Higher November 2017 Unit 2 Q4
4. A triangular prism of length 2 metres is shown below.
Diagram not drawn to scale
\(AC\) = 21 cm, \(BC\) = 35 cm and \(B\hat{A}C\) = 90°.
(a)
Give your answer in cm2.
You must show all your working. [5 + 2 OCW]
In this part of the question, you will be assessed on the quality of your organisation, communication and accuracy in writing.
Calculate the area of triangle \(ABC\).Give your answer in cm2.
You must show all your working. [5 + 2 OCW]
(b) Calculate the volume of the prism.
You must give the units of your answer. [3]
You must give the units of your answer. [3]
From the formula list: Volume of prism = area of cross-section × length
| Scheme | Marks | Comments |
|---|---|---|
| Work for 4(a) must be seen in 4(a) and not awarded retrospectively from work in 4(b). In (a) allow correctly working in metres BUT final answer must be in cm2. | ||
| 352 = 212 + AB2 OR (AB2 =) 352 − 212 | M1 | |
| ( AB2 =) 784 or (AB =) √784 | A1 | F.T. ’their784’ if M1 gained and if <1225 |
| (AB =) 28(cm) | A1 | |
| (Area ABC =) \(\dfrac{21 × 28}{2}\) | M1 | F.T. (21 × ‘their stated or shown AB’) / 2 AND (AB ≠ 35 and ≠ 21) |
| = 294(cm2) | A1 | |
| OC1 | Organisation and Communication. For OC1, candidates will be expected to:
| |
| W1 | Accuracy of writing. For W1, candidates will be expected to:
|
Alternative method.
| Scheme | Marks | Comments |
|---|---|---|
| Cos C = 21/35 | M1 | |
| C = cos−1 0·6 | m1 | |
| ACB = 53(·13..)(°) | A1 | |
| Area ABC = ½ × 21 × 35 × sin 53·13° | M1 | F.T. ‘their 53°’ |
| = 294(cm2) | A1 |
Answer from a ‘FT angle’ must be correct to at least 1dp. (Note using 53° leads to 293·498….)
| Scheme | Marks | Comments |
|---|---|---|
| Use of ‘Volume = area ABC × length’. | M1 | Work for 4(b) must be seen in 4(b). Allow this M1 even if using ‘mixed units’. Where ‘area ABC’ is that shown in 4(a) or calculated using ‘their AB’ from 4(a) AND the length is ‘2×10n’’. (Note: using ‘their AB’ as an area is M0.) |
| (Volume =) 294 × 200 OR 0·0294 × 2 | m1 | F.T. ‘their area of ABC’ OR 294 AND using ‘consistent’ units. |
| = 58800 cm3 OR 0·0588 m3. | A1 | Correct units must be shown. Mark final answer. An unsupported 588 × 10n implies M1. |