1 Unit AS 1: Pure Mathematics

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Question 72

Sketch the graph of a cubic function that has three distinct real roots and a positive coefficient of $x^3$ .

[2]

bi.

The vertical displacement, $s$ , of a mechanical component is modelled by the function

s(t) = k + 15at^2 - 2t^3

where $\ge 0$ is time, and $a$ and $k$ are constants with $a > 0$ .

Show that the curve $s (t)$ has a stationary point at its $s$ -intercept.

[3]

bii.

Given that the polynomial equation $s (t) = 0$ , when extended to all real values of $t$ , has three distinct real roots, determine the range of possible values for $k$ in terms of $a$ . You must use the second derivative to justify the nature of the stationary points used in your calculation.

[7]

Sketch the graph of a cubic function that has three distinct real roots and a positive coefficient of $x^3$ .

[2]

The vertical displacement, $s$ , of a mechanical component is modelled by the function

s(t) = k + 15at^2 - 2t^3

where $\ge 0$ is time, and $a$ and $k$ are constants with $a > 0$ .

Show that the curve $s (t)$ has a stationary point at its $s$ -intercept.

[7]

1 Unit AS 1: Pure Mathematics

Question 72

Markscheme

1 Unit AS 1: Pure Mathematics

Question 72

Markscheme

1 Unit AS 1: Pure Mathematics

Question 72

1 Unit AS 1: Pure Mathematics Questions

1 Unit AS 1: Pure Mathematics

Question 72

1 Unit AS 1: Pure Mathematics Questions