Higher June 2023 Paper 1R Q18
18 Diego builds a fence using fence panels.
The total length of the fence is 50 metres, correct to the nearest 5 metres.
The length of each fence panel is 1.3 metres, correct to the nearest 10 cm.
The cost of each fence panel is £8.65
Diego may only buy complete fence panels.
Diego only pays for the number of panels he needs to build the fence.
Work out the greatest difference in the possible amounts that Diego could pay to build the fence.
Show your working clearly.
(4)
| Scheme | Marks |
|---|---|
| 47.5 or 52.5 or 1.25 or 1.35 | B1 |
eg \(\dfrac{47.5}{1.35}\;(= 35.18\ldots)\) or \(\dfrac{52.5}{1.25}\;(= 42)\) | M1 |
| eg ("42" − "36") × 8.65 or “42” × 8.65 – “36” × 8.65 or 363.3 – 311.4 | M1 |
| Working required Answer: 51.9(0) | A1 |
| (4) | |
| (4 marks) |
Notes
B1: for a correct bound, accept 4750 or 5250 or 125 or 135 if working in cm
M1: for correct substitution of
\(47.5 \leqslant LB_F \lt 50\)
and \(1.3 \lt UB_{FP} \leqslant 1.35\)
or
\(50 \lt UB_F \leqslant 52.5\)
and \(1.25 \leqslant LB_{FP} \lt 1.3\)
M1: (dep on M1) for using their lower and upper bounds for the number of fence panels needed to find the cost – lower bound and/or upper bound must be an integer rounded up
A1: cao dep on M2