The point A, whose x-coordinate is 2, lies on the curve with equation y = x³ – 4x² + x + 1. The tangent to the curve at A meets the curve again at point B. Find the x-coordinate of B.

It is given that x − 1 is a factor of f(x), where f(x) = x³ – 6x² + ax + b.

Solve the equation 2x³ - 3x² - 11x + 6 = 0.

Show that 2x – 1 is a factor of 2x³ – 5x² + 10x – 4.

Given that a curve has equation y = 1/x + 2√x, where x > 0, find

A sector of a circle of radius r cm has an angle of θ radians, where θ < π. The perimeter of the sector is 30 cm.

Solutions to this question by accurate drawing will not be accepted. The points A(p,1), B(1, 6), C(4, q) and D(5, 4),…