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 $P - 2 Q = 3$ .

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

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

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

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 $P - 2 Q = 3$ .

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

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

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

1 Unit 1: Pure Mathematics A

Question 174

Markscheme

1 Unit 1: Pure Mathematics A

Question 174

Markscheme

1 Unit 1: Pure Mathematics A

Question 174

1 Unit 1: Pure Mathematics A Questions

1 Unit 1: Pure Mathematics A

Question 174

1 Unit 1: Pure Mathematics A Questions