Question The equation of the curve is . i. Show that ii. Find the equation of the tangent to the curve at the point (2, 4), giving your answer in the form ax+by=c. Solution i. We are given that; Therefore; Rule for differentiation of is: If and are functions […]
Question Solve the inequality . Solution SOLVING INEQUALITY: PIECEWISE Let, . We can write it as; We have to consider both moduli separately and it leads to following cases; When If then above four intervals translate to following with their corresponding inequality; When When When If then above four intervals translate to following with […]
Question In the diagram, ABED is a trapezium with right angles at E and D, and CED is a straight line. The lengths of AB and BC are and respectively, and angles BAD and CBE are and respectively. i. Find the length of CD in terms of . ii. Show that angle CAD = Solution From the given information we can […]
Question A curve is such that and (1, 4) is a point on the curve. i. Find the equation of the curve. ii. A line with gradient is a normal to the curve. Find the equation of this normal, giving your answer in the form . iii. Find the area of the region enclosed by the curve, the […]
Question The equation of a curve is and the equation of a line is , where is a constant. i. In the case where , find the coordinates of the points of intersection of and the curve. ii. Find the set of values of for which does not intersect the curve. iii. In the case where , one of the […]
Question Three points have coordinates A (2, 6), B (8, 10) and C (6, 0). The perpendicular bisector of AB meets the line BC at D. Find i. the equation of the perpendicular bisector of AB in the form ax + by = c, ii. the coordinates of D. Solution i. To write the equation of the perpendicular bisector of […]
Question The diagram shows the cross-section of a hollow cone and a circular cylinder. The cone has radius 6 cm and height 12 cm, and the cylinder has radius cm and height cm. The cylinder just fits inside the cone with all of its upper edge touching the surface of the cone. i. Express h in terms of r and […]
Question The equation of a curve is . i. Show that the whole of the curve lies above the x-axis. ii. Find the set of values of x for which is a decreasing function of x. The equation of a line is , where k is a constant. iii. In the case where k = 6, find the coordinates of the […]
Question A curve has equation . i. The normal to the curve at the point (4, 2) meets the x-axis at P and the y-axis at Q. Find the length of PQ, correct to 3 significant figures. ii. Find the area of the region enclosed by the curve, the x-axis and the lines x = 1 and […]
Question The diagram shows a rhombus ABCD. The points B and D have coordinates (2, 10) and (6, 2) respectively, and A lies on the x-axis. The mid-point of BD is M. Find, by calculation, the coordinates of each of M, A and C. Solution M is the mid-point of BD. To find the mid-point of a line we […]