Question A curve is defined by the parametric equations for . i. Find the exact gradient of the curve at the point for which . ii. Find the value of at the point where the gradient of the curve is 2, giving the value correct to 3 significant figures. Solution i. […]
Question The parametric equations of a curve are for . At the point P on the curve, the gradient of the curve is 2. i. Show that the value of the parameter at P satisfies the equation . ii. By first expressing in the form , where R > 0 and , find […]
Question The diagram shows the curve with equation for values of x such that . Find the x-coordinate of the stationary point M, giving your answer correct to 3 significant figures. Solution We are required to find the x-coordinate of stationary point M. A stationary point on the curve is the point where gradient […]
Question The diagram shows the curve with equation for . At the points P and Q on the curve, the gradient of the curve is 3. i. Find an expression for . ii. By first expressing in the form , where R > 0 and , find the x-coordinates of […]
Question The diagram shows the curve with equation for . At the points P and Q on the curve, the gradient of the curve is 3. i. Find an expression for . ii. By first expressing in the form , where R > 0 and , find the x-coordinates of […]
Question A curve has equation Find the equation of the tangent to the curve at the point where it crosses the y-axis. Solution We are given that curve with equation and we are required to find the equation of the tangent to the curve at point where it crosses the y-axis i.e. . To find […]
Question A curve has equation Find the equation of the tangent to the curve at the point where it crosses the y-axis. Solution We are given that curve with equation and we are required to find the equation of the tangent to the curve at point where it crosses the y-axis i.e. . To […]
Question The parametric equations of a curve are for . i. Find the gradient of the curve at the point for which radian. ii. Find the value of at the point on the curve where the tangent is parallel to the y-axis. Solution i. We are required to find gradient of […]
Question A curve has equation . Find the equation of the tangent to the curve at the point for which . Solution i. We are given that curve with equation and we are required to find the equation of the tangent to the curve at origin . To find the equation of […]
Question Find the gradient of the curve at the point . Solution We are required to find the gradient of the curve at point . Gradient (slope) of the curve at the particular point is the derivative of equation of the curve at that particular point. Gradient (slope) of the curve at a particular […]
Question The diagram shows the part of the curve for , and the stationary point M. i. Find the equation of the tangent to the curve at the origin. ii. Find the coordinates of M, giving each coordinate correct to 3 decimal places. Solution i. We are given that […]
Question The diagram shows the curve The curve crosses the y-axis at the point P and the gradient of the curve at P is m. The point Q on the curve has x-coordinate q and the gradient of the curve at Q is −m. i. Find the value of m and hence show that q […]
Question The equation of a curve is . The curve has a stationary point M in the interval . Find the coordinates of M, giving each coordinate correct to 3 significant figures. Solution We are required to find the x-coordinates of stationary point of the curve. A stationary point on the curve is the point […]
Question The diagram shows the curve The curve crosses the y-axis at the point P and the gradient of the curve at P is m. The point Q on the curve has x-coordinate q and the gradient of the curve at Q is −m. i. Find the value of m and hence show that […]
Question The diagram shows the curve with parametric equations for . The end-points of the curve are (1, 4) and (3, 3). i. Show that . ii. Find the coordinates of the minimum point, giving each coordinate correct to 3 significant figures. iii. Find the exact gradient of the normal to the curve […]
Question The diagram shows the curve with parametric equations for . The end-points of the curve are (1, 4) and (3, 3). i. Show that . ii. Find the coordinates of the minimum point, giving each coordinate correct to 3 significant figures. iii. Find the exact gradient of the normal to the curve […]
Question The diagram shows the curve with parametric equations for . i. Show that can be expressed in the form ii. Find the equation of the normal to the curve at the point where the curve crosses the positive y-axis. Give your answer in the form y = mx +c, where the constants […]
Question A curve has equation y = 2 sin 2x − 5 cos 2x +6 and is defined for 0 ≤ x ≤ π. Find the x-coordinates of the stationary points of the curve, giving your answers correct to 3 significant figures. Solution We are required to find the x-coordinates of stationary points of the […]
Question The diagram shows the curve with parametric equations for . The minimum point is M and the curve crosses the x-axis at points P and Q. i. Show that . ii. Find the coordinates of M. iii. Find the gradient of the curve at P and at Q. Solution i. […]
Question The diagram shows the curve with parametric equations for . The minimum point is M and the curve crosses the x-axis at points P and Q. i. Show that . ii. Find the coordinates of M. iii. Find the gradient of the curve at P and at Q. Solution i. […]