0606.14.8: Apply differentiation to practical problems involving maxima and minima: past paper questions

Real questions on 0606.14.8: apply differentiation to practical problems involving maxima and minima

The newest 11 of 11 written questions. Open one to see it on the real paper.

1. 0606/22 · February/March 2026 · Q7b[3]
   A ship is sailing with speed $v{\text{ km h}}^{-1}$. The sailing cost per hour, $C$, is given by $C=v^2+\frac{3000}{v}+100$. (b) Hence find the minimum sailing cost for a journey of $150\text{ km}$.See it on the paper →
2. 0606/02 · Specimen 2025 · Q11a[3]

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

   See it on the paper →
3. 0606/02 · Specimen 2025 · Q11b[6]

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

   See it on the paper →
4. 0606/22 · October/November 2024 · Q12[6]
   12 A metal tank is in the shape of a cuboid with a square base of side $x$ m and an open top. The tank has a volume of $5{\text{ m}}^3$. Given that $x$ can vary, and that the area of the metal used to make the tank is a minimum, find the dimensions of the tank.See it on the paper →
5. 0606/21 · May/June 2024 · Q11[7]

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

   See it on the paper →
6. 0606/23 · October/November 2020 · Q9b[6]
   [Diagram: A rectangle ABCDE with a diagonal line AC. The vertical side AB is labeled 300 m. The horizontal side AE is labeled 400 m. The top side is split into BC and CD, with BC labeled x m.] The rectangle $ABCDE$ represents a ploughed field where $AB=300\text{ m}$ and $AE=400\text{ m}$. Joseph needs to walk from...See it on the paper →
7. 0606/11 · May/June 2020 · Q8b[3]
   (b) Hence find $\int \frac{12x}{4x^2-9}\mathrm{d}x$, giving your answer as a single logarithm and an arbitrary constant.See it on the paper →
8. 0606/11 · May/June 2020 · Q8c[4]
   (c) Given that ${\int }_2^a\frac{12x}{4x^2-9}\mathrm{d}x=\ln 5\sqrt{5}$, where $a>2$, find the exact value of $a$.See it on the paper →
9. 0606/21 · May/June 2020 · Q15c[5]

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

   See it on the paper →
10. 0606/12 · February/March 2020 · Q2[5]
    2 Find the values of $k$ for which the line $y=kx+3$ is a tangent to the curve $y=2x^2+4x+k-1$. [5]See it on the paper →
11. 0606/22 · February/March 2020 · Q11[8]
    11 [Diagram: A circular cylinder with height $h$ and base radius $r$] A container is a circular cylinder, open at one end, with a base radius of $r$ cm and a height of $h$ cm. The volume of the container is $1000{\text{ cm}}^3$. Given that $r$ and $h$ can vary and that the total outer surface area of the container has a...See it on the paper →

What examiners said

Comprehensive responses • Many candidates calculated the cost per hour, using their value of v and the number of hours that the journey would take. There was a range of acceptable answers due to the different possible places where the candidates could have approximated their answers. Limited responses • Some candidates did not use 150 km in the correct context. • Some candidates calculated the c...

— Examiner report, February/March 2026, 0606/22 Q7(b) (Cambridge)

Many completely correct solutions were seen. The most common method and by far the simplest method was to equate the two given equations, form a quadratic equation equated to zero and then make use of the discriminant of this quadratic equation. Other methods included equating gradients and substitution of the resulting relationship into an appropriate equation to either the value of k, or the val...

— Examiner report, February/March 2020, 0606/12 Q2 (Cambridge)

A good number of candidates earned at least six of the eight marks available for this question. The overwhelming majority of candidates used the information given about the volume of the cylinder to write h as an expression in r. A good number of these candidates formed a correct expression for the surface area and went on to differentiate and solve correctly. Some candidates included both ends of...

— Examiner report, February/March 2020, 0606/22 Q11 (Cambridge)