Hits: 78
Hits: 78 Question The diagram shows part of the curve , and the lines x = 1 and x = 3. The point A on the curve has coordinates (2, 3). The normal to the curve at A crosses the line x = 1 at B. (i) Show that the normal AB has equation . […]
Hits: 37 Question A function is defined for and is such that . i. Find the set of values of for which f is decreasing. ii. It is now given that . Find . Solution i. We are given derivative of the function as; We are also given that it is […]
Hits: 77 Question The diagram shows part of the curve . The curve intersects the x-axis at A. The normal to the curve at A intersects the y-axis at B. i. Obtain expressions for and ii. Find the coordinates of B. iii. Find, showing all necessary working, the area of the shaded region. Solution […]
Hits: 27 Question A curve is such that , where is a constant. The points P(1, −1) and Q(4, 4) lie on the curve. Find the equation of the curve. Solution We are given that; We can find equation of the curve from its derivative through integration; Therefore; Rule for integration of is: If a […]
Hits: 65 Question The diagram shows a shaded region bounded by the y-axis, the line y = −1 and the part of the curve y = x2 + 4x + 3 for which x ≥ −2. i. Express y=x2+4x+3 in the form y=(x+a)2+b, where a and b are constants. Hence, for x ≥ −2, express […]
Hits: 52 Question A curve for which passes through the point (2,3). i. Find the equation of the curve. ii. Find . iii. Find the coordinates of the stationary point on the curve and, showing all necessary working, determine the nature of this stationary point. Solution i. We […]
Hits: 30 Question The diagram shows part of the curve with equation and the tangent to the curve at the point A. The x-coordinate of A is 4. i. Find the equation of the tangent to the curve at A. ii. Find, showing all necessary working, the area of the shaded […]
Hits: 23 Question A curve is such that . The curve has stationary points at (−1, 2) and (3, k). Find the values of the constants a, b and k. Solution We are given that derivative of the equation of the of the curve is; We are also given that curve has stationary points at […]
Hits: 508 Question The diagram shows part of the curve and the minimum point M. i.Find the expressions for and ii.Find the coordinates of M. The shaded region is bounded by the curve, the y-axis and the line through M parallel to the x-axis. iii.Find, showing all necessary working, the area of the shaded region. […]
Hits: 362 Question A curve is such that . The point P (2,9) lies on the curve. i. A point moves on the curve in such a way that the x-coordinate is decreasing at a constant rate of 0.05 units per second. Find the rate of change of the y-coordinate when the point is at […]
Hits: 263 Question The diagram shows part of the curve and a point P(2, 1) lying on the curve. The normal to the curve at P intersects the x-axis at Q. i. Show that the x-coordinate of Q is . ii. Find, showing all necessary working, the area of the shaded region. Solution […]
Hits: 144 Question A curve for which has a stationary point at (3, 6). i. Find the equation of the curve. ii. Find the x-coordinate of the other stationary point on the curve. iii. Determine the nature of each of the stationary points. Solution i. We can find equation of the curve […]
Hits: 203 Question The diagram shows part of the curve with equation . The shaded region is bounded by the curve, the x-axis and the line x = 3. i. Find, showing all necessary working, the volume obtained when the shaded region is rotated through 360O about the x-axis. ii. P is the […]
Hits: 166 Question A curve with equation y = f(x) passes through the points (0, 2) and (3, −1). It is given that , where is a constant. Find the value of . Solution i. We can find equation of the curve from its derivative through integration; For the given case; Therefore; Rule for […]