Edexcel IGCSE Math B 4.J graphs of equations

Practise equation-graph questions by plotting a smooth curve, drawing suitable straight lines and reading estimates to the requested accuracy.

[Maximum number: 5]

Figure for Question 4.J Graphs of equations question 1 — Edexcel IGCSE Math B

Diagrams NOT accurately drawn.

Figure 3 shows a rectangle with dimensions 20 cm by 10 cm from which a square with sides of length x cm is removed from each of the corners.
The shape in Figure 3 is then folded along the dotted lines to form a box, without a lid, in the shape of a cuboid, shown in Figure 4.
The volume of the box is $V\,\mathrm{cm}^3$ .

(a)

Figure for Question (a) — Edexcel IGCSE Math B

On the grid opposite, plot the points from your completed table and, using your answer to part (b), join them to form a smooth curve.

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Fully correct graph.

Marking notes:
Award B2 for a fully correct graph, allowing the maximum at $1.5<x\le2.5$ .
Award B1 for all points plotted correctly, or 4 points plotted correctly with a curve joining all plotted points.

(b)

Starting with a square of side 15 cm and removing a square with sides of length x cm from each corner, a second box without a lid is formed by folding as in part (a).
The volume of this box is $B\,\mathrm{cm}^3$ , where
$B=4x^3-60x^2+225x.$
Given that B=200, find, by drawing a suitable straight line on the grid, estimates, to one decimal place, of the possible values of x.

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4.J Graphs of equations question 1

Question (a)

Question (b)