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A curve has equation y = x^2 - 7x. P is a point on the curve, and the tangent to the curve at P has gradient 1. Work out the coordinates of P.

l1 and l2 are tangents of a circle. l1 intersects the circle at (3-√3,5) with a gradient of √3, and l2 intersects the circle at (3+√2,4+√2) with a gradient of -1. Find the centre of the circle, and hence find the radius of the circle.

The circle c has equation x^2+ y ^2=1 . The line l has gradient 3 and intercepts the y axis at the point (0, 1). c and l intersect at two points. Find the co-ordinates of these points.

How to solve the inequality 1 - 2(x - 3) > 4x

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