1 Unit AS 1: Pure Mathematics

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Question 59

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

[2]

bi.

A research team models the potential energy $V$ of a chemical system as a function of its configuration $x$ using the equation

V(x) = 2x^3 - 9ax^2 + k

where $a$ and $k$ are constants and $a > 0$ .

Verify that the energy profile has a stationary point where it intersects the vertical $V$ -axis.

[2]

bii.

Given that the equation $V (x) = 0$ has three distinct real roots, determine the range of possible values for $k$ in terms of $a$ by considering the nature and positions of the local maximum and local minimum points.

[5]

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

[2]

A research team models the potential energy $V$ of a chemical system as a function of its configuration $x$ using the equation

V(x) = 2x^3 - 9ax^2 + k

where $a$ and $k$ are constants and $a > 0$ .

Verify that the energy profile has a stationary point where it intersects the vertical $V$ -axis.

[5]

1 Unit AS 1: Pure Mathematics

Question 59

Markscheme

1 Unit AS 1: Pure Mathematics

Question 59

Markscheme

1 Unit AS 1: Pure Mathematics

Question 59

1 Unit AS 1: Pure Mathematics Questions

1 Unit AS 1: Pure Mathematics

Question 59

1 Unit AS 1: Pure Mathematics Questions