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1.5 B: Algebra and functions

1.5 B: Algebra and functions

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Question 213

The vertical displacement sss (in metres) of a high-performance drone during a test maneuver is modelled by the polynomial function

s(t)=2t4+pt3−8t2+qt+22 s(t) = 2t^4 + pt^3 - 8t^2 + qt + 22 s(t)=2t4+pt3−8t2+qt+22

where ttt represents the time in seconds after the maneuver begins, and ppp and qqq are constant coefficients.

a.

When s(t)s(t)s(t) is divided by (t+1)(t + 1)(t+1), the remainder is 777. Show that p+q=9p + q = 9p+q=9.

[2]
b.

When s(t)s(t)s(t) is divided by (t−2)(t - 2)(t−2), the remainder is 101010. Find the value of ppp and the value of qqq.

[4]
Markscheme

1.5 B: Algebra and functions Questions

  1. A Level
  2. /Maths
  3. /1.5 B: Algebra and functions

532 exam-style questions on AQA A Level Maths 1.5 B: Algebra and functions, 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). Each one has a worked solution and a mark scheme showing where the marks go.

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