Primary 6 PSLE Mathematics Measurement Quiz

Primary 6 PSLE Mathematics Quiz — Measurement (Answer Key)

Total Marks: 40

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Section A: Multiple Choice (1 mark each)

1. Answer: (C) 2 m

Explanation: A standard classroom door is about 2 metres tall. 2 cm is far too small (about a thumb width), 20 cm is too small (a ruler length), and 20 m is far too large (about 6 storeys). This tests estimation skills with standard units. Common mistake: Choosing (B) by confusing centimetres with metres.

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2. Answer: (B) 60 ℓ

Step-by-step working:

• Volume = length × width × height
• Volume = 50 cm × 40 cm × 30 cm = 60 000 cm³
• Since 1 ℓ = 1000 cm³: 60 000 ÷ 1000 = 60 ℓ

Concept: Capacity is volume expressed in litres. The conversion 1 ℓ = 1000 cm³ is essential for volume-capacity conversions. Common mistake: Forgetting to divide by 1000, giving 60 000 ℓ (D).

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3. Answer: (B) 7

Step-by-step working:

• Number of pieces = Total length ÷ Length per piece
• 5.6 ÷ 0.8 = 56 ÷ 8 = 7

Concept: Division with decimals. Eliminate decimals by multiplying both numbers by 10, then divide. Common mistake: Answering 0.7 by dividing incorrectly.

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4. Answer: (C) 20 000 g

Step-by-step working:

• Mass of 8 packets = 2.5 kg × 8 = 20 kg
• Convert to grams: 20 kg × 1000 = 20 000 g

Concept: Two-step conversion — first find total mass, then convert kg to g using 1 kg = 1000 g. Common mistake: Converting before multiplying (2.5 × 1000 = 2500, then × 8 = 20 000 g gives same answer, but 2500 g × 8 = 20 000 g is correct too; error is stopping at 2500 g or 2000 g).

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5. Answer: (A) 3 h 35 min

Step-by-step working:

• From 09:45 to 13:45 would be exactly 4 hours
• But we stop at 13:20, which is 25 minutes before 13:45
• 4 hours − 25 minutes = 3 hours 35 minutes

Alternative method:

• 09:45 to 13:20
• Hours: 13 − 9 = 4 hours, but minutes: 20 − 45 (can't do)
• Borrow 1 hour: 3 hours + (60 + 20) − 45 = 3 hours + 35 minutes = 3 h 35 min

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Section B: Short Answer (2 marks each)

6. Answer: 3450 m

Step-by-step working:

• 1 km = 1000 m
• 3.45 km = 3.45 × 1000 = 3450 m

Concept: When converting from larger to smaller units, multiply. The decimal point moves 3 places right. Marking: 1 mark for correct method, 1 mark for correct answer.

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7. Answer: 1250 ml

Step-by-step working:

• 1 ℓ = 1000 ml
• 1.25 ℓ = 1.25 × 1000 = 1250 ml

Concept: Litres to millilitres conversion. "Milli-" means one-thousandth, so 1 ℓ = 1000 ml. Marking: 1 mark for correct method, 1 mark for correct answer.

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8. Answer: 30 000 cm³

Step-by-step working:

• Volume of cuboid = base area × height
• Volume = 1200 cm² × 25 cm = 30 000 cm³

Concept: Volume = area of base × perpendicular height. This works for any prism. Marking: 1 mark for correct formula, 1 mark for correct answer.

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9. Answer: 18 kg

Step-by-step working:

• Total mass = 3.6 kg × 5
• 3.6 × 5 = (3 × 5) + (0.6 × 5) = 15 + 3 = 18 kg

Concept: Decimal multiplication. Break into whole and decimal parts for easier calculation. Marking: 1 mark for correct method, 1 mark for correct answer.

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10. Answer: 168 minutes

Step-by-step working:

• 2 hours = 2 × 60 = 120 minutes
• Total = 120 + 48 = 168 minutes

Concept: Time conversion. 1 hour = 60 minutes (not 100!). Common mistake: Converting to decimal (2.48) and getting confused. Marking: 1 mark for converting hours, 1 mark for final answer.

