; 1 mark for × before ÷/+ order; 1 mark for handling − then + left to right; 1 mark for final answer 127.
• Common mistake: computing $120 - 8 \times 12$ as $(120-8) \times 12$, or adding 15 before subtracting 8 (which coincidentally also gives 127 here — require the ordered working to be shown for full marks).

Question 18 (4 marks) Answer: $13,750

• Working:
  1. Money after buying the car: \95{,}000 - $68{,}500 = $26{,}500$
  2. Money after repairs: \26{,}500 - $12{,}750 = $13{,}750$
• Alternative: Total spent = \68{,}500 + $12{,}750 = $81{,}250$; then$$95{,}000 - $81{,}250 = $13{,}750$.
• Marking: 1 mark for a correct first subtraction (or total spending); 1 mark for the second subtraction; 1 mark for accurate arithmetic; 1 mark for final answer with the dollar sign/$ unit.
• Common mistake: subtracting only one expense, giving $26,500.

Question 19 (4 marks) Answer: 300

• Working (work backwards, reversing each step):
  1. Reverse "subtract 4,500": $25{,}500 + 4{,}500 = 30{,}000$
  2. Reverse "multiply by 100": $30{,}000 \div 100 = 300$
• Check forwards: $300 \times 100 = 30{,}000$; $30{,}000 - 4{,}500 = 25{,}500$. ✓
• Marking: 1 mark for reversing the subtraction (adding); 1 mark for reversing the multiplication (dividing); 1 mark for 300; 1 mark for a verification check or clearly labelled reverse steps.
• Common mistake: repeating the forward operations (subtracting 4,500 and dividing) instead of reversing them.

Question 20 (4 marks) Answer: (a) 611,205 (b) 610,000

• Working:
  1. Larger number $=$ smaller $+$ difference $= 486{,}205 + 125{,}000 = 611{,}205$
  2. Nearest ten thousand: check the thousands digit of 611,205, which is 1 (less than 5), so round down: $611{,}205 \rightarrow 610{,}000$
• Marking: (a) 2 marks: 1 for recognising addition is needed, 1 for 611,205. (b) 2 marks: 1 for checking the thousands digit, 1 for 610,000.
• Common mistake: subtracting 125,000 (confusing which number is larger), or rounding to 611,000 (rounding to the nearest thousand instead of the nearest ten thousand).

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END OF ANSWER KEY

Total: 60 marks