Percentages: Eduqas GCSE Higher June 2019 Paper 1 Q13

Higher June 2019 Paper 1 Q13

EduqasHigherCurrent spec8 marksPercentages Similar Shapes

13.

(a) Shabana is moving to a new house and is using boxes to pack.

(i)

Two mathematically similar packing boxes, labelled THIS WAY UP and FRAGILE HANDLE WITH CARE

Shabana has two mathematically similar packing boxes and says,

“The ratio of the lengths of two of my boxes is 2 : 3 so the ratio of their volumes must be 4 : 9.”

Give a reason why Shabana is incorrect and state the correct ratio of the volumes. [2]

Reason ……………
Correct ratio …… : ……

(ii)

A small square-based box and a large square-based box

Diagram not drawn to scale

Shabana has two different square-based boxes where:

the ratio of the lengths of the sides of the squares is 1 : 3,
the ratio of their heights is 1 : 4.

How many of the small boxes can the large box hold? [2]

(b) Shabana’s new house is further away from her workplace.
She estimates that there will be a 15% increase in the cost of getting to work.

From her old house, she:

drove 945 miles per month,
used petrol at the rate of 9 miles per litre,
paid 120p per litre for petrol.

How much more will it cost her to get to work each month after she has moved? [4]

Increased cost of getting to work £ ……………

Mark scheme (a)

Scheme	Marks	Comments
(a)(i) Valid reason e.g. ‘The parts of the ratio should be cubed’ or ‘4 : 9 is the area factor not the volume factor’ or ‘Because the correct ratio is 2³ : 3³.’	E1	Allow e.g. ‘Squaring does not find the volume.’
8 : 27 oe	B1	ISW
(a)(ii) 36	B2	B1 for \(3\times3\ (\times4)\) oe seen

Mark scheme (b)

Scheme	Marks	Comments
\((945 \div 9 =)\ 105\) (litres per month)	B1
\(105\times120\) (p) or \(105\times\) (£)1.2(0) (=12600 (p) or (£)126)	M1	FT ‘their 105’
(15% of (£)126 =) \(12.6(0) + \tfrac12\times12.6(0)\) oe	M1	FT ‘their (£)126’ provided M1 previously awarded; may be seen in stages
(£)18.9(0) or 1890 (p) ISW	A1	FT ‘their 105’; If units are given, they must be correct

Alternative methods could increase 120p, 945 or 105 by 15%:

Scheme	Marks	Comments
\((945 \div 9 =)\ 105\) (litres per month)	B1
\(12 + \tfrac12\times12\)	M1
‘their 105’ \(\times\) ‘their 18(p)’ oe	M1
(£)18.9(0) or 1890 (p)	A1

OR

Scheme	Marks	Comments
\(94.5 + \tfrac12\times94.5\)	M1
\((141.75 \div 9 =)\ 15.75\) or \((141.75\times120 =)\ 17010\)	B1
‘their 15.75’ \(\times\) 120 (p) oe or ‘their 17010’ \(\div\) 9	M1
(£)18.9(0) or 1890 (p)	A1

OR

Scheme	Marks	Comments
\((945 \div 9 =)\ 105\) (litres per month)	B1
\(10.5 + \tfrac12\times10.5\)	M1
‘their 15.75’ \(\times\) 120 (p) oe	M1
(£)18.9(0) or 1890 (p)	A1

(8)

Corrected by Westie's Workshop

The board's mark scheme printed “141.75 × 20 = 17010”. Changed to “141.75 × 120 = 17010” because 141.75 × 20 is 2835; the price is 120p per litre and 141.75 × 120 = 17010.
The board's mark scheme printed “120p, 945, 105 or by 15%”. Changed to “120p, 945 or 105 by 15%” because the list had a stray “or” followed by a gap; the three alternative methods below increase 120p, 945 or 105.
The board's mark scheme printed “may been seen”. Changed to “may be seen” because “been” should be “be”.

Original: see the board's mark scheme PDF (link above).