0580.E2.4.01 — 5x + 1 = 25x.: past paper questions

Real questions on 0580.e2.4.01 — 5x + 1 = 25x.

The newest 19 of 19 written questions. Open one to see it on the real paper.

1. 0580/11 · May/June 2026 · Q21a[1]
   (a) Make $T$ the subject of the formula. $P=Ty$See it on the paper →
2. 0580/42 · May/June 2026 · Q9[3]
   9 Solve the equation. $\frac{w+8}{4}=\frac{2w-3}{3}$See it on the paper →
3. 0580/43 · May/June 2026 · Q18a(i)[2]
   18 (a) $f(x)=3x+1$ $g(x)=5-3x$ (i) Find $x$ when $f(x)=g(x)$.See it on the paper →
4. 0580/43 · May/June 2026 · Q18a(ii)[2]
   18 (a) $f(x)=3x+1$ $g(x)=5-3x$ (ii) Find $g^{-1}(x)$.See it on the paper →
5. 0580/12 · February/March 2026 · Q20[4]
   20 Solve the simultaneous equations. \begin{align*} -5x - 7y &= 1 \\ 6x + 8y &= -2 \end{align*}See it on the paper →
6. 0580/11 · October/November 2025 · Q16a[2]
   16 (a) Complete the table of values for $y=\frac{9}{x}$. | $x$ | $-4.5$ | $-3$ | $-2$ | $-1.5$ | $-1$ | | $1$ | $1.5$ | $2$ | $3$ | $4.5$ | | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | | $y$ | $-2$ | $-3$ | | $-6$ | $-9$ | | $9$ | $6$ | $4.5$ | | $2$ |See it on the paper →
7. 0580/13 · October/November 2025 · Q17a[1]
   17 (a) $k^x\times k^5=k^{20}$ Find the value of $x$.See it on the paper →
8. 0580/43 · October/November 2025 · Q19d[3]
   19 $f(x)=5^x$ $g(x)=3x-2$ $h(x)=x^2+1$ (d) Find the positive solution of $gh(x)=364$.See it on the paper →
9. 0580/11 · May/June 2025 · Q12[2]
   12 Solve. $5x+8=3x-2$See it on the paper →
10. 0580/12 · May/June 2025 · Q24[3]
    24 Solve the simultaneous equations. $5x+2y=3$ $3x+4y=27$See it on the paper →
11. 0580/13 · May/June 2025 · Q4b[2]
    The diagram shows a quadrilateral with sides of equal length. [Diagram: A quadrilateral (rhombus) with all four sides marked as equal length. The interior angle at the bottom-left vertex is labeled $a^{\circ }$. The interior angle at the bottom-right vertex is labeled $2a^{\circ }$. The text "NOT TO SCALE" is written to the...See it on the paper →
12. 0580/11 · May/June 2024 · Q22[3]
    22 Solve the simultaneous equations. You must show all your working. $6x+2y=29$ $3x-4y=17$See it on the paper →
13. 0580/11 · October/November 2019 · Q23[4]

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

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14. 0580/11 · October/November 2019 · Q24a[2]

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

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15. 0580/21 · October/November 2019 · Q6[2]

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

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16. 0580/13 · May/June 2019 · Q20[3]

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

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17. 0580/42 · February/March 2019 · Q8f(ii)[4]

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

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18. 0580/42 · February/March 2019 · Q9c(i)[2]

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

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19. 0580/42 · February/March 2019 · Q10a[4]

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

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What examiners said

Comprehensive responses • Most candidates were clearly familiar with solving simultaneous equations, mostly by elimination, but this was a particularly demanding question with so many negatives in the question Limited responses • Some candidates made errors when deciding whether to add or subtract equations, particularly when working with negative signs. • When multiplying to make the coefficient...

— Examiner report, February/March 2026, 0580/12 Q20 (Cambridge)

There were a reasonable number of candidates getting this correct or showing one step correctly for a method mark. Some showed two steps in one line of working and if this was wrong, a method mark could not be given. Many made mistakes with both the signs meaning that often 5x + 3x = – 2 + 8 was seen. When the correct 5x – 3x = – 2 – 8 was given, candidates made arithmetic errors with the right-ha...

— Examiner report, May/June 2025, 0580/11 Q12 (Cambridge)

Most candidates were familiar with simultaneous equations and while some used a substitution method, the majority tackled the question using elimination. While most made good progress on multiplying one or both equations correctly, a common error was, for example, to subtract the x’s correctly but then to subtract the numbers the wrong way round, giving 21 instead of −21. Some multiplied the algeb...

— Examiner report, May/June 2025, 0580/12 Q24 (Cambridge)