Higher June 2018 Paper 2 Q24
24 A tank is a cuboid measuring 50 cm by 35 cm by 20 cm
All lengths are to the nearest centimetre.
A container has a capacity of exactly 34 litres.
1 litre = 1000 cm\(^3\)
Which has the greater capacity?
Tick one box.
- Tank
- Container
- Cannot tell
Show working to support your answer. [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| Any product of three valid dimensions that would give a volume \(\lt\) 34 000 or any product of three valid dimensions that would give a volume \(\gt\) 34 000 | M1 | eg \(49.5 \times 34.5 \times 19.5\) or \(50.5 \times 35.5 \times 20.5\) or \(50 \times 35 \times 20\) ignore any evaluations of products |
| Any product of three valid dimensions that would give a volume \(\lt\) 34 000 and any product of three valid dimensions that would give a volume \(\gt\) 34 000 | M1dep | eg \(49.5 \times 34.5 \times 19.5\) and \(50.5 \times 35.5 \times 20.5\) ignore any evaluations of products |
| \(34 \times 1000\) or 34 000 | M1 | converts to cm\(^3\) |
| their volume \(\lt\) 34 000 and their volume \(\gt\) 34 000 and 34 000 and ticks Cannot tell | A1 | both volumes in cm\(^3\) must see working for M3 answers for their volumes must be seen and be correct or rounded or truncated to at least 2 sf (unless 34 000 to 2 sf when must be to at least 3 sf) |
| Alternative method 2 | ||
| Any product of three valid dimensions that would give a volume \(\lt\) 34 000 or any product of three valid dimensions that would give a volume \(\gt\) 34 000 | M1 | eg \(49.5 \times 34.5 \times 19.5\) or \(50.5 \times 35.5 \times 20.5\) or \(50 \times 35 \times 20\) ignore any evaluations of products |
| Any product of three valid dimensions that would give a volume \(\lt\) 34 000 and any product of three valid dimensions that would give a volume \(\gt\) 34 000 | M1dep | eg \(49.5 \times 34.5 \times 19.5\) and \(50.5 \times 35.5 \times 20.5\) ignore any evaluations of products |
| one of their volumes \(\div\) 1000 | M1dep | dep on first M1 converts to litres |
| their volume \(\lt\) 34 and their volume \(\gt\) 34 and ticks Cannot tell | A1 | both volumes in litres must see working for M3 answers for their volumes must be seen and be correct or rounded or truncated to at least 2 sf (unless 34 000 to 2 sf when must be to at least 3 sf) |
Additional guidance
| There are an infinite number of sets of three valid dimensions Valid dimensions for 50 are [49.5, 50.5] for 35 are [34.5, 35.5] for 20 are [19.5, 20.5] | |
| \(49.5 \times 34.5 \times 19.5 = 33\,301.(\ldots)\) or 33 000 or 33 300 \(49.6 \times 34.6 \times 19.6 = [33\,636, 33\,637]\) or 33 000 or 33 600 or 33 630 or 33 640 \(49.7 \times 34.7 \times 19.7 = 33\,974.(\ldots)\) or 33 000 or 33 900 or 33 970 \(49.8 \times 34.8 \times 19.8 = 34\,314.(\ldots)\) or 34 300 or 34 310 \(49.9 \times 34.9 \times 19.9 = 34\,656.(\ldots)\) or 34 600 or 34 700 or 34 650 or 34 660 \(50 \times 35 \times 20 = 35\,000\) \(50.1 \times 35.1 \times 20.1 = 35\,346.(\ldots)\) or 35 000 or 35 300 or 35 340 or 35 350 \(50.2 \times 35.2 \times 20.2 = 35\,694.(\ldots)\) or 35 000 or 36 000 or 35 600 or 35 700 or 35 690 \(50.3 \times 35.3 \times 20.3 = 36\,044.(\ldots)\) or 36 000 or 36 040 \(50.4 \times 35.4 \times 20.4 = [36\,396, 36\,397]\) or 36 000 or 36 300 or 36 400 or 36 390 \(50.5 \times 35.5 \times 20.5 = 36\,751.(\ldots)\) or 36 000 or 37 000 or 36 700 or 36 800 or 36 750 | |
| Three valid dimensions do not have to follow a pattern eg \(49.6 \times 35 \times 20.4\) (\(= 35\,414.(\ldots)\) or 35 000 or 35 400 or 35 410) | M1 |
| 49.5 34.5 19.5 and 33 301 (answer implies multiplication signs) | M1 |
| 49.5 34.5 19.5 (no answer so multiplication signs not implied) | M0 |
| 33 301 but 49.5 34.5 19.5 not seen | M0 |
| Units do not have to be seen |