AQA GCSE Mathematics Paper 1 (Foundation), June 2025: Question 21

2 marks · Easy difficulty · Short Answer

Complete the drawing of the net of a cuboid measuring 5 cm by 3 cm by 2 cm on a centimetre grid.

Practise this question

Question

Diagram of a cuboid with dimensions labelled as length 5 cm, width 3 cm, and height 2 cm. Below the cuboid is a centimetre grid showing an incomplete net consisting of three connected rectangles: a 5 by 3 rectangle in the centre, an attached 5 by 2 rectangle above it, and an attached 3 by 2 rectangle to its left.

Mark scheme

Show the mark scheme Mark scheme for Question 21 giving B2 for a fully correct net and B1 for one or two correctly sized rectangles drawn in appropriate positions. Additional guidance shows ten diagrams illustrating various valid arrangements of the remaining three faces added to the given partially drawn net.

How to answer it

Completing the Net of a Cuboid

📋 What this question tests

This question assesses your spatial reasoning and understanding of 3D solids and their 2D nets:

  • Identifying the 6 rectangular faces of a cuboid with dimensions 5 cm × 3 cm × 2 cm.
  • Matching adjacent edge lengths so the 2D shape can fold without overlapping into a closed 3D solid.
  • Accurately transferring dimensions onto a centimetre grid using a ruler.
Question 21 • 2 Marks

Geometry: 3D Shapes and Nets

Completing the net of a 5 cm × 3 cm × 2 cm cuboid

💡 Key Knowledge: The Anatomy of a Cuboid

Every cuboid consists of 6 rectangular faces grouped into 3 identical pairs of opposite faces:

  • Pair A: Two faces of 5 cm × 3 cm
  • Pair B: Two faces of 5 cm × 2 cm
  • Pair C: Two faces of 3 cm × 2 cm

When completing a net, check off which faces are already given and which 3 faces you must draw.

📐 Face Audit & Dimensions

Given on the grid:

  • Given 1 × (2 cm × 3 cm) face on the left
  • Given 1 × (5 cm × 3 cm) face in the middle
  • Given 1 × (5 cm × 2 cm) face on the top

Remaining faces needed:

  • Need 1 × (2 cm × 3 cm) face
  • Need 1 × (5 cm × 3 cm) face
  • Need 1 × (5 cm × 2 cm) face

✅ Correct Answer & Construction

You must add exactly 3 correct rectangles connected in an arrangement that folds into the closed cuboid:

Most common, straightforward layout (T-band shape):

  1. Below the middle face: Draw a 5 cm × 2 cm rectangle connected to the bottom of the central 5 cm × 3 cm face.
  2. Below that face: Draw the second 5 cm × 3 cm rectangle attached directly beneath the 5 cm × 2 cm rectangle.
  3. Opposite end face: Draw a 2 cm × 3 cm rectangle extending to the right of the middle face (or attached to any corresponding 3 cm edge).

Note: Multiple alternative valid nets exist (as shown in the mark scheme), provided faces do not overlap when folded and stay entirely within the grid.

🧠 Exam Technique: "Fold It in Your Head"

  • Check shared edge lengths: Any two edges that meet when folded must have identical lengths (e.g. an edge of 2 cm cannot join an edge of 3 cm).
  • Use a ruler and pencil: Examiner mark schemes allow "intention", but lines must align neatly with the grid lines.
  • Stay on the grid: The mark scheme explicitly states the drawing "must be wholly on the grid". Plan your layout before drawing so it does not spill over the edges.
  • Tabs: You do not need to draw glue tabs. If you do draw them, examiners simply ignore them.

❌ Common Errors & Pitfalls

  • Drawing the wrong dimensions: Drawing faces as 3 × 3 or 5 × 5 instead of rectangular faces matching the dimensions 5, 3, and 2.
  • Overlapping faces: Attaching two opposite faces to the same edge or adjacent edges such that they would fold directly on top of each other, leaving one side of the cuboid open.
  • Running out of grid space: Extending the 5 cm long band too far to the right or bottom where it leaves the border of the grid, resulting in a loss of marks.
  • Missing one face: Forgetting that a cuboid requires a total of 6 faces and only drawing 2 additional rectangles.
Mark Scheme Breakdown:
  • B2: Fully correct net drawn wholly within the grid (all 6 faces present with correct dimensions and positions).
  • B1 (Partial Credit): One or two correctly sized rectangles drawn in appropriate positions.

Topics

Geometry and measures · 3.4.1 Properties and constructions

Question and mark scheme from the AQA GCSE Mathematics examination, Paper 1 (Foundation), June 2025. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.