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1.3 Functions

1.3 Functions

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Question 81

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

1.3 Functions Questions

  1. A Level
  2. /Maths
  3. /1.3 Functions

181 exam-style questions on OCR (MEI) A Level Maths 1.3 Functions, covering 1.3.1 Operations on polynomials, 1.3.2 Factor theorem, 1.3.3 Definition of a function (A-level only), 1.3.4 Composite functions (A-level only), 1.3.5 Inverse functions and their graphs (A-level only), 1.3.6 The modulus function (A-level only), 1.3.7 Inequalities with a modulus sign (A-level only), and 1.3.8 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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