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 AQA A Level Maths 1.11 H: Integration with exam-style questions for A Level Maths. 436 questions covering 1.11.1 Fundamental Theorem of Calculus, 1.11.2 Integrating standard functions, 1.11.3 Definite integrals and areas, 1.11.4 Integration as the limit of a sum (A-level only), 1.11.5 Integration by substitution and by parts (A-level only), 1.11.6 Integration using partial fractions (A-level only), 1.11.7 Differential equations with separable variables (A-level only), and 1.11.8 Interpreting solutions of 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.
