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1.5 B: Algebra and functions

1.5 B: Algebra and functions

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Question 232

A specialized drone's vertical displacement from a reference altitude, hhh (in meters), is modeled by the function

h(t)=at3+3t2+bt−10 h(t) = at^3 + 3t^2 + bt - 10 h(t)=at3+3t2+bt−10

where t t\,t is the time in seconds since the drone began its descent and a a\,a and b b\,b are constants.

When h(t)h(t)h(t) is divided by (t−3)(t - 3)(t−3), the remainder is 44.

a.

Use the remainder theorem to show that

9a+b=9 9a + b = 9 9a+b=9
[3]
b.

Given also that (t+1)(t + 1)(t+1) is a factor of h(t)h(t)h(t),

find the value of a a\,a and the value of bbb.

[3]
c.

Find h′(t)h'(t)h′(t).

[2]
d.

Hence find the exact coordinates of the stationary points of the curve with equation y=h(t)y = h(t)y=h(t).

[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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