2024 IGCSE Additional Mathematics October/November 0606/22 Q10

The diagram shows part of the curve \(y=x-\dfrac{x^2}4\) and the line \(y=-4\). The curve and the line intersect at the point \(A\).

1. The maximum point on the curve is at a perpendicular distance \(h\) from the line \(y=-4\). Find the value of \(h\).[4]
2. Find the exact \(x\)-coordinate of \(A\).[3]
3. Find the acute angle between the tangent to the curve at \(A\) and the line \(y=-4\).[4]