A mechanical system's power output G(t)G(t)G(t) at time ttt is modeled for t>3t > 3t>3 by the function
G(t)=t4−t3−4t2+3t−2t2−t−6 G(t) = \frac{t^4 - t^3 - 4t^2 + 3t - 2}{t^2 - t - 6} G(t)=t2−t−6t4−t3−4t2+3t−2Given that
G(t)≡t2+A+Bt−3 G(t) \equiv t^2 + A + \frac{B}{t - 3} G(t)≡t2+A+t−3Bfind the value of the constant AAA and show that B=5B = 5B=5.
The curve KKK has equation y=G(t)y = G(t)y=G(t) for t>3t > 3t>3.
Find the equation of the tangent to KKK at the point where t=4t = 4t=4. Give your answer in the form y=mt+cy = mt + cy=mt+c, where mmm and ccc are constants to be found.
The region SSS is bounded by the curve KKK, the ttt-axis, and the vertical lines with equations t=4t = 4t=4 and t=5t = 5t=5. Find the exact area of SSS, writing your answer in the form a+bln2a + b \ln 2a+bln2, where aaa and bbb are constants to be found.
Practise AQA A Level Maths 1.5 B: Algebra and functions with exam-style questions for A Level Maths. 358 questions covering 1.5.1 Laws of indices, 1.5.2 Surds, 1.5.3 Quadratic functions, 1.5.4 Simultaneous equations, 1.5.5 Linear and quadratic inequalities, 1.5.6 Polynomials and rational expressions, 1.5.7 Graphs of functions and proportion, 1.5.8 Composite and inverse functions (A-level only), 1.5.9 Transformations of graphs, 1.5.10 Partial fractions (A-level only), and 1.5.11 Functions in modelling (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.
