2D Area & Perimeter: WJEC GCSE Intermediate November 2024 Unit 1 Q5

Intermediate November 2024 Unit 1 Q5

WJECIntermediateCurrent spec6 marks2D Area & Perimeter Prisms

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

The diagram below shows the cross-section of a solid.

Cross-section: L-shape with top 12 cm, left side 16 cm, right side 12 cm, bottom 5 cm, all corners right angles

The solid has a height of 2 cm.

The solid: a flat L-shaped prism with height of 2 cm

Diagrams not drawn to scale

Find the volume of the solid.
You must show all your working. [4 + 2 OCW]

From the formula list: Volume of prism = area of cross-section × length

Mark scheme

Scheme	Marks	Comments
Complete method to find the volume For example: Square and rectangle (allow any equivalent valid method) 2 × (12 × 12 + 5 × (16 – 12)) 2 × (12 × 12 + 5 × 4) 2 × (144 + 20) 288 + 40 2 × 164 Two rectangles (allow any equivalent valid method) 2 × (5 × 16 + 12 × (12 – 5)) 2 × (5 × 16 + 12 × 7) 2 × (80 + 84) 160 + 168 2 × 164 Three rectangles (allow any equivalent valid method) 2 × (12 × (12 – 5) + 5 × 12 + 5 × 4) 2 × (12 × 7 + 5 × 12 + 5 × 4) 2 × (84 + 60 + 20) 168 + 120 + 40 2 × 164 Larger rectangle – smaller rectangle (allow any equivalent valid method) 2 × (16 × 12 – (16 – 12) × (12 – 5)) 2 × (16 × 12 – 4 × 7) 2 × (192 – 28) 2 × 164 384 – 56	M3	Note: check diagram for the area and missing lengths If not M3 award M2 or M1 depending on the entries in the table. Calculations such as 12 × 12 × 5 × 16 × 2 are awarded M0. For M2 and M1, FT ‘their (16 – 12)’ or ‘their (12 – 5)’ where appropriate. (See the M2/M1 table below.)
(Volume =) 328 (cm\(^3\))	A1	CAO
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

M2 / M1 table

Award M2 for one of the following: (summing two areas/subtracting two areas/finding one* volume)*	Award M1 for one of the following: (calculating one area)
Square and rectangle
12 × 12 + 5 × (16 – 12) 12 × 12 + 5 × 4 144 + 20 164 2 × 12 × 12 2 × 144 288 2 × 5 × (16 – 12) 2 × 5 × 4 2 × 20 40	12 × 12 144 5 × (16 – 12) 5 × 4 20
Two rectangles
5 × 16 + 12 × (12 – 5) 5 × 16 + 12 × 7 80 + 84 164 2 × (5 × 16) 2 × 80 160 2 × 12 × (12 – 5) 2 × 12 × 7 2 × 84 168	5 × 16 80 12 × (12 – 5) 12 × 7 84
Three rectangles
12×(12–5)+ 5 ×12+5×4 12 × 7 + 5 × 12 + 5 × 4 84 + 60 + 20 164 2 × 12 × (12 – 5) 2 × 12 × 7 2 × 84 168 2 × 5 × 12 2 × 60 120 2 × 5 × 4 2 × 20 40	12 × (12 – 5) 12 × 7 84 5 × 12 60 5 × 4 20
Larger rectangle – smaller rectangle
16 ×12–(16 –12)×(12–5) 16 × 12 – 4 × 7 192 – 28 164 2 × 16 × 12 2 × 192 384 2 × (16 – 12) × (12 – 5) 2 × 4 × 7 2 × 28 56	16 × 12 192 (16 –12)×(12 – 5) 4 × 7 28

Corrected by Westie's Workshop

The board's mark scheme printed “2 × (12 × (12 – 5) + 5 × 12 + 5 × 4))”. Changed to “2 × (12 × (12 – 5) + 5 × 12 + 5 × 4)” because there is one closing bracket too many.
The board's mark scheme printed “FT ‘their (16 – 12)’ or ‘their (12 – 5) where appropriate.”. Changed to “FT ‘their (16 – 12)’ or ‘their (12 – 5)’ where appropriate.” because the closing quotation mark was missing.

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