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Gerard Sayson TMUA Mock Paper 1 · Q2

Paper 1Algebra

It is given that

dydx=x3+a3x2−ax+a2\frac{\mathrm{d}y}{\mathrm{d}x}=\frac{x^3+a^3}{x^2-ax+a^2}

where aa is a constant, and y=2y=2 when x=1x=1. Find an expression for yy.

Ay=x22+ax+32−ay=\frac{x^2}{2}+ax+\frac32-a
By=x22−ax+32+ay=\frac{x^2}{2}-ax+\frac32+a
Cy=x22+32y=\frac{x^2}{2}+\frac32
Dy=ax+2−ay=ax+2-a
Ey=x22+ax+2y=\frac{x^2}{2}+ax+2

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