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Hits: 42 Question i. The tangent to the curve y = x3 − 9×2 + 24x − 12 at a point A is parallel to the line y = 2 − 3x. Find the equation of the tangent at A. ii. The function f is defined by f(x) = x3 − 9×2 + 24x […]
Hits: 821 Question The diagram shows part of the curve . The line y = 4 intersects the curve at the points P and Q. i. Show that the tangents to the curve at P and Q meet at a point on the line y = x. ii. Find, showing all necessary working, the volume […]
Hits: 350 Question i. Solve the equation for . ii. Sketch, on the same diagram, the graphs of and for . iii. Use your answers to parts (i) and (ii) to find the set of values of x for for which . Solution i. We have the equation; We know that […]
Hits: 329 Question A curve is such that and (2,5) is a point on the curve. i. Find the equation of the curve. ii. A point P moves along the curve in such a way that the y-coordinate is increasing at a constant rate of 0.06 units per second. Find the rate of […]
Hits: 337 Question Points A and B have coordinates (h, h) and (4h + 6, 5h) respectively. The equation of the perpendicular bisector of AB is 3x + 2y = k. Find the values of the constants h and k. Solution We are given that line AB has coordinates of the two points and . […]
Hits: 427 Question The function is defined by for . i. Express in the form , where a and b are constants. ii. State the coordinates of the stationary point on the curve y = f(x). The function is defined by for . iii. State the smallest value of k for […]
Hits: 549 Question The diagram shows points A and B on a circle with centre O and radius r. The tangents to the circle at A and B meet at T. The shaded region is bounded by the minor arc AB and the lines AT and BT. Angle AOB is radians. i. In the […]
Hits: 156 Question The diagram shows a three-dimensional shape. The base OAB is a horizontal triangle in which angle AOB is 90o. The side OBCD is a rectangle and the side OAD lies in a vertical plane. Unit vectors and are parallel to OA and OB respectively and the unit vector is vertical. The position […]
Hits: 209 Question The function f, is such that for . It is given that and . i. Find the values of the constants a and b. ii. Find the set of values of k for which the equation f(x) = k has no solution. Solution i. We are given the function […]
Hits: 240 Question A company producing salt from sea water changed to a new process. The amount of salt obtained each week increased by 2% of the amount obtained in the preceding week. It is given that in the first week after the change the company obtained 8000 kg of salt. i. Find the amount […]
Hits: 163 Question The equation of a curve is , where is a constant. i. Find the set of values of for which the whole of the curve lies above the x-axis. ii. Find the value of for which the line y + 2x = 7 is a tangent to the curve. Solution […]
Hits: 192 Question The coefficient of in the expansion of is 330. Find the value of the constant a. Solution We can find the coefficient of in the expansion of given expression by finding coefficients of in the expansion of individual terms of expression and then adding them. Let us first find the coefficient of […]