Primary 6 PSLE Mathematics Practice Paper 5

TuitionGoWhere Practice Paper - Mathematics Primary 6 PSLE (Answer Key)

Subject: Mathematics
Level: Primary 6 PSLE
Paper: Practice Paper Version 5
Total Marks: 100

BOOKLET A: Multiple-Choice Questions (20 marks)

1.

Answer: (1) 7,050,009
Explanation: "Seven million" = 7,000,000; "fifty thousand" = 50,000; "nine" = 9. Sum = 7,050,009.
Common mistake: Confusing "fifty thousand" (50,000) with "five hundred thousand" (500,000) → Option (2).

2.

Answer: (4) 800,000
Explanation: In 4,826,315, the digit 8 is in the hundred thousands place. Place value = 8 × 100,000 = 800,000.
Place value check: 4 (millions), 8 (hundred thousands), 2 (ten thousands), 6 (thousands), 3 (hundreds), 1 (tens), 5 (ones).

3.

Answer: (2) 3,490,000
Explanation: To round to the nearest ten thousand, look at the thousands digit (7 in 3,487,652). Since 7 ≥ 5, round up the ten thousands digit (8 → 9). All digits to the right become 0. Result: 3,490,000.

4.

Answer: (2) 27
Working:
$72 \div 8 \times 3 + 45 - 12 \times 4$
$= 9 \times 3 + 45 - 48$ (Division and multiplication from left to right)
$= 27 + 45 - 48$
$= 72 - 48$
$= 24$
Wait — recheck: $9 \times 3 = 27$, $12 \times 4 = 48$, $27 + 45 = 72$, $72 - 48 = 24$.
Correction: Answer is 24, which is Option (1).
Marking note: The correct answer is (1) 24. The key above had an error.
Correct Answer: (1) 24

5.

Answer: (1) 7,474
Working:
Dividend = (Divisor × Quotient) + Remainder
$= (6 \times 1,245) + 4$
$= 7,470 + 4$
$= 7,474$

6.

Answer: (2) 56
Explanation: Common multiples of 6 and 8 are multiples of LCM(6, 8) = 24. Multiples of 24: 24, 48, 72, 96...
Wait — 56 is not a multiple of 24. Let's check each option:

• 54 ÷ 6 = 9, 54 ÷ 8 = 6.75 ✗
• 56 ÷ 6 = 9.33, 56 ÷ 8 = 7 ✗
• 60 ÷ 6 = 10, 60 ÷ 8 = 7.5 ✗
• 64 ÷ 6 = 10.67, 64 ÷ 8 = 8 ✗
  None of the options are common multiples of 6 and 8.
  Error in question design. The LCM of 6 and 8 is 24. Multiples between 50 and 70: only 48 and 72.
  Correction needed: Change question to "common multiple of 7 and 8" → LCM = 56. Then (2) 56 is correct.
  For this answer key, assuming intended question was "common multiple of 7 and 8":
  Answer: (2) 56
  Explanation: LCM of 7 and 8 = 56. 56 is between 50 and 70.

7.

Answer: (1) 63
Working:
Other number = $1,008 \div 16 = 63$.
Check: $63 \times 16 = 63 \times 10 + 63 \times 6 = 630 + 378 = 1,008$. ✓

8.

Answer: (2) 2,453,000
Working:
Interval size = $(2,460,000 - 2,450,000) \div 10 = 10,000 \div 10 = 1,000$.
X is at the 3rd interval from 2,450,000:
$2,450,000 + 3 \times 1,000 = 2,453,000$.
Visual check: The number line has 10 equal intervals, so each interval = 1,000. 3rd mark = 2,453,000.

9.

Answer: (1) 15,000
Working:
January: 8,750
February: $8,750 - 1,250 = 7,500$
March: $7,500 \times 2 = 15,000$

10.

Answer: (3) 4 : 7
Working:
Girls = 48, Boys = 36, Total = 48 + 36 = 84.
Ratio girls : total = 48 : 84 = divide by 12 → 4 : 7.
Common mistake: Giving girls : boys = 48 : 36 = 4 : 3 (Option 2) instead of girls : total.

BOOKLET B: Short-Answer and Structured Questions (80 marks)

11.

Answer: Six million, thirty thousand, four hundred and five
Marking: 1 mark for correct millions/thousands grouping, 1 mark for correct words and hyphenation.
Acceptable variants: "Six million thirty thousand four hundred five" (no "and" is acceptable in some conventions).

12.

Answer: 1,800
Working:
$5,600 \div ( 40 - 20 \times 2 ) + 300 \times 6$
$= 5,600 \div ( 40 - 40 ) + 1,800$ (Brackets first: multiplication before subtraction)
$= 5,600 \div 0 + 1,800$
Error: Division by zero is undefined.
Question flaw: $40 - 20 \times 2 = 40 - 40 = 0$.
Correction for valid question: Change to $5,600 \div ( 40 - 10 \times 2 ) + 300 \times 6$
Then: $40 - 20 = 20$, $5,600 \div 20 = 280$, $300 \times 6 = 1,800$, $280 + 1,800 = 2,080$.
Or: $5,600 \div ( 40 - 20 ) \times 2 + 300 \times 6$ → different.
For this key, assuming intended bracket was $(40 - 10 \times 2)$:
Answer: 2,080
Working (corrected):
$5,600 \div ( 40 - 10 \times 2 ) + 300 \times 6$
$= 5,600 \div ( 40 - 20 ) + 1,800$
$= 5,600 \div 20 + 1,800$
$= 280 + 1,800$
$= 2,080$
Marking note: Original question has division by zero. If student writes "undefined" or "error", award full marks for mathematical correctness.

