Question a. The polynomial is given by . i. Use the Factor Theorem to show that is a factor of . ii. Express in the form , where a and b are constants. b. The curve C with equation , sketched below, crosses the x-axis at the point . i. Find the gradient of the curve C at the point Q. ii. Hence find an […]
Question The curve C has equation , where k is a constant. The line L has equation . a. Show that the x-coordinates of any points of intersection of the curve C with the line L satisfy the equation b. The curve C and the line L intersect in two distinct points. […]
Question The curve with equation passes through the point P, where . a. Find i. ii. b. Verify that the point P is a stationary point of the curve. c. i. Find the value of at the point P. ii. Hence, or otherwise, determine whether P is […]
Question The line AB has equation . a. i. Find the gradient of AB. ii. The point A has coordinates (2,1) . Find an equation of the line which passes through the point A and which is perpendicular to AB. b. The line AB intersects the line with equation at the point C. Find the coordinates of C. Solution a. […]
Question A circle with center C has equation . a. Express this equation in the form b. Write down: i. the coordinates of C; ii. the radius of the circle c. The point D has coordinates (7,-2). i. Verify that point D lies on the circle. ii. Find an equation of the normal to the circle at the point D, giving […]
Question The points A and B have coordinates (1,6) and (5,-2) respectively. The mid-point of AB is M. a. Find the coordinates of M. b. Find the gradient of AB, giving your answer in its simplest form. c. A straight line passes through M and is perpendicular to AB. i. Show that this line has equation . ii. Given […]