Higher November 2017 Paper 2 Q6
6 The graph shows information about prisms with the same volume.
(a) Give one example to show the volume is 24 cm\(^3\) [1 mark]
(b) The diagram shows a prism with volume 24 cm\(^3\)
The height of the triangular cross section is \(h\).
Work out the height, \(h\). [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Correct product using a point on the curve or correct division using a point on the curve | B1 | eg \(2 \times 12\) (\(= 24\)) or \(3 \times 8\) (\(= 24\)) or \(5 \times 4.8\) (\(= 24\)) or \(6 \times 4\) (\(= 24\)) or \(10 \times 2.4\) (\(= 24\)) or \(24 \div 2 = 12\) or \(24 \div 6 = 4\) |
Additional guidance
| \(1 \times 24\) (\(= 24\)) | B0 |
| \(12 + 12\) (\(= 24\)) | B0 |
| \(3 \times 4 \times 2 = 24\) | B0 |
| For multiplication, 24 does not have to be shown | |
| Ignore any units seen | |
| Ignore any lines on the graph | |
| \(8 \times 3 = 24\) and \(12 + 12 = 24\) (choice) | B0 |
| area 6 and length 4 and volume 24 | B0 |
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| Reading from 5 on the graph to give [4.7, 4.9] | M1 | |
| \(\dfrac{1}{2} \times 6 \times h = [4.7, 4.9]\) or \([4.7, 4.9] \div \left(\dfrac{1}{2} \times 6\right)\) | M1dep | oe |
| [1.56, 1.64] | A1 | |
| Alternative method 2 | ||
| \(24 \div 5\) or 4.8 or \(\dfrac{1}{2} \times 6 \times h\) or \(\dfrac{1}{2} \times 6 \times h \times 5\) | M1 | oe |
| \(\dfrac{1}{2} \times 6 \times h = 24 \div 5\) or \(24 \div 5 \div \left(\dfrac{1}{2} \times 6\right)\) or \(\dfrac{1}{2} \times 6 \times h \times 5 = 24\) or \(15h = 24\) or \(24 \div \left(\dfrac{1}{2} \times 6 \times 5\right)\) or \(24 \div 15\) | M1dep | oe |
| 1.6 | A1 | |