Mathematics Pure Math 1 9709: INTEGRATION Topical Past Paper Questions

The diagram shows the curve with equation $ y = x^{2} - 12x + 37 $ and the line $ y = -4x + 30 $. Find the area of the shaded region.

The diagram shows the curve with equation $ y = 4x^2 - x^3 $ and the tangent to the curve at the point $ P $. The point $ P $ has $ x $-coordinate 3. (a) Find the equation of the tangent to the curve at the point $P$. Give your answer in the form $y = mx + c$. [5] (b) The shaded…

The equation of a curve is $ y = kx^{\frac{1}{2}} - 4x^{2} + 2 $, where k is a constant. (a) Find $ \frac{dy}{dx} $ and $ \frac{d^{2}y}{dx^{2}} $ in terms of k. [2] (b) It is given that k = 2. Find the coordinates of the stationary point and determine its nature. [4] (c) Points $…