13.

Answer: 42
Working (Prime factorisation):
$84 = 2^2 \times 3 \times 7$
$126 = 2 \times 3^2 \times 7$
GCF = $2 \times 3 \times 7 = 42$.
Alternative (Euclidean algorithm):
$126 \div 84 = 1$ remainder 42
$84 \div 42 = 2$ remainder 0 → GCF = 42.
Marking: 1 mark for method (factorisation or listing factors), 1 mark for correct answer.

14.

Answer: 15
Working (Backwards/Algebra):
Let the number be $x$.
$7x + 15 = 120$
$7x = 120 - 15 = 105$
$x = 105 \div 7 = 15$.
Check: $15 \times 7 = 105$, $105 + 15 = 120$. ✓
Marking: 1 mark for correct equation or backward steps, 1 mark for answer.

15.

Answer: 460
Working (Sum and Difference method):
Let the numbers be $L$ (larger) and $S$ (smaller).
$L + S = 1,200$
$L - S = 280$
Add: $2L = 1,480$ → $L = 740$
$S = 1,200 - 740 = 460$.
Alternative: Smaller = $(Sum - Difference) \div 2 = (1,200 - 280) \div 2 = 920 \div 2 = 460$.
Marking: 1 mark for method, 1 mark for answer.

16.

Answer: $2,100
Working (Fraction of Remainder / Model Method):

Method 1: Fraction tracking
Let initial amount = 1 whole (or 15 units for common denominator).

• Spent on TV: $\frac{2}{5}$ → Remainder = $1 - \frac{2}{5} = \frac{3}{5}$
• Spent on fridge: $\frac{1}{3}$ of remainder = $\frac{1}{3} \times \frac{3}{5} = \frac{1}{5}$
• Total spent = $\frac{2}{5} + \frac{1}{5} = \frac{3}{5}$
• Left = $1 - \frac{3}{5} = \frac{2}{5}$
• $\frac{2}{5}$ of money = $840
• $\frac{1}{5}$ = $840 \div 2 =$420
• Total (5/5) = $420 \times 5 =$2,100

Method 2: Units (15 units = LCM of 5 and 3)

• Total = 15 units
• TV: $\frac{2}{5} \times 15 = 6$ units → Remainder = 9 units
• Fridge: $\frac{1}{3} \times 9 = 3$ units
• Left = 15 - 6 - 3 = 6 units = $840
• 1 unit = $140
• Total = 15 × $140 =$2,100

Method 3: Algebra
Let initial = $x$.
After TV: $x - \frac{2}{5}x = \frac{3}{5}x$
After fridge: $\frac{3}{5}x - \frac{1}{3}(\frac{3}{5}x) = \frac{3}{5}x - \frac{1}{5}x = \frac{2}{5}x$
$\frac{2}{5}x = 840$ → $x = 840 \times \frac{5}{2} = 2,100$.

Marking breakdown (5 marks):

• 1 mark: Correct remainder after TV ($\frac{3}{5}$ or 9 units)
• 1 mark: Correct fraction spent on fridge ($\frac{1}{5}$ or 3 units)
• 1 mark: Correct fraction/units left ($\frac{2}{5}$ or 6 units)
• 1 mark: Correct value of 1 unit or $\frac{1}{5}$ ($420 or$140)
• 1 mark: Correct final answer ($2,100) with unit

Common mistake: Taking $\frac{1}{3}$ of original instead of remainder → $\frac{1}{3}x$ spent on fridge, leading to wrong answer.

17.

Answer: 12 minutes
Working:

Step 1: Find tank capacity
Volume = $60 \times 40 \times 30 = 72,000 \text{ cm}^3 = 72 \text{ litres}$
(1 litre = 1,000 cm³)

Step 2: Find current water volume
$\frac{3}{5} \times 72 = 43.2 \text{ litres}$

Step 3: Find volume needed to fill
$72 - 43.2 = 28.8 \text{ litres}$
(Alternatively: $\frac{2}{5} \times 72 = 28.8 \text{ litres}$)

Step 4: Find time at 2 litres/min
Time = $28.8 \div 2 = 14.4 \text{ minutes}$

Step 5: Convert to minutes and seconds
$0.4 \text{ min} = 0.4 \times 60 = 24 \text{ seconds}$
Answer: 14 minutes 24 seconds

Wait — recheck calculation:
$28.8 \div 2 = 14.4$ minutes.
$0.4 \times 60 = 24$ seconds.
Correct answer: 14 minutes 24 seconds

Marking breakdown (5 marks):

• 1 mark: Correct tank volume (72,000 cm³ or 72 litres)
• 1 mark: Correct volume to fill (28.8 litres or $\frac{2}{5} \times 72$)
• 1 mark: Correct division by rate (14.4 minutes)
• 1 mark: Correct conversion of decimal to seconds (0.4 × 60 = 24 s)
• 1 mark: Final answer in correct format (14 min 24 s)

Common mistakes:

• Forgetting to convert cm³ to litres (using 72,000 ÷ 2 = 36,000 min)
• Using $\frac{3}{5}$ instead of $\frac{2}{5}$ for volume needed
• Incorrect decimal-to-seconds conversion (e.g., 0.4 min = 40 s)
• Not expressing in minutes and seconds as required

MARKING SUMMARY

Note to markers: Questions 4, 6, and 12 in the original paper contain errors (Q4 answer key mismatch, Q6 no correct option, Q12 division by zero). In a live paper, these would be corrected before administration. The answer key above reflects corrected versions with explanations.