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Hits: 112 Question The diagram shows the curve . i. Find the equation of the tangent to the curve at the point . ii. Show that the x-coordinates of the points of intersection of the line and the curve are given by the equation . Hence find these x- coordinates. iii. The region shaded in the diagram is […]
Hits: 82 Question A curve has equation , where is a positive constant. Find, in terms of , the values of for which the curve has stationary points and determine the nature of each stationary point. Solution A stationary point on the curve is the point where gradient of the curve is equal to zero; We are given that; […]
Hits: 218 Question The diagram shows sector OAB with centre O and radius 11 cm. Angle radians. Points C and D lie on OA and OB respectively. Arc CD has centre O and radius 5 cm. i. The area of the shaded region ABDC is equal to k times the area of the unshaded region OCD. Find k. […]
Hits: 74 Question The point A has coordinates and the point B has coordinates . The point C is the mid-point of AB. i. Find the equation of the line through A that is perpendicular to . ii. Find the distance AC. Solution i. We are required to find equation of a line that passes through and is […]
Hits: 57 Question A curve has equation . It is given that and that . Find . Solution We are given that curve and we are required to find the equation of the curve for which . We can find equation of the curve from its derivative through integration; For the given case; Therefore; Rule for integration of is: Rule […]
Hits: 57 Question Solve the inequality . Solution We have; We solve the following equation to find critical values of ; Now we have two options; Hence the critical points on the curve for the given condition are & 2. Standard form of quadratic equation is; The graph of quadratic equation is a parabola. If (‘a’ is positive) then parabola […]
Hits: 99 Question a) Find the possible values of for which , giving your answers correct to 3 decimal places. b) Solve the equation for giving in terms of in your answers. Solution a) We have; We can rearrange the equation as; We know that; Therefore we can write above equation as; b) To solve the equation for , let […]
Hits: 219 Question The diagram shows a pyramid OABC in which the edge OC is vertical. The horizontal base OAB is a triangle, right-angled at O, and D is the mid-point of AB. The edges OA, OB and OC have lengths of 8 units, 6 units and 10 units respectively. Unit vectors , and are parallel to , […]
Hits: 85 Question The function is defined by for , where is a constant. It is given that f is a one-one function. i. State the range of in terms of and find the smallest possible value of . The function is defined by for , where and are positive constants. It is given that, when , and . ii. Write down two equations […]
Hits: 150 Question a) In a geometric progression, the sum to infinity is equal to eight times the first term. Find the common ratio. b) In an arithmetic progression, the fifth term is 197 and the sum of the first ten terms is 2040. Find the common difference. Solution a) From the given information, we can […]
