0607.C5.1.24 — regular and irregular polygons.: past paper questions

Real questions on 0607.c5.1.24 — regular and irregular polygons.

The newest 12 of 12 written questions. Open one to see it on the real paper.

1. 0607/21 · October/November 2025 · Q16b[4]
   (b) [Diagram: A prism with a regular hexagonal base. The prism is vertical. A stick is shown as a line segment from point $A$ on the bottom edge to point $B$ on the top edge. The height of the prism is labeled $15\text{ cm}$. The side length of the base is labeled $10\text{ cm}$. The text "NOT TO SCALE" is present.]...See it on the paper →
2. 0607/52 · February/March 2025 · Q2a[1]
   2 (a) The diagram shows an equilateral triangle. Complete the diagram to show that equilateral triangles fit together at a point.See it on the paper →
3. 0607/52 · February/March 2025 · Q2b[1]
   (b) The diagram shows a regular hexagon. Complete the diagram to show that regular hexagons fit together at a point.See it on the paper →
4. 0607/52 · February/March 2025 · Q2c[1]
   (c) Show how 2 equilateral triangles and 2 regular hexagons can fit together at a point.See it on the paper →
5. 0607/52 · February/March 2025 · Q3[1]
   The rest of this investigation is about 3 regular polygons fitting together at a point. The diagram shows a square and 2 congruent polygons fitting together at a point. [Diagram: A square at the top, with two congruent regular octagons labelled $B$ attached to its lower-left and lower-right sides, all meeting at a cent...See it on the paper →
6. 0607/52 · February/March 2025 · Q4a[1]
   This is the formula for the size of each interior angle of a regular polygon. Interior angle = $180^{\circ }-(360^{\circ }÷\text{number of sides})$ (a) Use the formula to show that the size of each interior angle of polygon $B$ is $135^{\circ }$.See it on the paper →
7. 0607/52 · February/March 2025 · Q4b[2]
   This is the formula for the size of each interior angle of a regular polygon. Interior angle $=180^{\circ }-(360^{\circ }÷\text{number of sides})$ (b) Complete the sentences to explain why the 3 polygons fit together at a point. Each interior angle of polygon $B$ is $135^{\circ }$. Each interior angle of a square i...See it on the paper →
8. 0607/52 · February/March 2025 · Q5[3]
   Use the formula in **Question 4** to complete the table. | Number of sides | 5 | 6 | 8 | 9 | 10 | 12 | 18 | 20 | | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | | Interior angle in degrees | 108 | | 135 | | 144 | 150 | | 162 |See it on the paper →
9. 0607/52 · February/March 2025 · Q6a[1]
   The diagram shows regular polygons $P$ and $Q$ and part of regular polygon $R$. [Diagram: A regular polygon $Q$ on the left, an equilateral triangle $P$ attached to its right side, and part of a regular polygon $R$ attached to the top-right vertex of $P$. The interior angle of $R$ at this vertex is marked $x^{\circ }$. Th...See it on the paper →
10. 0607/52 · February/March 2025 · Q6b[1]
    The diagram shows regular polygons $P$ and $Q$ and part of regular polygon $R$. [Diagram: A regular decagon labelled $Q$ on the left. Attached to its right side is an equilateral triangle labelled $P$. Attached to the top-right vertex of $P$ (which is also a vertex of $Q$) is part of a regular polygon labelled $R$. The...See it on the paper →
11. 0607/52 · February/March 2025 · Q6c[1]
    The diagram shows regular polygons $P$ and $Q$ and part of regular polygon $R$. [Diagram: A regular decagon labelled $Q$ on the left. Attached to its right side is an equilateral triangle labelled $P$. Attached to the top-right vertex of $P$ is part of a regular polygon labelled $R$. The angle between the side of $R$ a...See it on the paper →
12. 0607/12 · February/March 2024 · Q11[2]

    2-mark “Draw” question — its maths and diagrams are best seen on the paper.

    See it on the paper →

What examiners said

The majority of candidates correctly showed six equilateral triangles making a hexagon. A few interpreted the question as requiring triangles fitting along an edge and so only drew two triangles.

— Examiner report, February/March 2025, 0607/52 Q2(a) (Cambridge)

Most candidates showed three hexagons fitting together at a point. Some went further, without penalty, and drew a complete tiling of hexagons. A very small number only showed two hexagons meeting along an edge or at a point.

— Examiner report, February/March 2025, 0607/52 Q2(b) (Cambridge)

The large majority of candidates showed the triangles and hexagons fitting around a point. A few candidates did not understand what was required.

— Examiner report, February/March 2025, 0607/52 Q2(c) (Cambridge)