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1.5 Algebraic Division

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Question 24

The fuel consumption rate $S (t)$ (in kg/s) of a prototype hypersonic engine, where $t$ is the time in minutes since ignition, is modelled by the polynomial $S(t) = 2t^3 + Pt^2 + Qt - 20$ , where $P$ and $Q$ are constants.

It is given that:

when $S (t)$ is divided by $(t - 1)$ , the remainder is $R$
when $S (t)$ is divided by $(t + 2)$ , the remainder is $2 R + 6$

Show that $P - 2 Q = 3$ .

[4]

Given also that $(2 t - 5)$ is a factor of $S (t)$ ,

Find the value of $P$ and the value of $Q$ .

[3]

Hence find the quadratic expression $g (t)$ such that $S (t) = (2 t - 5) g (t)$ .

[2]

Markscheme

1.5 Algebraic Division Questions

A Level
Maths
1.5 Algebraic Division

65 exam-style questions on Edexcel A Level Maths 1.5 Algebraic Division. Each one has a worked solution and a mark scheme showing where the marks go.

1.5 Algebraic Division

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1.5 Algebraic Division

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Question 24

It is given that:

when $S (t)$ is divided by $(t - 1)$ , the remainder is $R$
when $S (t)$ is divided by $(t + 2)$ , the remainder is $2 R + 6$

Show that $P - 2 Q = 3$ .

[4]

Given also that $(2 t - 5)$ is a factor of $S (t)$ ,

Find the value of $P$ and the value of $Q$ .

[3]

Hence find the quadratic expression $g (t)$ such that $S (t) = (2 t - 5) g (t)$ .

[2]

Markscheme

1.5 Algebraic Division Questions

A Level
Maths
1.5 Algebraic Division

65 exam-style questions on Edexcel A Level Maths 1.5 Algebraic Division. Each one has a worked solution and a mark scheme showing where the marks go.