Question The diagram shows part of the curve intersecting the x-axis at the origin O and at . The line AB intersects the y-axis at B and has equation . i. Show that AB is the tangent to the curve at A. ii. Show that the area of the shaded region can be […]
Question The functions f and g are defined by for for . i. a. State the range of the function f. b. State the range of the function g. c. State the range of the function fg. ii. Explain why the function gf cannot be formed. iii. Find the set of values […]
Question A curve has equation and a line has equation , where is a constant. i.Find the set of values of for which the curve and the line meet. ii.The line is a tangent to the curve for two particular values of . For each of these values find the x-coordinate of the point at […]
Question A curve has equation . i.Find the x-coordinates of the stationary points. ii.Find . iii.Find, showing all necessary working, the nature of each stationary point. Solution i. We are required to find the coordinates of the stationary point of the curve. Coordinates of stationary point on the curve can be found from the derivative […]
Question Fig. 1 shows a rectangle with sides of 7 units and 3 units from which a triangular corner has been removed, leaving a 5-sided polygon OABCD. The sides OA, AB, BC and DO have lengths of 7 units, 3 units, 3 units and 2 units respectively. Fig. 2 shows the polygon OABCD forming the […]
Question The diagram shows a sector POQ of a circle of radius 10 cm and centre O. Angle POQ is 2.2 radians. QR is an arc of a circle with centre P and POR is a straight line. i. Show that the length of PQ is 17.8 cm, correct to 3 significant figures. […]
Question a. Express the equation as a quadratic equation in and hence solve the equation for . b. The diagram shows part of the graph of , where and are constants and . Find the value of and the value of . Solution a. We are required to solve this quadratic equation for . […]
Question A straight line cuts the positive x-axis at A and the positive y-axis at B(0, 2). Angle radians, where O is the origin. i. Find the exact value of the x-coordinate of A. ii. Find the equation of the perpendicular bisector of AB, giving your answer in the form y = mx […]
Question On a certain day, the height of a young bamboo plant was found to be 40 cm. After exactly one day its height was found to be 41.2 cm. Two different models are used to predict its height exactly 60 days after it was first measured. · Model A assumes that the daily amount […]
Question i. Find the coefficients of and in the expansion of . ii. Hence find the coefficient of in the expansion of . Solution i. Expression for the general term in the Binomial expansion of is: First we rewrite the expression in the standard form; In the given case: Hence; Since we […]