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###### Ten-Year-Series (TYS) Solutions | Past Year Exam Questions

# 2010 A Level H2 Math

These Ten-Year-Series (TYS) worked solutions with video explanations for 2010 A Level H2 Mathematics are suggested by Mr Gan. For any comments or suggestions please contact us at support@timganmath.edu.sg.

**2010 A Level H2 Math Paper 1 Question 7**

**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).

**Suggested Video Solutions**

**Suggested Handwritten Solutions**

**2010 A Level H2 Math Paper 2 Question 7**

**Suggested Handwritten and Video Solutions**

**2010 A Level H2 Math Paper 2 Question 9**

**Suggested Handwritten and Video Solutions**

Paper 1

Paper 2

- Q7
- Q9

- I
- II
- III

- I
- II
- III

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(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.

[6]

(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.

[6]

(ii)

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

[2]

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

[2]

(iii)

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

[2]

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

[2]

(iv)

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

[2]

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

[2]

- (i)
- (ii)
- (iii)
- (iv)

- (i)
- (ii)
- (iii)
- (iv)

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- Q7
- Q9

- (i)
- (ii)
- (iii)
- (iv)
- (v)

- (i)
- (ii)
- (iii)
- (iv)
- (v)

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- (i)
- (ii)
- (iii)

- (i)
- (ii)
- (iii)

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