0580.C4.1.11 — congruent.: past paper questions

Real questions on 0580.c4.1.11 — congruent.

The newest 20 of 22 written questions. Open one to see it on the real paper.

1. 0580/21 · October/November 2025 · Q14b(i)[2]
   A, B, C, D and E lie on the circle. $AC$ and $BD$ intersect at $X$. Angle $ACD=55^{\circ }$ and angle $CXD=88^{\circ }$. [Diagram: A circle with points A, B, C, D, E on its circumference. Chords AC and BD intersect at point X inside the circle. Angle ACD is marked as 55°. Angle CXD is marked as 88°.] (b) Triangle $CXD$ i...See it on the paper →
2. 0580/33 · May/June 2025 · Q23[2]
   23 The diagram shows a right-angled triangle. [Diagram: A right-angled triangle with the top horizontal side labelled $35\text{ cm}$, the right vertical side labelled $22\text{ cm}$, and the hypotenuse labelled $h\text{ cm}$. The right angle is at the top-right corner. The text "NOT TO SCALE" is to the right of the...See it on the paper →
3. 0580/33 · May/June 2025 · Q24[2]
   The diagram shows a right-angled triangle. [Diagram: A right-angled triangle with the right angle at the bottom right. The vertical side on the right is labelled $18.4\text{ cm}$. The horizontal side at the bottom is labelled $y\text{ cm}$. The angle at the top vertex is $52^{\circ }$. The text "NOT TO SCALE" is present...See it on the paper →
4. 0580/32 · February/March 2024 · Q3b(i)[1]
   [Diagram: A grid containing seven triangles labelled $T$, $A$, $B$, $C$, $D$, $E$, $F$, $G$. Triangle $T$ is shaded grey.] (i) Write down the letter of the triangle that is congruent to triangle $T$.See it on the paper →
5. 0580/32 · February/March 2024 · Q3b(ii)[1]
   (b) [Diagram: A grid containing seven triangles labelled $T$, $A$, $B$, $C$, $D$, $E$, $F$, $G$. Triangle $T$ is a right-angled triangle with a vertical side of length 3 units and a horizontal side of length 2 units. Triangle $A$ is a right-angled triangle with a vertical side of length 2 units and a horizontal side of...See it on the paper →
6. 0580/32 · February/March 2024 · Q3c(i)[3]
   (c) [Diagram: An isosceles triangle with base $7\text{ cm}$ and base angles of $62^{\circ }$. A dashed line representing the perpendicular height $h$ is drawn from the top vertex to the base, meeting it at a right angle. The two equal sides are marked with tick marks. The diagram is labelled "NOT TO SCALE".] The diagram s...See it on the paper →
7. 0580/32 · February/March 2024 · Q3c(ii)[1]
   [Diagram: An isosceles triangle with base $7\text{ cm}$ and base angles $62^{\circ }$. A dashed line of height $h$ is drawn from the top vertex to the base, meeting it at a right angle. The two equal sides are marked with tick marks. The diagram is labelled "NOT TO SCALE".] The diagram shows an isosceles triangle. (ii)...See it on the paper →
8. 0580/32 · February/March 2024 · Q3c(iii)[3]
   (c) The diagram shows an isosceles triangle. [Diagram: An isosceles triangle with base $7\text{ cm}$, base angles $62^{\circ }$, and height $h$ indicated by a dashed line from the apex to the base.] (iii) Kalpit tries to arrange some of these triangles to make a regular polygon with centre $O$. [Diagram: A partial regular...See it on the paper →
9. 0580/32 · February/March 2024 · Q4a(i)[1]
   (a) A shop sells 58 televisions in one week. The bar chart shows the number of televisions that the shop sells on five of the days. [Diagram: A bar chart with the y-axis labelled "Number of televisions" with a scale from 0 to 16 in increments of 2. The x-axis lists days of the week: Monday, Tuesday, Wednesday, Thursday...See it on the paper →
10. 0580/32 · February/March 2024 · Q4a(ii)[1]
    (a) A shop sells 58 televisions in one week. The bar chart shows the number of televisions that the shop sells on five of the days. [Diagram: A bar chart with y-axis "Number of televisions" from 0 to 16 in steps of 2, and x-axis days Monday to Sunday. Bars are present for Monday (height 3), Tuesday (height 4), Thursday...See it on the paper →
11. 0580/32 · February/March 2024 · Q4a(iii)[4]

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

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12. 0580/32 · February/March 2024 · Q4a(iv)[1]
    (a) A shop sells 58 televisions in one week. The bar chart shows the number of televisions that the shop sells on five of the days. [Diagram: Bar chart with y-axis "Number of televisions" from 0 to 16 in steps of 2, and x-axis days Monday to Sunday. Bars: Monday=3, Tuesday=4, Wednesday=0, Thursday=4, Friday=0, Saturday...See it on the paper →
13. 0580/32 · February/March 2024 · Q4b[2]
    (b) A television has a price of $550. This price is reduced by $4\%$. Calculate the new price of this television.See it on the paper →
14. 0580/32 · February/March 2023 · Q5b(ii)[1]
    5 The diagram shows three triangles, $A$, $B$ and $C$, on a $1{\text{ cm}}^2$ grid. [Diagram: A coordinate grid with $x$ and $y$ axes. Triangle $A$ is shaded grey with vertices at $(2,0)$, $(2,6)$, and $(5,9)$. Triangle $B$ has vertices at $(-2,0)$, $(-2,2)$, and $(-1,3)$. Triangle $C$ has vertices at $(2,0)$, $(2,-6)$,...See it on the paper →
15. 0580/11 · October/November 2022 · Q4[2]

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

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16. 0580/13 · May/June 2022 · Q17a[1]

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

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17. 0580/13 · May/June 2022 · Q17b[2]

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

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18. 0580/21 · October/November 2020 · Q20[4]

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

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19. 0580/21 · October/November 2020 · Q21[3]

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

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20. 0580/21 · October/November 2020 · Q23a[3]

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

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What examiners said

This question was answered well with the majority finding the correct hypotenuse. A few recognised the method as Pythagoras’ theorem but only got as far as 352 + 222 = 1709 or subtracted 352 – 222 or gave the answer correct to only 2 significant figures. Other incorrect methods involved incorrect trigonometry or addition of the sides 35 + 22.

— Examiner report, May/June 2025, 0580/33 Q23 (Cambridge)

A good number, but not a majority, of correct responses were seen. Although most candidates recognised the question required trigonometry, many errors in its application were seen. The most common were either selecting the wrong trigonometric ratio (using sine or cosine in place of tangent) or setting up the ratio incorrectly (usually with the fraction inverted). Incorrect notation caused problems...

— Examiner report, May/June 2025, 0580/33 Q24 (Cambridge)

This part was less well answered, with common errors of B and C seen. .

— Examiner report, February/March 2024, 0580/32 Q3(b)(ii) (Cambridge)