Functions Notes and examples: past paper questions

Real questions on functions notes and examples

The newest 20 of 41 written questions. Open one to see it on the real paper.

1. 4024/12 · October/November 2025 · Q15a[1]
   15 (a) Complete the table for $y=x^3-4x^2+12$. | $x$ | $-2$ | $-1$ | $0$ | $1$ | $2$ | $3$ | $4$ | | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | | $y$ | $-12$ | $7$ | $12$ | $9$ | $4$ | $3$ | |See it on the paper →
2. 4024/23 · May/June 2025 · Q10a[1]
   $f(x)=3x-5$ $g(x)=2-6x$ (a) Find $f(2)$ .See it on the paper →
3. 4024/23 · May/June 2025 · Q10b[2]
   $f(x)=3x-5$ $g(x)=2-6x$ (b) Solve $g(x)=18$ .See it on the paper →
4. 4024/23 · May/June 2025 · Q10c[2]
   $f(x)=3x-5$ $g(x)=2-6x$ (c) Find $fg(4)$ .See it on the paper →
5. 4024/23 · May/June 2025 · Q10d[2]
   $f(x)=3x-5$ $g(x)=2-6x$ (d) The domain of $g(x)$ is $x>-8$ . Find the range of $g(x)$ .See it on the paper →
6. 4024/23 · May/June 2025 · Q12a[1]
   12 These are the first four terms of a sequence. 16 13 10 7 (a) Write down the next term of the sequence.See it on the paper →
7. 4024/23 · May/June 2025 · Q12b[2]
   12 These are the first four terms of a sequence. 16 13 10 7 (b) Find an expression for the $n$th term of the sequence.See it on the paper →
8. 4024/21 · October/November 2024 · Q3a[2]

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

   See it on the paper →
9. 4024/22 · October/November 2024 · Q6a[1]
   6 (a) Complete the table for $y=\frac{x}{4}(2x^2-x-10)$. | $x$ | $-3$ | $-2$ | $-1$ | $0$ | $1$ | $2$ | $3$ | | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | | $y$ | | $0$ | $1.75$ | $0$ | $-2.25$ | $-2$ | $3.75$ |See it on the paper →
10. 4024/11 · May/June 2024 · Q19a[1]
    $f(x)=2x-5$ (a) Find $f(11)$.See it on the paper →
11. 4024/11 · May/June 2024 · Q19b[2]
    19 $f(x)=2x-5$ (b) Find $f^{-1}(x)$.See it on the paper →
12. 4024/21 · May/June 2024 · Q8a(ii)[3]

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

    See it on the paper →
13. 4024/11 · October/November 2023 · Q5a[1]
    5 Yasmin asks 20 people how many pets they own. The results are shown in the bar chart. [Diagram: A bar chart with the y-axis labelled "Frequency" with values 0 to 8, and the x-axis labelled "Number of pets" with values 0, 1, 2, 3, 4. The bars have heights: 3 for 0 pets, 4 for 1 pet, 7 for 2 pets, 5 for 3 pets, and 1 f...See it on the paper →
14. 4024/11 · October/November 2023 · Q22a[1]
    22 \qquad f(x) = \frac{x}{4} + 3 \qquad g(x) = 2(x-1) (a) Find $f(-8)$.See it on the paper →
15. 4024/11 · October/November 2023 · Q22b[2]
    22          $f(x)=\frac{x}{4}+3$           $g(x)=2(x-1)$ (b) Find $f^{-1}(x)$.See it on the paper →
16. 4024/11 · October/November 2023 · Q22c[3]
    22 $f(x)=\frac{x}{4}+3$ $g(x)=2(x-1)$ (c) $f(p)=g(p+5)$ Find the value of $p$.See it on the paper →
17. 4024/12 · October/November 2023 · Q16a[1]
    $T=\sqrt{P-4}$ (a) Work out the value of $T$ when $P=40$. $T=$See it on the paper →
18. 4024/21 · October/November 2023 · Q4b[5]
    (b) An expression for the $n$th term of a different sequence is $n^2+an+b$. The 1st term of the sequence is 3. The 3rd term of the sequence is 19. Find the 6th term of the sequence.See it on the paper →
19. 4024/21 · October/November 2023 · Q6c[1]
    ABCD is a rectangle with area $30{\text{ cm}}^2$. $AB=x\text{ cm}$. Rectangle $DEFG$ is removed from the corner of rectangle $ABCD$. $AE=CG=2\text{ cm}$. (c) Complete the table for $y=2x+\frac{60}{x}-4$. Write your answer correct to 1 decimal place. | $x$ | 2 | 3 | 4 | 6 | 8 | 10 | 12 | 14 | | :--- | :-...See it on the paper →
20. 4024/22 · October/November 2023 · Q6a(i)[1]
    Complete the table for $y=\frac{4^x}{10}$. | $x$ | 0 | 0.5 | 1 | 1.5 | 2 | 2.5 | 3 | | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | | $y$ | | 0.2 | 0.4 | 0.8 | 1.6 | 3.2 | 6.4 |See it on the paper →

What examiners said

This part was answered very well and the majority of candidates gave the correct answer.

— Examiner report, October/November 2023, 4024/11 Q22(a) (Cambridge)

Many candidates found the correct inverse function. It was very common for many to start correctly x y with y = + 3 or x = + 3 but then forget to multiply the 3 when multiplying throughout by 4, 4 4 leading to the incorrect answer of 4x – 3.

— Examiner report, October/November 2023, 4024/11 Q22(b) (Cambridge)

Most candidates gave the correct answer. Common errors were answers of 36, 36 or 62.

— Examiner report, October/November 2023, 4024/12 Q16(a) (Cambridge)