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Longhand

Before the final

Writing the constraint from habit rather than the situation

The habit: Draw the picture and read the condition off it: count the sides fenced, the faces priced, whether there is a top.

4 practice questions are built to catch it, in 1 topic.

Practise against it: 3 questions

What it looks like

A question from optimization, with the answer this slip gives beside the right one.

Standard3 marks · 5 min

A rectangular plot is fenced on three sides, with a straight river forming the fourth side. With 240 m of fencing available, what is the largest area that can be enclosed?

Give the area in square metres.

With the slip
3600\displaystyle 3600
Worked through
Amax⁡=7200 m2\displaystyle A_{\max} = 7200 \ \text{m}^{2}

2x + 2y = 240 fences all four sides and gives a 60 m square of 3600 m². The river is the fourth side, so the fencing gives 2x + y = 240.

See the worked solution

Where it comes up

Practise against it

Each of these has an answer this slip gives. Work them on paper: if you fall into it, the verdict names it and the question comes back in review.

  1. 01
    An open-topped box with a square base must hold 32 00032\,000 cm³. Let xx be the side of the base, in centimetres. Write the area AA of material the box needs, in cm², as a function of xx alone.

    OptimizationStandard

  2. 02
    A poster is to carry 200200 cm² of printed text, with margins of 44 cm at the top and the bottom and 22 cm at each side. Let xx be the width of the printed text, in centimetres. Write the total area AA of the poster, in cm², as a function of xx alone.

    OptimizationStandard

  3. 03
    A rectangular vegetable bed is to be edged all the way round and split into three equal strips by two inner rows of edging, each parallel to one pair of sides. The outer edging costs $4 per metre and the inner edging $2 per metre, and the budget is $120. Find the largest total area the bed can have.

    OptimizationStandard

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