A deep-sea research probe is descending through a thermal layer. Its altitude h h\,h in metres, relative to the layer's boundary, is modeled by the function h(t)h(t)h(t) for t>0t > 0t>0, where t t\,t is the time in seconds since the descent began. It is known that:
Show that 4a+b=−84a + b = -84a+b=−8.
Given also that a+2b=−23a + 2b = -23a+2b=−23
Find, in simplest form, the expression for h(t)h(t)h(t).
The probe's mission data is later adjusted by a time-shift, such that the altitude is modeled by H(t)=h(t−3)H(t) = h(t - 3)H(t)=h(t−3). Given that point P P\,P on the original model is transformed to point Q Q\,Q on the new model,
State the coordinates of QQQ.
Practise Edexcel A Level Maths Integration with exam-style questions for A Level Maths. 437 questions covering 11.1 Integrating Standard Functions, 11.2 Integrating f(ax + b), 11.3 Using Trigonometric Identities, 11.4 Reverse Chain Rule, 11.5 Integration by Substitution, 11.6 Integration by Parts, 11.7 Partial Fractions, 11.8 Finding Areas, 11.9 The Trapezium Rule, 11.10 Solving Differential Equations, and 11.11 Modelling with Differential Equations, matched to the Edexcel A Level Maths (9MA0) 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.
