Direct & Inverse Proportion: WJEC GCSE Numeracy Higher November 2019 Unit 2 Q8

Numeracy Higher November 2019 Unit 2 Q8

WJECHigherCurrent spec5 marksDirect & Inverse Proportion

8. Gary and Carys are fire officers.

Last week, they recorded that 5 engines were able to pump 26 000 gallons of water onto a fire in 3 minutes.

(a) Show that 9 engines would be able to pump 143 000 gallons of water in under 9 minutes 15 seconds. [4]

(b) Give one possible reason why the 9 engines may not be able to pump 143 000 gallons of water in under 9 minutes 15 seconds. [1]

Mark scheme (a)

Scheme

Marks

Comments

A table method altering all 3 at the same time is M0

3 × \(\dfrac{5}{9}\) × \(\dfrac{143\ (000)}{26\ (000)}\) OR

3 × 0.555… × 5.5 or equivalent

M1 for the correct use of 3 with either 5/9 or 143(000)/26(000)

e.g.	Time	Engines	Gallons
	16.5	5	143 000
OR	1²/₃	9	26 000

= 9.16(6…) or 9.2 (mins)

CAO

= 9 mins 10 sec or 9 mins 12 sec OR
e.g. ‘which is less than 9.25 (mins)’

FT from M1 or M2 previously awarded, provided of equivalent difficulty
A correct comparison needed

Alternative

Alternative method 1:

Scheme

Marks

Comments

A table method altering all 3 at the same time is M0

5 × \(\dfrac{3\ (\text{or } 180)}{9.25\ (\text{or } 555)}\) × \(\dfrac{143\ (000)}{26\ (000)}\) OR

5 × 0.324… × 5.5 or equivalent OR

5 × 0.3278… × 5.5 or equivalent if 9.15 used

Allow use of 9.15 for 9.25 for M marks only
M1 for the correct use of 5 with either 3/9.25 or 143(000)/26(000)
e.g. Engines Time Gallons
27.5 3 143 000
OR 1.6216.. 9.25 26 000
OR 1.639.. 9.15 26 000 (using 9.15)

= 8.9(18…) (engines) AND a statement e.g.
‘9 engines would do it quicker’

CAO
A1 for 8.9(18…) (engines) without a correct statement
OR
A1 for ‘their 8.9(18…) from premature approximation with a correct statement

Alternative

Alternative method 2:

Scheme

Marks

Comments

A table method altering all 3 at the same time is M0

26000 × \(\dfrac{9}{5}\) × \(\dfrac{9.25\ (\text{or } 555)}{3\ (\text{or } 180)}\) OR

26000 × 1.8 × 3.08… or equivalent OR

26000 × 1.8 × 3.05 or equivalent if 9.15 used

Allow use of 9.15 for 9.25 for M marks only
M1 for the correct use of 26(000) with either 9/5 or 9.25/3
e.g. Gallons Engines Time
46800 9 3
OR 80166.6.. 5 9.25
OR 79300 5 9.15 (using 9.15)

= 144 300 (gallons) AND a statement e.g.
‘quicker to pump 143 000 (gallons)’

CAO
A1 for 144 300 (gallons) without a correct statement
OR
A1 for ‘their 144300’ from premature approximation with a correct statement

Alternative

Alternative method 3:

Scheme	Marks	Comments
\(\dfrac{26\,000}{5 \times 3}\) AND \(\dfrac{143\,000}{9 \times 9.25}\)	M2	M1 for 1 correct calculation Allow use of 9.15 for 9.25 for M marks only
= 1733.3(3…) AND = 1717.7… AND (galls/engine/min) (galls/engine/min) Statement e.g. ‘last week’s rate was quicker’	A2	Must come from M2 A1 for 2 correct rates without a correct statement OR A1 for 1 correct rate with a correct statement

Mark scheme (b)

Scheme	Marks	Comments
Valid reason e.g. ‘Engines may not deliver water at the same rate’ or ‘May not have enough water available’, or ‘Not enough room for 9 engines’, or ‘Not enough water pressure available’, or ‘They may not be able to work for that long’, or ‘One (or more) of the engines may be faulty’	E1	Ignore additional spurious comments Do not allow e.g. ‘The fire may have gone out’