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11. Answer: 21 cm

Step-by-step working:

• Perimeter of square = 4 × side length
• 4 × side = 84 cm
• Side = 84 ÷ 4 = 21 cm

Concept: In a square, all four sides are equal. Perimeter is the total distance around the shape. From the diagram with perimeter 84 cm and four equal sides marked, we divide by 4. Marking: 1 mark for correct division setup, 1 mark for correct answer.

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12. Answer: 240 cm³

Step-by-step working:

• Volume of cuboid = length × width × height
• Volume = 8 cm × 6 cm × 5 cm
• 8 × 6 = 48; 48 × 5 = 240 cm³

Concept: Volume of a cuboid formula. Multiply three dimensions. Marking: 1 mark for correct formula/substitution, 1 mark for correct answer.

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13. Answer: 80 km/h

Step-by-step working:

• Average speed = Total distance ÷ Total time
• Speed = 240 km ÷ 3 h = 80 km/h

Concept: Speed is distance per unit time. Units must match (km and h give km/h). Marking: 1 mark for correct formula, 1 mark for correct answer.

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14. Answer: 7 minutes 30 seconds (or 7 min 30 s)

Step-by-step working:

• 1 minute = 60 seconds
• 450 ÷ 60 = 7 remainder 30
• So 450 s = 7 minutes 30 seconds

Concept: Division with remainder for time conversion. 7 × 60 = 420, and 450 − 420 = 30. Marking: 1 mark for correct division (7 min), 1 mark for remainder converted correctly.

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15. (a) Answer: 7 cm

Step-by-step working:

• Radius = diameter ÷ 2
• Radius = 14 cm ÷ 2 = 7 cm

Concept: Diameter passes through the centre; radius is half the diameter. From the diagram showing diameter 14 cm across the circular face. Marking: 1 mark for correct answer.

15. (b) Answer: 3080 cm³

Step-by-step working:

• Volume of cylinder = $\pi r^2 h$
• Volume = $\frac{22}{7} \times 7 \times 7 \times 20$
• = $\frac{22}{7} \times 49 \times 20$
• = $22 \times 7 \times 20$ (since 49 ÷ 7 = 7)
• = $154 \times 20$ = 3080 cm³

Concept: The formula $\pi r^2 h$ finds the space inside a cylinder. The diagram shows radius 7 cm (from part a) and height 20 cm. Using $\frac{22}{7}$ simplifies nicely since r = 7. Marking: 1 mark for correct formula and substitution, 1 mark for correct calculation.

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Section C: Problem Solving (3 marks each)

16. Answer: 60 ℓ

Step-by-step working:

Method: Using fractions

• Difference in water level: $\frac{3}{4} - \frac{1}{2} = \frac{3}{4} - \frac{2}{4} = \frac{1}{4}$
• So $\frac{1}{4}$ of tank = 15 ℓ
• Full tank: 15 ℓ × 4 = 60 ℓ

Concept: The 15 ℓ poured out represents the difference between $\frac{3}{4}$-full and $\frac{1}{2}$-full. Find this difference as a fraction of the whole, then scale up. Marking scheme: [1] Correct fraction difference, [1] Correct unit value, [1] Correct final answer.

Common mistake: Adding 15 to original amount without finding what fraction 15 ℓ represents.

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17. Answer: 54 cm

Step-by-step working:

From the diagram: rectangle with length 14 cm, width 10 cm, semicircle on top with diameter 14 cm (radius 7 cm).

The perimeter of the composite figure includes:

• Three sides of the rectangle (the top side is covered by semicircle diameter, not part of perimeter)
• The curved part of the semicircle

Rectangle sides in perimeter:

• Two widths: 10 cm + 10 cm = 20 cm
• One length (bottom): 14 cm

Semicircle arc length:

• Circumference of full circle = $2\pi r = 2 \times \frac{22}{7} \times 7 = 44$ cm
• Semicircle arc = $44 \div 2 = 22$ cm

Total perimeter = 20 + 14 + 22 = 56 cm

Wait — let me recheck: The figure shows semicircle ON TOP of rectangle. The perimeter = bottom (14) + two sides (10 + 10) + semicircle arc.

