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Algebraic Methods

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Question 149

The displacement of a particle sss (in meters) from a reference point at time ttt (in seconds) is modeled by the function:

s(t)=(t−2)(3t2+10t+k)+48 s(t) = (t - 2)(3t^2 + 10t + k) + 48 s(t)=(t−2)(3t2+10t+k)+48

where k k\,k is a constant.

a.

State the remainder when s(t)s(t)s(t) is divided by (t−2)(t - 2)(t−2).

[2]
b.

Given that the particle is at the reference point (s=0s = 0s=0) when t=23\displaystyle t = \frac{2}{3}t=32​, show that k=28k = 28k=28.

[4]
ci.

Hence

fully factorise the expression for s(t)s(t)s(t),

[3]
cii.

Hence

find the number of real solutions of the equation s(t)=0s(t) = 0s(t)=0, giving a reason for your answer.

[3]
Markscheme

Algebraic Methods Questions

  1. A Level
  2. /Maths
  3. /Algebraic Methods

368 exam-style questions on Edexcel A Level Maths Algebraic Methods, covering 1.1 Proof by Contradiction, 1.2 Algebraic Fractions, 1.3 Partial Fractions, 1.4 Repeated Factors, and 1.5 Algebraic Division. Each one has a worked solution and a mark scheme showing where the marks go.

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