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

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

The newest 20 of 24 written questions. Open one to see it on the real paper.

1. 0980/21 · October/November 2025 · Q23[4]
   23 Find the coordinates of the turning point on the graph of $y=7-2x-x^2$.See it on the paper →
2. 0980/41 · October/November 2025 · Q24b[4]
   Martha walks a distance of $10\text{ km}$ at a speed of $x\text{ km/h}$. She then runs a distance of $5\text{ km}$ at a speed of $(x+4)\text{ km/h}$. The total time taken for the whole journey is $3.5$ hours. (b) Show that $7x^2-2x-80=0$.See it on the paper →
3. 0980/41 · October/November 2025 · Q24c[3]
   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. (c) Solve $7x^2-2x-80=0$, giving your answers correct to 2 decimal places. You must show all your working.See it on the paper →
4. 0980/21 · October/November 2024 · Q17[4]
   17 Solve. $3x^2-7x-16=0$ You must show all your working and give your answers correct to 2 decimal places.See it on the paper →
5. 0980/21 · October/November 2024 · Q18b[2]
   18 $g(x)=4^{x+3}$ (b) Find $g^{-1}\left(\frac{1}{16}\right)$.See it on the paper →
6. 0980/41 · October/November 2024 · Q10a(i)[5]
   10 (a) [Diagram: A rectangle with vertical side labelled $(x+1)\text{ cm}$ and horizontal side labelled $(2x+3)\text{ cm}$. Text "NOT TO SCALE" is to the right of the rectangle.] This rectangle has area $190{\text{ cm}}^2$. (i) By forming and solving an equation, show that $x=8.5$.See it on the paper →
7. 0980/42 · May/June 2024 · Q5d(i)[4]
   (d) (i) Show that $(3x+5)+\frac{7}{x-2}=x$ simplifies to $2x^2+x-3=0$.See it on the paper →
8. 0980/42 · May/June 2024 · Q5d(ii)[3]
   (ii) Solve by factorisation $2x^2+x-3=0$. $x=$ ………… or $x=$ …………See it on the paper →
9. 0980/21 · October/November 2023 · Q5b[1]
   5 Factorise completely. (b) $h^2-144$See it on the paper →
10. 0980/41 · October/November 2023 · Q2c[2]
    (c) Expand and simplify. $3(5x-8)-2(3x-7)$See it on the paper →
11. 0980/41 · October/November 2023 · Q6a[14]
    6 (a) | Sequence | 1st term | 2nd term | 3rd term | 4th term | 5th term | | $n$th term | | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | | A | $-7$ | $-3$ | $1$ | $5$ | | | | | B | $7$ | $13$ | $23$ | $37$ | | | | | C | $\frac{2}{27}$ | $\frac{3}{81}$ | $\frac{4}{243}$ | $\frac{5}{729}$ | | | | Complete the...See it on the paper →
12. 0980/41 · October/November 2023 · Q6b[1]
    (b) In a sequence, the sum of the first 49 terms is 7644. The sum of the first 50 terms is 7975. Find the 50th term of this sequence.See it on the paper →
13. 0980/22 · May/June 2023 · Q9b[1]
    9 $F$ is the point $(1,-4)$, $\overrightarrow{FG}=\left(\begin{array}{c}8\\ -3\end{array}\right)$ and $\overrightarrow{GH}=\left(\begin{array}{c}-12\\ 35\end{array}\right)$. Find (b) $\overrightarrow{FG}+\overrightarrow{GH}$See it on the paper →
14. 0980/41 · October/November 2021 · Q4a(ii)[3]
    4 (a) Solve. (ii) $\frac{2x}{x-5}=\frac{2}{3}$See it on the paper →
15. 0980/41 · October/November 2021 · Q4b(i)[3]
    (b) Factorise completely. (i) $2x^2-288y^2$See it on the paper →
16. 0980/41 · October/November 2021 · Q4b(ii)[2]
    (b) Factorise completely. (ii) $5x^2+17x-40$See it on the paper →
17. 0980/41 · October/November 2021 · Q4c[5]
    (c) Solve $x^3+4x^2-17x=x^3-9$. You must show all your working and give your answers correct to 2 decimal places.See it on the paper →
18. 0980/41 · October/November 2021 · Q6c[4]

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

    See it on the paper →
19. 0980/41 · October/November 2021 · Q8b(i)[3]
    (b) $g(x)=18-3x-x^2$ (i) Write $g(x)$ in the form $b-(a+x{)}^2$.See it on the paper →
20. 0980/41 · October/November 2020 · Q8f(i)[3]
    (f) Alan invests $200atarateof$r\%$ per year compound interest. After 2 years the value of his investment is $206.46$ . (i) Show that $r^2+200r-323=0$.See it on the paper →

What examiners said

Many candidates recognised the difference of two squares. Some gave incorrect alternatives such as (h – 12)2, (h – 72)(h– 2) or (h – 1)(h – 144).

— Examiner report, October/November 2023, 0980/21 Q5(b) (Cambridge)

Many candidates correctly expanded and simplified 3 ( 5 x − 8 ) − 2 ( 3 x − 7 ) to reach 9 x − 10 . The most common error was the sign error 15 x − 24 − 6 x − 14 to reach 9 x − 38 and some other candidates after expanding the brackets, equated to 0 and solved their equation.

— Examiner report, October/November 2023, 0980/41 Q2(c) (Cambridge)

Sequence A: Most candidates were clearly familiar with tackling problems with linear sequences and were able to state the next term as 9. The common difference of 4 together with trial and error or using a + (n – 1)d usually resulted in the correct nth term, 4n – 11. Weaker candidates often tried to use term to term rules and a common wrong answer was n+4. Sequence B: Using 1st and 2nd difference...

— Examiner report, October/November 2023, 0980/41 Q6(a) (Cambridge)