0580.E2.2.04 — ax2 + bx + c.: past paper questions

Real questions on 0580.e2.2.04 — ax2 + bx + c.

The newest 20 of 32 written questions. Open one to see it on the real paper.

1. 0580/11 · May/June 2026 · Q21b[2]
   (b) Expand the brackets and simplify. $(x+8)(x-5)$See it on the paper →
2. 0580/22 · May/June 2026 · Q21a[2]
   21 (a) Write $x^2+8x-7$ in the form $(x+a{)}^2+b$ where $a$ and $b$ are integers.See it on the paper →
3. 0580/22 · May/June 2026 · Q21b[1]
   (b) Write down the coordinates of the turning point of the curve $y=x^2+8x-7$.See it on the paper →
4. 0580/22 · May/June 2026 · Q25[5]
   25 The straight line $y=7-4x$ intersects the curve $y=4+3x-2x^2$ at two points. Find the coordinates of these two points.See it on the paper →
5. 0580/42 · May/June 2026 · Q17a[1]
   17 f(x) = 20 - 3x g(x) = \frac{64}{2^x} h(x) = 7 + 2x (a) Find $f(4)$.See it on the paper →
6. 0580/42 · May/June 2026 · Q17b[2]
   17 \quad f(x) = 20 - 3x \qquad g(x) = \frac{64}{2^x} \qquad h(x) = 7 + 2x (b) Find $h^{-1}(x)$.See it on the paper →
7. 0580/42 · May/June 2026 · Q17c[2]
   17 $f(x)=20-3x$ $g(x)=\frac{64}{2^x}$ $h(x)=7+2x$ (c) Find $gg(5)$.See it on the paper →
8. 0580/42 · May/June 2026 · Q17d[2]
   17     $f(x)=20-3x$     $g(x)=\frac{64}{2^x}$     $h(x)=7+2x$ (d) Solve the equation   $g^{-1}(x)=8$.See it on the paper →
9. 0580/43 · May/June 2026 · Q20a[7]

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

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10. 0580/43 · May/June 2026 · Q20b[3]

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

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11. 0580/12 · February/March 2026 · Q22a[2]
    (a) Expand the brackets and simplify. $(2x+5)(x+3)$See it on the paper →
12. 0580/12 · February/March 2026 · Q22b[3]
    (b) [Diagram: An L-shaped polygon with right-angle markers at all vertices. The top horizontal side is labelled $2x+5$. The left vertical side is labelled $x+3$. The bottom horizontal side is labelled $x+1$. The inner horizontal side is labelled $2x$. The text "NOT TO SCALE" is to the right of the shape.] Find an expre...See it on the paper →
13. 0580/02 · Specimen 2025 · Q18a(i)[1]

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

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14. 0580/02 · Specimen 2025 · Q18a(ii)[1]

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

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15. 0580/02 · Specimen 2025 · Q18b[2]

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

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16. 0580/02 · Specimen 2025 · Q18c[3]

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

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17. 0580/02 · Specimen 2025 · Q18d[2]

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

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18. 0580/22 · October/November 2025 · Q15b[2]
    15 Factorise. (b) $5x(x-2y)+6(x-2y{)}^2$See it on the paper →
19. 0580/23 · May/June 2025 · Q22a[1]
    $f(x)=2x+5$ $g(x)=x-4$ $h(x)=5^x$ (a) Find $f(3)$.See it on the paper →
20. 0580/23 · May/June 2025 · Q22b[2]
    22 $f(x)=2x+5$ (b) Find $f^{-1}(x)$.See it on the paper →

What examiners said

Comprehensive responses • Most candidates were familiar with expanding brackets and there were many fully correct solutions. Limited responses • The common errors were adding 5 and 3 instead of multiplying them and having 11 instead of 11x for the addition of 5x and 6x or simply missing the x on one of these terms. • A small proportion of candidates did not understand how to start this question o...

— Examiner report, February/March 2026, 0580/12 Q22(a) (Cambridge)

Comprehensive responses • The few successful solutions almost entirely came from splitting the shape into rectangles. Limited responses • Only a tiny number used the result of part (a) in order to work out a solution from subtracting the areas of the two rectangles. • Very few candidates managed to work out the remaining two sides of the shape in order to calculate two areas of rectangles and the...

— Examiner report, February/March 2026, 0580/12 Q22(b) (Cambridge)

Almost all responses gave the correct answer of 11. A few candidates thought the question was asking for 3f(x) and gave the answer 6x + 15 or 21x.

— Examiner report, May/June 2025, 0580/23 Q22(a) (Cambridge)