Question a. The polynomial is given by i. Find the remainder when is divided by . ii. Use the Factor Theorem to show that is a factor of . iii. Express in the form , where b and c are integers. iv. The equation has one root equal to -2. Show that equation has no other real roots. […]
Question a. i. Express in the form , where p and q are integers. ii. Hence show that is always positive. b. A curve has equation . i. Write down the coordinates of the minimum point of the curve. ii. Sketch the curve, showing the value of the intercept on the y-axis. […]
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 a. i. Express in the form , where p and q are integers. ii. Hence write down the minimum value of . iii. State the value of for which the minimum value of occurs. b. The point A has coordinates (5,4) and the point B has coordinates (x,7-x) . i. Expand . […]
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 a. Factorise . b. Hence, or otherwise, solve the inequality Solution a. We are given the expression; b. We are required to solve the inequality; We solve the following equation to find critical values of ; From (a) we know that this equation can be written as; Now we have two options. Hence the critical points on […]