Higher June 2023 Paper 5 Q4
4 The diagram shows a prism of length 10 cm.
The cross-section of the prism is a right-angled triangle.
The base, \(b\) cm, is 2 cm longer than the height, \(h\) cm.
The volume of the prism is 240 cm3.
A student is explaining how they worked out the value of \(b\).
They say
\(b\) is 6 because that means \(h\) is 4 and 6 × 4 × 10 = 240.
Describe the student’s error and find the correct value of \(b\). [3]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| Correct explanation \(\frac{1}{2}\) omitted from the area of the cross section oe | 1 | See appendix 1 Do not ignore incorrect statements | |
| 8 | 2 | M1 for \(\frac{1}{2} \times b \times h = 24\) seen, either as a formula or with values | M1 implied by \(b \times h = 48\) or a correct factor pair of 48 or e.g. \(h(h + 2) = 48\) oe M1 may be seen in their explanation of the error |
Appendix 1: exemplar responses for Q4
| Response | Mark | |
|---|---|---|
| 1 | Has found [the volume of] a cuboid | 1 |
| 2 | He needs to halve the volume of a cuboid (BOD referring to the calculation rather than 240) | 1 |
| 3 | They forgot to ÷2 to work out the area of the front face | 1 |
| 4 | He did not divide the [area of the] cross section by 2 | 1 |
| 5 | She did not do half base [times height] | 1 |
| 6 | The area of the cross section is ½ \(b \times h\) | 1 |
| 7 | The area of the triangle needs to be halved | 1 |
| 8 | It has the cross section of a triangle so it needs to be divided by 2 (referring to cross section) | 1 |
| 9 | That the student has to divide \(h \times b\) by 2 | 1 |
| 10 | It’s a triangle, they didn’t half 24 after they did 4 × 6 | 1 |
| 11 | So it would be 6 × 4 / 2=12 | 1 |
| 12 | 6 × 4 / 2 × 10 =120 (BOD describes that triangle should be divided by 2) | 1 |
| 13 | He forgot to half the 10 (incorrect – needs to refer to triangle area) | 0 |
| 14 | They didn’t find the area of the triangle before ×10 (not sufficient does not describe the error) | 0 |
| 15 | The student did not work out that it is a triangle. (similar to above) | 0 |
| 16 | Calculated a cube instead of a triangle (incorrect) | 0 |
| 17 | He did not halve it (not referring to what the ‘it’ is) | 0 |
| 18 | They did not multiply the volume by 2 (the volume is given as 240) | 0 |
| 19 | He did not divide the volume by 2 | 0 |
| 20 | Wrong formula | 0 |
| 21 | They did not halve the answer (not specific to the cross section) | 0 |
| 22 | They needed to divide by 2 (not specific to cross section) | 0 |