0580.C2.10.01 — ax + b.: past paper questions

Real questions on 0580.c2.10.01 — ax + b.

The newest 15 of 15 written questions. Open one to see it on the real paper.

1. 0580/32 · February/March 2026 · Q18a[2]

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

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2. 0580/32 · February/March 2026 · Q18b[1]
   (b) Write down the equation of the line that • passes through the point $(0,7)$ and • has gradient $0$.See it on the paper →
3. 0580/04 · Specimen 2025 · Q16b[4]

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

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4. 0580/23 · October/November 2025 · Q14a[1]
   14 The minimum point on a quadratic curve is $(-3,-5)$. (a) Find the equation of the line of symmetry of the curve.See it on the paper →
5. 0580/23 · October/November 2025 · Q22[3]
   22 The equation of line $L$ is $y=-\frac{1}{2}x+7$. Find an equation of the line perpendicular to line $L$ that passes through the point $(3,5)$. Give your answer in the form $y=mx+c$.See it on the paper →
6. 0580/23 · October/November 2025 · Q26b[3]
   26 Write as a single fraction in its simplest form. (b) $\frac{3}{2x-5}+\frac{4}{x-3}$See it on the paper →
7. 0580/23 · October/November 2025 · Q27[6]
   27 Solve the simultaneous equations. $y=x^2-8x+22$ $y+2=3x$See it on the paper →
8. 0580/23 · October/November 2025 · Q28[4]
   28 Simplify. $\frac{2x^2-11x-21}{x^2-49}$See it on the paper →
9. 0580/41 · October/November 2025 · Q17[3]
   17 Find the equation of the straight line that passes through the points $(2,0)$ and $(0,4)$. Give your answer in the form $y=mx+c$. $y=$See it on the paper →
10. 0580/41 · October/November 2025 · Q18a[2]
    The diagram shows part of the speed–time graph for an athlete in a race. [Diagram: A speed-time graph. The vertical axis is labelled "Speed (m/s)" with a marked value of 8. The horizontal axis is labelled "Time (seconds)" with marked values 0, 2, and 10. The graph line starts at the origin (0,0), increases linearly to...See it on the paper →
11. 0580/41 · October/November 2025 · Q18b[2]
    [Diagram: A speed-time graph. The vertical axis is labelled "Speed (m/s)" with a tick mark at 8. The horizontal axis is labelled "Time (seconds)" with tick marks at 0, 2, and 10. A solid line segment starts at the origin (0,0) and goes to the point (2,8). A horizontal solid line segment starts at (2,8) and extends to t...See it on the paper →
12. 0580/41 · October/November 2025 · Q19[3]
    The mass of a radioactive substance decays exponentially at a rate of $10\%$ per day. The initial mass of the substance is $20\text{ g}$. Find the number of whole days it takes for the mass of the substance to first be less than $1\text{ g}$.See it on the paper →
13. 0580/12 · October/November 2020 · Q16b[1]

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

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14. 0580/22 · February/March 2020 · Q17[4]

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

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15. 0580/32 · February/March 2019 · Q8a[3]

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

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What examiners said

Comprehensive responses • Many candidates drew the correct ruled line across the whole grid. Limited responses • Some lines passed through the correct intercept (0, 3) with an incorrect positive or negative gradient. A common line was y = 3. • Other incorrect lines included y = 0.5, y = 3.5 and lines that joined (–4, 0) to (0, 4) for example, making reference to the numbers appearing within the q...

— Examiner report, February/March 2026, 0580/32 Q18(a) (Cambridge)

Comprehensive responses • Many correct equations were given, some in the unsimplified form y = 0x + 7. Limited responses • Common incorrect answers were y = x + 7 and y = 7x + 0 • Many other incorrect answers were given and a significant number did not attempt this part.

— Examiner report, February/March 2026, 0580/32 Q18(b) (Cambridge)

Very few candidates gained credit for this part and many did not make any attempt at an answer. Some did know that the gradient had to be the same and occasionally a correct intercept was quoted. Many seemed to think it was related specifically to values in the previous part or produced calculations to work out, unnecessarily, gradient and intercept once again.

— Examiner report, October/November 2020, 0580/12 Q16(b) (Cambridge)