Question a. i. Sketch the curve with equation ii. Show that the equation can be expressed as b. 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. c. Hence show that […]
Question a. i. Express in the form . ii. Hence write down the equation of the line of symmetry of the curve with equation . b. The curve C has equation and the line L has equation , where k is a constant. i. Show that the x-coordinates of any points of intersection of the curve C with the line L […]
Question A circle has centre C(-3,1) and radius . a. i. Express the equation of the circle in the form ii. Hence find the equation of the circle in the form where m, n and p are integers. b. The circle cuts the y-axis at the points A and B. Find the distance AB. c. i. Verify that the […]
Question The curve sketched below passes through the point A(-2,0) . The curve has equation and the point P(1,12) lies on the curve. a. i. Find the gradient of the curve at the point P. ii. Hence find the equation of the tangent to the curve at the point P, giving your answer in the […]
Question The line AB has equation . The point C has coordinates (2,-7). a. i. Find the gradient of AB. ii. The line which passes through C and which is parallel to AB crosses the y-axis at the point D. Find the y-coordinate of D. b. The line with equation intersects the line AB at the point A. Find […]
Question a. Simplify . b. Express in the form Solution a. We are given; b. We are given the expression; If we need a rational number in the denominator of a fraction, we need to follow procedure of “denominator rationalization” as given below. ü If the denominator is of the form then multiply both numerator and denominator by […]
Question The curve with equation passes through the point P where . a. Find . b. Show that the point P is a stationary point of the curve and find the other value of x where the curve has a stationary point. c. […]