0580.E2.13.01 — f (x) = 3x – 5.: past paper questions

Real questions on 0580.e2.13.01 — f (x) = 3x – 5.

The newest 14 of 14 written questions. Open one to see it on the real paper.

1. 0980/42 · May/June 2024 · Q7d(ii)[2]
   (d) $f(x)=\frac{1}{4x-1},x\ne \frac{1}{4}$ $g(x)=3^x$ (ii) Find $gg(2)$.See it on the paper →
2. 0980/42 · May/June 2024 · Q7d(iii)[2]
   (d) $f(x)=\frac{1}{4x-1},x\ne \frac{1}{4}$ $g(x)=3^x$ (iii) Find $k$ when $g(k)=f(7)$.See it on the paper →
3. 0980/41 · October/November 2022 · Q7a(i)[1]
   f(x) = 10 - x \qquad g(x) = \frac{2}{x}, \ x \neq 0 \qquad h(x) = 2^x \qquad j(x) = 5 - 2x (a) (i) Find $g\left(\frac{1}{2}\right)$.See it on the paper →
4. 0980/41 · October/November 2022 · Q7a(ii)[1]
   f(x) = 10 - x \qquad g(x) = \frac{2}{x}, \ x \neq 0 \qquad h(x) = 2^x \qquad j(x) = 5 - 2x (ii) Find hg\left(\frac{1}{2}\right).See it on the paper →
5. 0980/41 · October/November 2022 · Q7b[1]
   f(x) = 10 - x g(x) = \frac{2}{x}, x \neq 0 g(h(x)) = 2^x j(x) = 5 - 2x (b) Find $x$ when $f(x)=7$.See it on the paper →
6. 0980/41 · October/November 2022 · Q7c[2]
   f(x) = 10 - x \quad g(x) = \frac{2}{x}, x \neq 0 \quad h(x) = 2^x \quad j(x) = 5 - 2x (c) Find $x$ when $g(x)=h(3)$.See it on the paper →
7. 0980/41 · October/November 2022 · Q7d[2]
   f(x) = 10 - x \qquad g(x) = \frac{2}{x}, \ x \neq 0 \qquad h(x) = 2^x \qquad j(x) = 5 - 2x (d) Find $j^{-1}(x)$.See it on the paper →
8. 0980/41 · October/November 2022 · Q7e[3]
   f(x) = 10 - x \qquad g(x) = \frac{2}{x}, \ x \neq 0 (e) Write $f(x)+g(x)+1$ as a single fraction in its simplest form.See it on the paper →
9. 0980/41 · October/November 2022 · Q7f[4]
   f(x) = 10 - x (f) ${\left(f(x)\right)}^2-ff(x)=a{x}^2+bx+c$ Find the values of $a$, $b$ and $c$.See it on the paper →
10. 0980/41 · October/November 2022 · Q7g[2]
    f(x) = 10 - x \quad g(x) = \frac{2}{x}, x \neq 0 \quad h(x) = 2^x \quad j(x) = 5 - 2x (g) Find $x$ when $h^{-1}(x)=10$.See it on the paper →
11. 0980/31 · October/November 2021 · Q10b[4]

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

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12. 0980/31 · October/November 2021 · Q10c[2]

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

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13. 0980/41 · October/November 2021 · Q8a(i)[2]
    (a) $f(x)=3-5x$ (i) Find $x$ when $f(x)=-5$.See it on the paper →
14. 0980/41 · October/November 2021 · Q8a(ii)[2]
    (a) $f(x)=3-5x$ (ii) Find $f^{-1}(x)$.See it on the paper →

What examiners said

This question part on composite functions was also answered well. Occasionally the errors 1 1 1 h( ) × g or gh were seen. 2 2 2

— Examiner report, October/November 2022, 0980/41 Q7(a)(ii) (Cambridge)

This question part required candidates to be rigorous with their use of brackets. Many candidates understood that (f ( x ))2 was (10 − x )2 and that ff ( x ) was 10 − (10 − x ) but the most common first line of working for (f ( x ))2 − ff( x ) from candidates of all abilities was (10 − x )2 − 10 − (10 − x ) . From here many candidates were able to expand (10 − x )2 correctly but the omission of th...

— Examiner report, October/November 2022, 0980/41 Q7(f) (Cambridge)

Most candidates did not recall that the most efficient way to solve h−1 ( x ) = 10 is to evaluate h(10) . Many candidates attempted to find the inverse function and inevitably were unsuccessful as logarithms are not on the syllabus. Another common error was to try to solve h ( x ) = 10 or 1 = 10 using trial and error. h( x )

— Examiner report, October/November 2022, 0980/41 Q7(g) (Cambridge)