 # 2010 A Level H2 Math

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Paper 1
Paper 2
##### Suggested Handwritten and Video Solutions        ##### 2010 A Level H2 Math Paper 1 Question 9 A company requires a box made of cardboard of negligible thickness to hold $300$ cm$^{3}$ of powder when full. The length of the box is $3x$ cm, the width is $x$ cm and the height is $y$ cm. The lid has depth $ky$ cm, where $0<k\le 1$ (see diagram).

(i)

Use differentiation to find, in terms of $k$, the value of $x$ which gives a minimum total external surface area of the box and the lid.



(i) Use differentiation to find, in terms of $k$, the value of $x$ which gives a minimum total external surface area of the box and the lid.



(ii)

Find also the ratio of the height to the width, $\frac{y}{x}$, in this case, simplifying your answer.



(ii) Find also the ratio of the height to the width, $\frac{y}{x}$, in this case, simplifying your answer.



(iii)

Find the values between which $\frac{y}{x}$ must lie.



(iii) Find the values between which $\frac{y}{x}$ must lie.



(iv)

Find the value of $k$ for which the box has square ends.



(iv) Find the value of $k$ for which the box has square ends.



##### Suggested Handwritten Solutions          ##### Suggested Handwritten and Video Solutions          ##### Suggested Handwritten and Video Solutions        