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Hits: 388 Question The curve with equation passes through the origin. i. Show that the curve has no stationary points. ii. Denoting the gradient of the curve by m, find the stationary value of m and determine its nature. Solution i. We are required to show that curve has no stationary points. […]
Hits: 344 Question Functions f and g are defined for by; i.Find the points of intersection of the graphs of y = f(x) and y = g(x). ii.Find the set of values of x for which f(x) > g(x). iii.Find an expression for fg(x) and deduce the range of fg. The function h […]
Hits: 340 Question a) A geometric progression has a second term of 12 and a sum to infinity of 54. Find the possible values of the first term of the progression. b) The nth term of a progression is p + qn, where p and q are constants, and Sn is the sum of the […]
Hits: 212 Question Relative to an origin O, the position vectors of points A, B and C are given by and i. Find . ii. The point M is the mid-point of AC. Find the unit vector in the direction of . iii. Evaluate and hence […]
Hits: 560 Question The diagram shows a circle with centre O and radius r cm. The points A and B lie on the circle and AT is a tangent to the circle. Angle radians and OBT is a straight line. i. Express the area of the shaded region in terms of r and . […]
Hits: 364 Question The diagram shows a kite OABC in which AC is the line of symmetry. The coordinates of A and C are (0, 4) and (8, 0) respectively and O is the origin. i. Find the equations of AC and OB. ii. Find, by calculation, the coordinates of B. Solution […]
Hits: 176 Question i.Prove the identity ii.Hence solve the equation for . Solution i. We have the trigonometric identity; ii. We have the equation; From (i) we know that left hand side of given equation can be written as; Therefore; […]
Hits: 140 Question A curve is such that . The point (1,1) lies on the curve. Find the coordinates of the point at which the curve intersects the x-axis. Solution We are required to find the coordinates of the point at which the curve intersects the x-axis. The point at which a line or curve intersects […]
Hits: 144 Question A point is moving along the curve in such a way that the x-coordinate is increasing at a constant rate of 0.02 units per second. Find the rate of change of the y-coordinate when x = 1. Solution i. We are given that; We are required to find; We know […]
Hits: 269 Question i. Find the first three terms in the expansion, in ascending powers of , of . ii. Given that the coefficient of in the expansion of is 12, find the value of the constant a. Solution i. Expression for the Binomial expansion of is: First rewrite the given expression […]