A specialized surveillance drone follows a path CCC in a 2D plane defined by the parametric equations
x=3t2+1,y=2t3−15t+k x = 3t^2 + 1, \quad y = 2t^3 - 15t + k x=3t2+1,y=2t3−15t+kwhere kkk is a constant and t≥0t \ge 0t≥0 represents time.
Find an expression for dydx\frac{dy}{dx}dxdy in terms of ttt.
The line lll is the normal to the path at point AAA where t=1t = 1t=1.
Given that lll is also a tangent to the path at point BBB where t=Tt = Tt=T,
show that TTT is a solution of the equation
6T2−4T−15=0 6T^2 - 4T - 15 = 0 6T2−4T−15=0Hence find the xxx-coordinate of point BBB, justifying your answer.
Given that the yyy-intercept of the line lll is 13\frac{1}{3}31,
find the value of kkk.
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.
