Edexcel A-Level Mathematics A2 Fp2 4 1 Further Solution of First Order Questions

Practise Edexcel IAL FP2.4.1 by using a point to determine the integration constant, then sketching solution branches, turning behaviour and asymptotes.

Exam points

Use a point on the solution curve to find the constant in the first-order solution.
Sketch the resulting curve with branches, turning behaviour and vertical or horizontal asymptotes.

[Maximum number: 5]

Sketch the solution curve that passes through the point (-1,-1).

On your sketch show clearly the equation of any horizontal or vertical asymptotes.

You do not need to find the coordinates of any intercepts with the coordinate axes or the coordinates of any stationary points.

Table for Question Edexcel A-Level Mathematics A2 Fp2 4 1 Further Solution of First Order Questions question 1 — Edexcel A-Level Mathematics A2

-1=2(-1)+\frac{1}{1+c}\Rightarrow c=0

y=2x+\frac{1}{x^2}

Sketch attempted for the correct curve.

Figure for Answer to Question Edexcel A-Level Mathematics A2 Fp2 4 1 Further Solution of First Order Questions question 1 — Edexcel A-Level Mathematics A2

Two branches, both tending to infinity as x tends to ±infinity, with a minimum in the first quadrant.

B1ft

x=0\text{ is the vertical asymptote}

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Edexcel A-Level Mathematics A2 Fp2 4 1 Further Solution of First Order Questions question 1