Units & Time: WJEC GCSE Higher June 2024 Unit 2 Q4

Higher June 2024 Unit 2 Q4

WJECHigherCurrent spec8 marksUnits & Time Volume & Surface Area

4. In this question, you will be assessed on the quality of your organisation, communication and accuracy in writing.

The diagram below shows a water container.
It is formed from an open rectangular tank with a solid cylinder attached to its base inside the tank.

Open cuboid tank 70 cm long, 40 cm wide and 30 cm high, with a shaded cylinder of height 30 cm standing on its base inside

Diagram not drawn to scale

The base radius of the cylinder is 10 cm.
The height of the cylinder is 30 cm.

How many litres of water can the container hold?
You must show all your working. [6 + 2 OCW]

Mark scheme

Scheme	Marks	Comments
(Volume of tank =) 70 × 40 × 30	M1	Answer line takes precedence. May be seen in stages.
= 84000 (cm³)	A1
(Volume of cylinder =) \(\pi\) × 10² × 30	M1	May be seen in stages.
= 9424(·7…cm³) or 3000 \(\pi\) (cm³)	A1	Accept answers between 9420 and 9426 inclusive.
(Capacity = 84000 – 9424(·7 =) 74575(·…cm³)	B1	Accept answers between 74574 and 74580 inclusive. FT ‘their derived volume of tank’– ‘their derived volume of cylinder’, provided: M1 previously awarded \(\pi\) used when calculating the volume of the cylinder ‘their derived volume of tank’ > ‘their derived volume of cylinder’.
74·575(…litres)	B1	FT ‘their volume/capacity in cm³’ ÷ 1000. Award B1 for a final answer of 74·6 (litres) 74·5 (litres) 74·58 (litres) 74·57 (litres) 75 (litres) 74 (litres) provided from correct workings. This final B1 can be awarded if the volume of the cylinder and tank are converted to litres correctly before the subtraction. An unsupported final answer of 74575(·…cm³) is awarded M1A1M1A1B1B0. Unsupported answers in the above list are awarded M1A1M1A1B1B1.
Organisation and Communication.	OC1	For OC1, candidates will be expected to: present their response in a structured way explain to the reader what they are doing at each step of their response lay out their explanation and working in a way that is clear and logical write a conclusion that draws together their results and explains what their answer means
Accuracy of writing	W1	For W1, candidates will be expected to: show all their working make few, if any, errors in spelling, punctuation and grammar use correct mathematical form in their working use appropriate terminology, units, etc.

4. Alternative method

Scheme	Marks	Comments
(Interior base area of container =) 70 × 40 − \(\pi\) × 10²	M2	Award M1 for an appropriate 70 × 40 OR \(\pi\) × 10² within a subtraction
= 2485(·8…cm²) (cm²) or 2800 − 100\(\pi\)	A1	CAO Accept answers between 2485·8 and 2486 inclusive.
(Capacity of container =) 2485(·8…) × 30	M1	FT ‘their derived base area’, provided at least M1 previously awarded.
74575(·…cm³)	A1	Accept answers between 74574 and 74580 inclusive.
74·575(…litres)	B1	FT ‘their volume/capacity in cm³’ ÷ 1000. Award B1 for a final answer of 74·6 (litres) 74·5 (litres) 74·58 (litres) 74·57 (litres) 75 (litres) 74 (litres) provided from correct workings.

Corrected by Westie's Workshop

The board's mark scheme printed “Unsupported answers in the above list is awarded”. Changed to “Unsupported answers in the above list are awarded” because “answers” is plural, so the verb needs to be “are”.

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