Question Relative to an origin , the position vectors of the points , , and are given by and where and are constants. Find i. the unit vector in the direction of , ii. the value of p for which angle , iii. the values of for which the length of is 7 units. Solution i. A […]
Question Functions and are defined by , , i. Find the set of values of for which . ii. Find the range of and state, with a reason, whether has an inverse. iii. Show that the equation has no real solutions. iv. Sketch, on a single diagram, the graphs of and , making clear the relationship between the graphs. Solution […]
Question i. Show that the equation can be written as a quadratic equation in . ii. Hence, or otherwise, solve the equation in part (i) for . Solution i. First we need to manipulate the given equation to write it in a single trigonometric ratio i.e. ; Dividing the entire equation by ; Using the relation ; This is the […]
Question The diagram shows a glass window consisting of a rectangle of height m and width m and a semicircle of radius m. The perimeter of the window is 8 m. i. Express in terms of . ii. Show that the area of the window, A m2, is given by Given that can vary, iii. find the value […]
Question The diagram shows part of the graph of and the normal to the curve at . This normal meets the -axis at R. The point Q on the -axis and the point S on the curve are such that PQ and SR are parallel to the -axis. i. Find the equation of the normal at P […]
Question The curve and the line intersect at two points. Find i. the coordinates of the two points, ii. the equation of the perpendicular bisector of the line joining the two points. Solution i. To find the coordinates of intersection points; If two lines (or a line and a curve) intersect each other at a point then […]
Question In the diagram, OCD is an isosceles triangle with cm and angle COD =0.8 radians. The points A and B, on OC and OD respectively, are joined by an arc of a circle with centre O and radius 6 cm. Find i. the area of the shaded region, ii. the perimeter of the shaded region. Solution i. […]
Question Evaluate Solution Writing the given expression in standard form; Rule for integration of is: In the given case;
Question Find the coefficient of in the expansion of i. ii. Solution i. Expression for the general term in the Binomial expansion of is: In the given case: Hence; Since we are looking for the term with , we can equate Finally substituting in: Therefore the coefficient of is . ii. To find the coefficient of in the expansion […]
Question A geometric progression has first term 64 and sum to infinity 256. Find i. the common ratio ii. the sum of the first ten terms. Solution i. From the given information, we can compile following data for Arithmetic Progression (A.P); Expression for the sum to infinity of the Geometric Progression (G.P) when or ; ii. Sum of […]