Upper & Lower Bounds: Eduqas GCSE Foundation November 2022 Paper 1 Q21

Foundation November 2022 Paper 1 Q21

EduqasFoundationCurrent spec4 marksUpper & Lower Bounds

21.

(a)

Mary and Paul run 100 metres.

Mary’s time is between 14 and 15 seconds inclusive.
Paul’s time is between 12 and 13 seconds inclusive.

Complete the inequality to show the least and greatest possible difference between the times of these two runners. [2]

............ \(\leqslant\) time difference \(\leqslant\) ............

(b)

Peter wants to go by ferry to France.
He is taking a van and a small trailer.
He knows:

The ferry company uses the following rules for the length of vehicles.

Small trailer: maximum length 2 m

Van: maximum length 6 m

Peter thinks that the length of his van and the length of his trailer will both fit the rules.

Use lengths to give one example to show how Peter may be correct, and one example to show how Peter may not be correct. [2]

May be correct ............

May not be correct ............

Scheme	Marks	Comments
\(1 \leqslant\) time difference \(\leqslant 3\)	B2	Not from wrong working B1 for one end correct in the inequality or for sight of both values

Mark scheme (b)

Scheme	Marks	Comments
		Accept a statement such as ‘The van is always less than 6 m long/the maximum length acceptable’ stated once only; may be written anywhere If lengths are given, they must be within the appropriate limits.
Valid example for may be correct e.g. Van 590 cm AND trailer 198 cm	E1	For the van accept any statement such as ‘The van is always less than 6 m long/the maximum length acceptable’ or any values satisfying: 585 cm \(\leqslant\) length of the van < 595 cm AND 195 cm \(\leqslant\) length of the trailer \(\leqslant\) 200 cm Allow e.g. ‘The trailer could be less than 200 (cm).’ Example might use the values given in the question (590 cm and 200 cm) and not consider the values are rounded to the nearest 10 cm.
Valid example for may not be correct e.g. (Van 590 cm and) trailer 201 cm	E1	(For the van accept any statement such as ‘The van is always less than 6 m long’ or any values satisfying: 585 cm \(\leqslant\) length of the van < 595 cm AND) 200 cm < length of the trailer < 205 cm Allow e.g. ‘The trailer could be more than 200 (cm)/the maximum length acceptable’ or ‘the length of the trailer could be 205 (cm)’.
	(4)