The pressure PPP, in pascals, within a test chamber is modeled by the function P(x)=kx3−29x2−5x+6P(x) = kx^3 - 29x^2 - 5x + 6P(x)=kx3−29x2−5x+6, where x x\,x represents the horizontal displacement in metres from a fixed source and k k\,k is a constant.
Given that the pressure is zero at a displacement of 3 metres,
show that k=10k = 10k=10.
Using algebraic division and showing each step of your working, fully factorise P(x)P(x)P(x).
Determine all solutions for 0∘≤θ<360∘ 0^\circ \le \theta < 360^\circ\,0∘≤θ<360∘ to the equation
10cos3θ−29cos2θ−5cosθ+6=0 10\cos^3 \theta - 29\cos^2 \theta - 5\cos \theta + 6 = 0 10cos3θ−29cos2θ−5cosθ+6=0giving your answers to one decimal place.
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.
