The diagram shows the curve y = (x − 2)² and the line y + 2x = 7, which intersect at points A and B. Find the area of the shaded region.

the equation of the curve $y=\frac{4}{3x-4}$ 
and P(2, 2) is a point on the curve. The equation of the tangent to the curve at P and the angle that this tangent makes with the x-axis respectively 

The diagram shows part of the curve $y=4\sqrt{x}-x$  
The curve has a maximum point at M and meets the x-axis at O and A. Find the volume obtained when the shaded region is rotated through 360o about the x-axis, givingyour answer in terms of π

The equation of a curve is $y=4\sqrt{x}+\frac{2}{\sqrt{x}}$  
A point is moving along the curve in such a way that              the x-coordinate is increasing at a constant rate of 0.12 units per second. Find the rate of change of the y-coordinate when x = 4

The diagram shows part of the curve y = −x² + 8x − 10 which passes through the points A and B. The curve has a maximum point at A and the gradient of the line BA is 2. evaluate the area of the shaded region.

A curve is such that  $\frac{dy}{dx}=\frac{6}{x^2}$  and (􏰎2, 9)􏰏 is a point on the curve. Find the equation of the curve

The straight line y = mx + 14 is a tangent to the curve $y=\frac{12}{x}+2$  
at the point P. Find the value of the constant m and the coordinates of P

The diagram shows the curve  $y=\sqrt{1+4x}$  
which intersects the x-axis at A and the y-axis at B. The normal to the curve at B meets the x-axis at C. the area of the shaded region