Geometrical terms Notes and examples: past paper questions

Real questions on geometrical terms notes and examples

The newest 20 of 82 written questions. Open one to see it on the real paper.

1. 4024/11 · October/November 2025 · Q16a[2]
   [Diagram: A circle with centre $O$. Points $S,T,Q,R$ lie on the circumference. $SOQV$ is a straight line passing through the centre, with $V$ outside the circle. $UV$ is a tangent to the circle at $T$. Lines connect $S$ to $T$, $S$ to $Q$, $T$ to $Q$, $T$ to $R$, and $Q$ to $R$. The angle $\angle QST$ is marked as $...See it on the paper →
2. 4024/11 · October/November 2025 · Q16b[2]
   Points $Q,R,S$ and $T$ lie on a circle, centre $O$. $UV$ is a tangent to the circle at $T$. $SOQV$ is a straight line. Angle $QST=32^{\circ }$. (b) Find angle $TQS$.See it on the paper →
3. 4024/11 · October/November 2025 · Q16c[2]
   Points $Q,R,S$ and $T$ lie on a circle, centre $O$. $UV$ is a tangent to the circle at $T$. $SOQV$ is a straight line. Angle $QST=32^{\circ }$. [Diagram: A circle with centre $O$. Points $S,T,Q,R$ are on the circumference in counterclockwise order. $SOQV$ is a straight line passing through the centre, with $V$ out...See it on the paper →
4. 4024/22 · October/November 2025 · Q4b[1]
   In triangle $ABC$, $AB=8.5\text{ cm}$, $AC=6\text{ cm}$ and $BC=7\text{ cm}$. (b) Measure angle $BAC$.See it on the paper →
5. 4024/13 · May/June 2025 · Q3b[2]
   [Diagram: Triangle PQR with angle P = 46°, angle Q = y°, and tick marks indicating PQ = PR. Labelled NOT TO SCALE.] $PQR$ is an isosceles triangle with $PQ=PR$. Angle $QPR=46^{\circ }$. Work out the value of $y$.See it on the paper →
6. 4024/22 · May/June 2025 · Q1[1]
   1 [Diagram: A 6 by 6 grid of squares. A pattern is partially drawn. There is a shaded square in the second column, first row from the top. A solid line segment goes from the bottom-left corner of this shaded square diagonally down-right to the centre of the grid (intersection of the 3rd and 4th vertical and horizontal...See it on the paper →
7. 4024/22 · May/June 2025 · Q15a[1]
   15 These are the first four patterns in a sequence made from black beads and from white beads. [Diagram: Four patterns of beads. Pattern 1: 3 white beads. Pattern 2: 5 white beads. Pattern 3: 7 white beads. Pattern 4: 9 white beads.] (a) Complete the table for Pattern 5. | Pattern number | 1 | 2 | 3 | 4 | 5 | | :--- |...See it on the paper →
8. 4024/23 · May/June 2025 · Q19a[4]
   The diagram shows triangle $ABC$ and triangle $ABD$. [Diagram: A geometric figure showing triangle $ABC$ with an internal point $D$ connected to $A$ and $B$. The side $AB$ is labeled 12. The side $BD$ is labeled 7. The side $AD$ is labeled 6. The angle $DAC$ is marked as $32^{\circ }$. The angle $BCA$ is marked as $48^\ci...See it on the paper →
9. 4024/23 · May/June 2025 · Q19b[4]
   The diagram shows triangle $ABC$ and triangle $ABD$. [Diagram: A geometric figure showing triangle $ABC$ with an internal point $D$ connected to $A$ and $B$. Side $AB$ is labeled 12. Side $BD$ is labeled 7. Side $AD$ is labeled 6. Angle $DAC$ is marked as $32^{\circ }$. Angle $BCA$ is marked as $48^{\circ }$. The text "NOT T...See it on the paper →
10. 4024/11 · October/November 2024 · Q4b[1]