Actually, re-reading: if semicircle is attached to the 14 cm side, the perimeter includes:

• The semicircle arc: $\frac{1}{2} \times \pi \times d = \frac{1}{2} \times \frac{22}{7} \times 14 = 22$ cm
• The two vertical sides: 10 cm + 10 cm = 20 cm
• The bottom side: 14 cm

Total = 22 + 20 + 14 = 56 cm

Concept: Perimeter is the outer boundary only. The diameter line where semicircle meets rectangle is internal, not part of perimeter. Must identify which sides are exposed. Marking scheme: [1] Correct identification of perimeter components, [1] Correct semicircle arc calculation, [1] Correct final answer.

Common mistake: Including the diameter (14 cm) in perimeter, giving 70 cm; or forgetting one side.

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18. (a) Answer: 84 000 cm³

Step-by-step working:

• Volume of water = length × width × water height
• = 60 cm × 40 cm × 35 cm
• = 2400 × 35
• = 84 000 cm³

Concept: The water forms a smaller cuboid with the tank's base dimensions but only 35 cm height. Marking: [1] correct substitution, [1] correct answer.

18. (b) Answer: 36 ℓ

Step-by-step working:

• Empty height = 50 − 35 = 15 cm
• Volume of empty space = 60 × 40 × 15 = 36 000 cm³
• Convert to litres: 36 000 ÷ 1000 = 36 ℓ

Alternative method:

• Total tank volume = 60 × 40 × 50 = 120 000 cm³ = 120 ℓ
• Water volume = 84 000 cm³ = 84 ℓ
• Empty = 120 − 84 = 36 ℓ

Concept: Either find empty space directly or subtract water from total. Both methods valid. Marking: [1] correct empty volume in cm³ or method, [1] correct conversion to litres, [1] correct final answer.

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19. Answer: 1.15 kg (or 1$\frac{3}{20}$ kg or $\frac{23}{20}$ kg)

Step-by-step working:

• Total mass of oil = 5.75 kg
• Mass used = 2.3 kg
• Remaining oil = 5.75 − 2.3 = 3.45 kg
• Mass in each small bottle = 3.45 ÷ 3 = 1.15 kg

Checking: 1.15 × 3 = 3.45 ✓

Concept: Multi-step word problem requiring subtraction then division. The diagram shows 5 bottles total → used portion → redistribution into 3 equal shares. Marking scheme: [1] Correct remaining mass, [1] Correct division by 3, [1] Correct final answer with unit.

Common mistake: Dividing 5.75 by 3 directly, ignoring the "used 2.3 kg" information.

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20. Answer: 280 km

Step-by-step working:

Journey A to B:

• Time = 2 h 15 min = 2.25 h (or $2\frac{1}{4}$ h)
• Distance = speed × time = 80 × 2.25 = 80 × $\frac{9}{4}$ = $\frac{720}{4}$ = 180 km

Alternative: 80 × 2 = 160; 80 × 0.25 = 20; total = 180 km

Journey B to C:

• Time = 1 h 40 min = 1$\frac{2}{3}$ h = $\frac{5}{3}$ h
• Distance = 60 × $\frac{5}{3}$ = $\frac{300}{3}$ = 100 km

Alternative conversion: 1 h 40 min = 100 minutes = $\frac{100}{60}$ h = $\frac{5}{3}$ h

Total distance:

• 180 km + 100 km = 280 km

Concept: Distance = speed × time. Must convert mixed time units to hours (or all to minutes, then adjust). The diagram shows two segments with different speeds and times. Marking scheme: [1] Correct distance A to B, [1] Correct distance B to C, [1] Correct total.

Common mistakes:

• Using 2.15 instead of 2.25 for 2 h 15 min
• Using 1.4 instead of 1$\frac{2}{3}$ for 1 h 40 min
• Forgetting to add distances at the end

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END OF ANSWER KEY

Section Totals: A: 5 marks | B: 20 marks | C: 15 marks | Total: 40 marks