Mathematical Studies: Differential Calculus Topical Past Paper Questions

Hyungmin designs a concrete bird bath. The bird bath is supported by a pedestal. This is shown in the diagram. diagram not to scale The interior of the bird bath is in the shape of a cone with radius r, height h and a constant slant height of 50 cm. (a) Write down an equation in…

The Maxwell Ohm Company is designing a portable Bluetooth speaker. The speaker is in the shape of a cylinder with a hemisphere at each end of the cylinder. The dimensions of the speaker, in centimetres, are illustrated in the following diagram where $r$ is the radius of the hemis…

Consider the curve $ y = 5x^{3} - 3x $. (a) Find $ \frac{dy}{dx} $. [2] The curve has a tangent at the point P(-1, -2). (b) Find the gradient of this tangent at point P. (c) Find the equation of this tangent. Give your answer in the form $ y = mx + c $. [2] ## Working: vworking:…