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

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

The newest 17 of 17 written questions. Open one to see it on the real paper.

1. 0980/41 · October/November 2025 · Q24a[1]
   Martha walks a distance of $10$ km at a speed of $x$ km/h. She then runs a distance of $5$ km at a speed of $(x+4)$ km/h. The total time taken for the whole journey is $3.5$ hours. (a) Write down an expression in terms of $x$ for the time Martha is walking.See it on the paper →
2. 0980/42 · May/June 2025 · Q10[3]
   A group of 12 adults and 9 children travel on a bus. The cost of an adult ticket is $n$. The cost of a child ticket is $(n-10)$. The total cost of the tickets is $277.50$. Find the cost of one adult ticket.See it on the paper →
3. 0980/41 · October/November 2024 · Q8a(ii)[2]
   8 (a) $f(x)=7-3x$ $g(x)=x^2-16$ (ii) Find $f^{-1}(x)$.See it on the paper →
4. 0980/41 · October/November 2024 · Q8a(iii)[3]
   8 (a) $f(x)=7-3x$ $g(x)=x^2-16$ (iii) Find $gf(x)+1$, giving your answer in its simplest form.See it on the paper →
5. 0980/42 · May/June 2024 · Q11a[2]
   The point $(-1,6)$ lies on a curve. This curve has the derived function $\frac{dy}{dx}=-4x^3-9x^2+5$. Show that $(-1,6)$ is a stationary point of the curve.See it on the paper →
6. 0980/42 · May/June 2024 · Q11b(i)[3]
   (b) A different curve has equation $y=2x^3-6x+8$. (i) Calculate the gradient of the tangent to this curve at the point $(-2,2)$.See it on the paper →
7. 0980/42 · May/June 2024 · Q11b(ii)[2]
   (b) A different curve has equation $y=2x^3-6x+8$. (ii) Find the $x$-coordinates of the stationary points of this curve.See it on the paper →
8. 0980/11 · October/November 2022 · Q16a[2]
   16 (a) Complete the table of values for $y=\frac{5}{x}$. | $x$ | $-5$ | $-4$ | $-2.5$ | $-2$ | $-1$ | | $1$ | $2$ | $2.5$ | $4$ | $5$ | |---|---|---|---|---|---|---|---|---|---|---|---| | $y$ | $-1$ | | $-2$ | $-2.5$ | $-5$ | | $5$ | $2.5$ | $2$ | | $1$ |See it on the paper →
9. 0980/21 · October/November 2021 · Q16b[3]
   16 Find the $n$th term of each sequence. (b) $\frac{2}{1}$, $\frac{3}{4}$, $\frac{4}{16}$, $\frac{5}{64}$, $\frac{6}{256}$, $\cdots$See it on the paper →
10. 0980/41 · October/November 2021 · Q4a(i)[3]
    (a) Solve. (i) $6(7-2x)=3x-8$See it on the paper →
11. 0980/32 · May/June 2021 · Q4f(i)[1]
    (f) A tin of soup costs $tandapacketofbiscuitscosts$p. (i) 3 tins of soup and 2 packets of biscuits cost $15.50. Complete the equation. $3t+2p=\dots$ [1]See it on the paper →
12. 0980/32 · May/June 2021 · Q4f(ii)[1]
    (f) A tin of soup costs $t$ and a packet of biscuits costs $p$. (ii) 5 tins of soup and 4 packets of biscuits cost $28.50$. Write down another equation in terms of $t$ and $p$.See it on the paper →
13. 0980/32 · May/June 2021 · Q4f(iii)[3]
    (f) A tin of soup costs $t$ and a packet of biscuits costs $p$. (iii) Solve the two simultaneous equations. You must show all your working.See it on the paper →
14. 0980/32 · May/June 2021 · Q5a[3]
    5 (a) Complete the table of values for $y=\frac{18}{x}$. | $x$ | $-8$ | $-6$ | $-4$ | $-3$ | $-2$ | | $2$ | $3$ | $4$ | $6$ | $8$ | |---|---|---|---|---|---|---|---|---|---|---|---| | $y$ | | $-3$ | | $-6$ | | | | $6$ | | $3$ | |See it on the paper →
15. 0980/32 · May/June 2021 · Q5b[4]

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

    See it on the paper →
16. 0980/42 · May/June 2021 · Q2b[3]
    The table shows some values for $y=2\times 0.5^x-1$. | $x$ | $-1$ | $-0.5$ | $0$ | $0.5$ | $1$ | $1.5$ | $2$ | | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | | $y$ | $3$ | $1.83$ | | $0.41$ | $0$ | $-0.29$ | | (b) By drawing a suitable straight line, solve the equation $2\times 0.5^x+2x-3.5=0$...See it on the paper →
17. 0980/12 · May/June 2020 · Q14[4]
    14 Rovers, United and City are football teams. Rovers scored $x$ goals. United scored 8 goals more than Rovers. City scored 3 goals less than twice the number of goals scored by Rovers. The three teams scored a total of 117 goals. Write down and solve an equation to find the value of $x$. $x=$See it on the paper →

What examiners said

Many candidates were able to set up the correct equation 12n + 9(n – 10) = 277.50 and then solve it to reach the correct answer for an adult ticket of $17.50. Some, after correctly setting up the equation, made an error in either multiplying the brackets or in rearranging; a common error was to subtract 90 instead of adding. A few, after finding 17.50, spoilt their answer by multiplying by 12 to g...

— Examiner report, May/June 2025, 0980/42 Q10 (Cambridge)

Most candidates completed the table correctly. Some rounded or truncated their answers to one decimal place. Occasionally the signs of one or both answers were incorrect.

— Examiner report, October/November 2022, 0980/11 Q16(a) (Cambridge)

This question part was answered very well. Those candidates who expanded the bracket as their first step and then collected the terms together were the most successful in solving this equation. The minority of candidates who chose to divide by 6 first found this more problematic and made errors with both the fraction calculations and the signs when collecting the x’s together. Most errors seen wer...

— Examiner report, October/November 2021, 0980/41 Q4(a)(i) (Cambridge)