A curved profile for a glass sculpture C C\,C is modeled by the parametric equations
x=14t2+1,y=2t−8t,t>0 x = \frac{1}{4}t^2 + 1, \quad y = 2t - \frac{8}{t}, \quad t > 0 x=41t2+1,y=2t−t8,t>0The curve C C\,C intersects the xxx-axis at the point QQQ.
Find the xxx-coordinate of QQQ.
The line l l\,l is the normal to C C\,C at the point PPP. Given that t=4t = 4t=4 at PPP:
Write down the coordinates of PPP.
Using calculus, show that an equation of l l\,l is
4x+5y=50 4x + 5y = 50 4x+5y=50The region R R\,R is bounded by the curve CCC, the line lll, and the xxx-axis.
Using algebraic integration, find the exact volume of the solid of revolution formed when the region R R\,R is rotated through 2π 2\pi\,2π radians about the xxx-axis.
Practise AQA A Level Maths 1.10 G: Differentiation with exam-style questions for A Level Maths. 321 questions covering 1.10.1 The derivative and second derivative, 1.10.2 Differentiating standard functions, 1.10.3 Applications of differentiation, 1.10.4 Product, quotient and chain rules (A-level only), 1.10.5 Implicit and parametric differentiation (A-level only), and 1.10.6 Constructing differential equations (A-level only), matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
