Higher November 2023 Paper 5 Q15
15 The diagram shows a town T and a straight road AB.
Scale: 2 cm represents 1 km
A new straight road is built from town T to the road AB.
The road is the shortest possible distance from town T to the road AB.
(a) Using ruler and compasses only, construct the road from town T to the road AB. [2]
(b) The new road costs £200 000 per kilometre to build.
The road constructor says
The road constructor says
| The new road will cost over £600 000 to build. |
Show that the road constructor is incorrect. [3]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| Accurate ruled perpendicular from T to AB with correct construction arcs | 2 | B1 for accurate ruled perpendicular from T to AB with no/incorrect construction arcs ±2° | For 2 marks or B1 must reach/cross AB Correct arcs could be e.g. Kite method Condone dashed/dotted lines Multiple lines treat as choice |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 520 000 to 560 000 with correct working oe OR that would be 6 cm on the map but it only measures 5.2 to 5.6 cm oe OR This money would build 3 km but it only measures 2.6 to 2.8 km oe | 3 | B1FT for [road = ] 5.2 to 5.6 [cm] or 2.6 to 2.8 [km] or their (a) measured ± 2 mm M1FT for (their 5.2 to 5.6) ÷ 2 × 200 000 oe or 600 000 ÷ 200 000 [× 2] | For 3 marks accept e.g. it will be 40 000 to 80 000 less than this B1 may be seen on diagram Accept FT given in km as their(a) ÷ 2 M1 implied by 6 cm or 3 km Method can be implied by correct figures For 3 marks accept e.g. 3 × 200 000 is greater than 2.7 × 200 000 |