2D Area & Perimeter: WJEC GCSE Foundation November 2024 Unit 1 Q14

Foundation November 2024 Unit 1 Q14

WJECFoundationCurrent spec4 marks2D Area & Perimeter Prisms

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

L-shaped cross-section with right angles: top edge 12 cm, left edge 16 cm, right edge 12 cm, bottom edge 5 cm

The solid has a height of 2 cm.

The L-shaped solid drawn in 3D, labelled height of 2 cm

Diagrams not drawn to scale

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

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

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.

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

(Volume =) 328 (cm³)

CAO

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 next line shows the expression with matching brackets.

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