0580.E2.2.01 — ax + bx + kay + kby.: past paper questions

Real questions on 0580.e2.2.01 — ax + bx + kay + kby.

The newest 10 of 10 written questions. Open one to see it on the real paper.

1. 0580/22 · October/November 2025 · Q20a(ii)[2]
   20 $f(x)=\frac{21}{2x-1}$, $x\ne \frac{1}{2}$ $g(x)=3x+4$ (a) Find (ii) $gf(-1)$See it on the paper →
2. 0580/22 · October/November 2025 · Q20a(iii)[3]
   20 $f(x)=\frac{21}{2x-1}$, $x\ne \frac{1}{2}$ $g(x)=3x+4$ (a) Find (iii) $f^{-1}(x)$.See it on the paper →
3. 0580/22 · October/November 2025 · Q20b[5]
   f(x) = \frac{21}{2x-1}, x \ne \frac{1}{2} \qquad g(x) = 3x + 4 (b) Solve $f(x)=g(x)$.See it on the paper →
4. 0580/22 · October/November 2025 · Q22[3]
   22 A graph with equation $y=x^2+bx+c$ has a minimum point at $(-5,12)$. Find the value of $b$ and the value of $c$.See it on the paper →
5. 0580/22 · October/November 2025 · Q24[2]
   24 $27^{nx}=(9^x{)}^2$ Find the value of $n$.See it on the paper →
6. 0580/43 · October/November 2025 · Q19c[2]
   19 $f(x)=5^x$ $g(x)=3x-2$ $h(x)=x^2+1$ (c) Find $g^{-1}(x)$.See it on the paper →
7. 0580/43 · October/November 2025 · Q19e[1]
   19 $f(x)=5^x$ $g(x)=3x-2$ $h(x)=x^2+1$ (e) Find $h^{-1}(12)$.See it on the paper →
8. 0580/13 · May/June 2024 · Q13[2]
   13 Factorise completely. $4x^{2}y-5x{y}^2$See it on the paper →
9. 0580/13 · May/June 2024 · Q19[2]
   19 Solve the simultaneous equations. $5t-2w=19$ $3t+2w=5$See it on the paper →
10. 0580/12 · October/November 2020 · Q7[2]

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

    See it on the paper →

What examiners said

This question was answered well by stronger candidates, but many incorrect responses were also seen. Some only removed the common factors xy and gave their final answer as 4 x − 5y , others thought the x in 5xy 2 was squared and gave their solution as xy (4 x − 5 xy ) . Some candidates combined the terms as like terms and gave the answer −1xy . Some factorised the expression correctly with either...

— Examiner report, May/June 2024, 0580/13 Q13 (Cambridge)

Many correct answers were seen to this straightforward simultaneous equation. Common incorrect answers were t = 7 , w = −8 or t = 7 , w = 8 , from subtracting rather than adding the pair of simultaneous equations.

— Examiner report, May/June 2024, 0580/13 Q19 (Cambridge)

This linear equation was well understood and solved correctly by the majority of candidates. Some wrote 3x – 2x instead of 3x + 2x as the first stage while others worked out the final stage as 5 ÷ 6 instead of 6÷5.

— Examiner report, October/November 2020, 0580/12 Q7 (Cambridge)