0606.14.1: Understand the idea of a derived function: past paper questions

Real questions on 0606.14.1: understand the idea of a derived function

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

1. 0606/11 · May/June 2026 · Q10[8]
   10 A curve has equation $y=f(x)$, where $f^{\prime \prime }(x)=(2x+10{)}^{-\frac{1}{2}}-2x$. The curve has a stationary point at $\left(3,\frac{64}{3}\right)$. Find the equation of the curve.See it on the paper →
2. 0606/12 · May/June 2025 · Q8b[1]
   It is given that $y=\frac{\ln (3x^2+16)}{x+2}$. (b) Given that $x$ increases from $0$ to $h$, where $h$ is small, write down the approximate change in $y$.See it on the paper →
3. 0606/12 · February/March 2024 · Q6b(ii)[1]

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

   See it on the paper →
4. 0606/22 · February/March 2024 · Q4a(i)[4]
   Given that $y=3{\sin }^{2}x+\cos x$, show that $y+\cot x\frac{\mathrm{d}y}{\mathrm{d}x}=k(1+{\cos }^{2}x)$, where $k$ is an integer.See it on the paper →
5. 0606/22 · February/March 2024 · Q4a(ii)[4]
   (ii) Using your value of $k$, solve the equation $k(1+{\cos }^{2}x)=4$ for $-\pi ⩽x⩽\pi$.See it on the paper →
6. 0606/22 · February/March 2024 · Q4b(i)[2]
   (b) (i) Differentiate $y=\tan (x-\sqrt{x})$ with respect to $x.$See it on the paper →
7. 0606/22 · February/March 2024 · Q4b(ii)[2]
   (ii) Hence find $\int \frac{2\sqrt{x}-1}{\sqrt{x}{\cos }^2(x-\sqrt{x})}\mathrm{d}x$.See it on the paper →
8. 0606/22 · February/March 2024 · Q5[4]
   5 Variables $x$ and $y$ are related by the equation $y=\frac{x}{\ln 3x}$. Use differentiation to find the approximate change in $y$ when $x$ increases from $1$ to $1+h$, where $h$ is small.See it on the paper →
9. 0606/12 · May/June 2022 · Q11d(i)[1]
   In this question all lengths are in kilometres and time is in hours. A particle $P$ moves in a straight line such that its displacement, $s$, from a fixed point at time $t$ is given by $s=(t+2)(t-5{)}^2$, for $t⩾0$. (d) (i) Write down an expression for the acceleration of $P$ at time $t$.See it on the paper →
10. 0606/22 · May/June 2019 · Q11i[1]

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

    See it on the paper →

What examiners said

Most candidates realised that multiplication of their answer to part (a) by h was needed, but a mark was awarded only if their answer to part (a) was a single logarithm and there was also no ambiguity in the way the answer was written.

— Examiner report, May/June 2025, 0606/12 Q8(b) (Cambridge)

Most candidates were able to state in some form or other that the velocity was always positive when t > 0, or that the velocity was never zero for t > 0. It was also acceptable to state that the acceleration was always positive for t > 0. Some candidates however thought, incorrectly, that because the particle was travelling in a straight line, its direction could not be changed.

— Examiner report, February/March 2024, 0606/12 Q6(b)(ii) (Cambridge)

Candidates found this question to be reasonably challenging. Most candidates were able to differentiate cosx correctly. A small number of candidates were able to differentiate 3sin2x correctly. Many candidates gave 6cosx as the derivative of this term. A few candidates rewrote 3sin2x as 3 – 3 cos2x before they differentiated. This was not necessary and did not make the solution simpler. A good pro...

— Examiner report, February/March 2024, 0606/22 Q4(a)(i) (Cambridge)