Question a. Show that b. Find the exact value of showing all necessary working. Solution a. We are required to show; Rule for integration of is: Division Rule; Power Rule; b. We are required to find; We know that Therefore, we can rearrange; Hence; Similarly, we know that; Therefore, we can rearrange; […]
Question The curve with equation crosses the x-axis at only one point. This point has coordinates . i. Show that satisfies the equation ii. Show by calculation that 0.75 < p < 0.85. iii. Use an iterative formula based on the equation in part (i) to find the value of p correct to 5 […]
Question Find the gradient of the curve at the point (0, 2). Solution We are required to find gradient of the curve ta the point (0 , 2). 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 […]
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 A curve has parametric equations i. Find the equation of the tangent to the curve at the origin. ii. Find the coordinates of the stationary point, giving each coordinate correct to 2 decimal places. Solution i. We are required to find the equation of tangent to the curve at the origin. […]
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 parametric equations i. Find the equation of the tangent to the curve at the origin. ii. Find the coordinates of the stationary point, giving each coordinate correct to 2 decimal places. Solution i. We are required to find the equation of tangent to the curve at the origin. […]
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 i. Find the x-coordinate of the stationary point. ii. Determine whether the stationary point is a maximum or minimum point. Solution i. First we are required to find the x-coordinate of the stationary point of the curve. A stationary point on the curve is the point where […]
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 A curve has equation i. Find the x-coordinate of the stationary point. ii. Determine whether the stationary point is a maximum or minimum point. Solution i. First we are required to find the x-coordinate of the stationary point of the curve. A stationary point on the curve is the point where […]
Question The diagram shows the curve . The curve crosses the x-axis at the point P and has a maximum point M. i. Find the gradient of the curve at the point P. ii. Show that the x-coordinate of the point M satisfies the equation iii. Use an iterative formula based on […]
Question The diagram shows part of the curve defined by the parametric equations The curve has a minimum point at M and crosses the x-axis at the point P. i. Find the gradient of the curve at P. ii. Find the coordinates of the point M. iii. The value of the gradient […]
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 […]