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

    See it on the paper →
11. 4024/21 · October/November 2024 · Q9a[4]
    9 (a) [Diagram: Triangle $ABD$ with point $E$ on $AD$ and point $C$ on $BD$. Line $EC$ is drawn. Angle $BAD=54^{\circ }$. Angle $AEB=x^{\circ }$. Angle $BEC=28^{\circ }$. Angle $CDE=y^{\circ }$. Tick marks indicate $AB\parallel EC$ and $CD=DE$.] $ABD$ is a triangle. $C$ is a point on $BD$ and $E$ is a point on $AD$. $AB...See it on the paper →
12. 4024/21 · October/November 2024 · Q9b[6]
    (b) [Diagram: A circle with centre $O$. Points $P$ and $R$ are on the circumference. A line segment $PR$ is drawn. A line segment $PQ$ passes through $O$ and extends to a point $Q$ outside the circle. A line segment $RQ$ is drawn, tangent to the circle at $R$. The angle $\angle RPQ$ is marked as $35^{\circ }$. The length...See it on the paper →
13. 4024/22 · October/November 2024 · Q8a[3]
    [Diagram: Triangle $ABC$ with a line $DE$ parallel to $BC$. Points $D$ and $E$ are on $AB$ and $AC$ respectively. $BD=2.7$, $DE=5.6$, $BC=9.8$, $CE=3.9$. Arrows indicate $DE\parallel BC$.] $ADB$ and $AEC$ are straight lines. $BC$ is parallel to $DE$. $BC=9.8\text{ cm}$, $BD=2.7\text{ cm}$, $DE = 5.6 \tex...See it on the paper →
14. 4024/22 · October/November 2024 · Q8b[5]
    [Diagram: Triangle $ABC$ with points $D$ on $AB$ and $E$ on $AC$. Line segment $DE$ is parallel to $BC$. Lengths are marked: $BD=2.7$, $DE=5.6$, $BC=9.8$, $CE=3.9$. Arrows indicate $DE\parallel BC$.] $ADB$ and $AEC$ are straight lines. $BC$ is parallel to $DE$. $BC=9.8\text{ cm}$, $BD=2.7\text{ cm}$, $DE...See it on the paper →
15. 4024/22 · October/November 2024 · Q8c[3]
    [Diagram: Triangle ABC with points D on AB and E on AC. Line segment DE is parallel to BC. Lengths are given: BD = 2.7, DE = 5.6, BC = 9.8, CE = 3.9.] $ADB$ and $AEC$ are straight lines. $BC$ is parallel to $DE$. $BC=9.8\text{ cm}$, $BD=2.7\text{ cm}$, $DE=5.6\text{ cm}$ and $CE=3.9\text{ cm}$. (c) Calculat...See it on the paper →
16. 4024/22 · October/November 2024 · Q8d[2]
    [Diagram: Triangle $ABC$ with points $D$ on $AB$ and $E$ on $AC$. Line segment $DE$ is parallel to $BC$. Lengths are marked: $BD=2.7$, $DE=5.6$, $BC=9.8$, $CE=3.9$. Text "NOT TO SCALE" is present.] $ADB$ and $AEC$ are straight lines. $BC$ is parallel to $DE$. $BC=9.8\text{ cm}$, $BD=2.7\text{ cm}$, $DE =...See it on the paper →
17. 4024/22 · October/November 2024 · Q9a[5]
    [Diagram: A circle with centre $O$. Points $A,B,C,D$ are on the circumference. $AOD$ is a straight line (diameter). $OCE$ is a straight line. $DE$ is a tangent to the circle at $D$. Angle $ABC$ is marked as $126^{\circ }$. The length of segment $DE$ is marked as $10.5$. The diagram is labelled "NOT TO SCALE".] $A, B, C...See it on the paper →
18. 4024/22 · October/November 2024 · Q9b[5]
    (b) [Diagram: A circle with centre $O$. Points $P$ and $Q$ are on the circumference. The angle $\angle POQ$ is marked as $82^{\circ }$. The diagram is labelled "NOT TO SCALE".] $P$ and $Q$ are points on a different circle, centre $O$. The angle of the minor sector $POQ$ is $82^{\circ }$. The length of the minor arc $PQ$ is $...See it on the paper →
19. 4024/11 · May/June 2024 · Q1a[1]
    [Diagram: A box containing the word G R A N T] From this word write down the letters which have (a) a line of symmetrySee it on the paper →
20. 4024/11 · May/June 2024 · Q1b[1]
    [Diagram: A box containing the word G R A N T] From this word write down the letters which have (b) rotational symmetry.See it on the paper →

What examiners said

A good proportion of candidates were able to construct the perpendicular bisector of the line AB. Some could draw the line in the correct position but did so without using a compass and were only awarded a partial mark. Some had no understanding of the requirement of the question and many incorrect lines were drawn somewhere on the diagram.

— Examiner report, October/November 2023, 4024/11 Q12(b) (Cambridge)

Many candidates found the correct angle. There were many different incorrect answers but the most common were 38° and 90°.

— Examiner report, October/November 2023, 4024/11 Q15(a) (Cambridge)

Many candidates found the correct angle and there were many different incorrect answers, a common one being 2 × 38 = 76°.

— Examiner report, October/November 2023, 4024/11 Q15(b) (Cambridge)