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Hits: 79 Question The diagram shows a solid cylinder standing on a horizontal circular base with centre O and radius 4 units. Points A, B and C lie on the circumference of the base such that AB is a diameter and angle BOC = 90o. Points P, Q and R lie on the upper surface […]
Hits: 78 Question The diagram shows a solid figure OABCDEF having a horizontal rectangular base OABC with OA = 6 units and AB = 3 units. The vertical edges OF, AD and BE have lengths 6 units, 4 units and 4 units respectively. Unit vectors , and are parallel to , and respectively. i. […]
Hits: 93 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 […]
Hits: 102 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 […]
Hits: 230 Question The diagram shows a pyramid OABCD with a horizontal rectangular base OABC. The sides OA and AB have lengths of 8 units and 6 units respectively. The point E on OB is such that OE = 2 units. The point D of the pyramid is 7 units vertically above E. Unit vectors […]
Hits: 327 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: 349 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 […]