AQA Level 2 Certificate Further Maths
Topic questions Pure mathematics Stationary points
9 questions · 43 marks · about 1 hour
A 60 cm piece of wire is bent to form three sides of a rectangle. It is then attached to a fixed rod as shown in the diagram.
The area of the rectangle is A cm2
Show that A = x (60 – 2 x)
Work out the maximum value of A as x varies.
For a curve y = f(x)
Show that the curve has a turning point where x = 3
Use 
to work out the nature of the turning point. You must show your working.
The equation of a curve is y = x3 – 3x2 + 5
Work out the stationary points of the curve and determine their nature. You must show your working.
f is a cubic function. The curve y = f(x) has a minimum point at (a, 0) and a maximum point at (1, b)
Tick one box for each statement.
The curve y = ax3 + bx2 + 7 has a stationary point at (–2, 11)
Work out the values of a and b.
The dimensions of the cuboid are given in centimetres.
The total length of all 12 edges is 300 cm
The volume of the cuboid is V cm3
Use calculus to work out the maximum value of V as x varies.
The curve y = x4 – 18x2 has three stationary points.
Work out the coordinates of the three stationary points and determine their nature. You must show your working.
y = f(x) is the graph of a cubic function.
The function is
Draw a possible sketch of y = f(x) for values of x from – 2 to 6
Memes
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