Question The functions and are defined by for for i. Express in terms of and solve the equation . ii. On the same diagram sketch the graphs of and , showing the coordinates of their point of intersection and the relationship between the graphs. iii. Find the set of values of which satisfy . Solution i. We […]
Question The diagram shows the line and the curve , meeting at and . i. Find the area of the shaded region. ii. Find the volume obtained when the shaded region is rotated through 360◦ about the y-axis. Solution i. It is evident from the diagram that; To find the area of region under the curve , we […]
Question A curve has a stationary point at . It is given that, where k is a constant. i. Show that and hence find the x-coordinate of the other stationary point, Q. ii. Find and determine the nature of each of the stationary points P and Q. iii. Find . Solution i. A stationary point on the […]
Question i. A straight line passes through the point (2, 0) and has gradient . Write down the equation of the line. ii. Find the two values of for which the line is a tangent to the curve . For each value of , find the coordinates of the point where the line touches the curve. iii. […]
Question Relative to an origin , the position vectors of points A and B are and , respectively. i. Use a scalar product to calculate angle BOA. The point C is the mid-point of AB. The point D is such that . ii. Find . Solution i. We recognize that angle BOA is between and . Therefore, we need […]
Question i. Given that Show that, for real values of ii. Hence solve the equation for . Solution i. We have the equation; We have the trigonometric identity; We can rewrite it as; Thus Now we have two options; NOT POSSIBLE So we are left with ONLY option; ii. To solve the equation , for […]
Question In the diagram, ABCD is a parallelogram with AB=BD=DC=10cm and angle ABD= 0.8 radians. APD and BQC are arcs of circles with centres B and D respectively. i. Find the area of the parallelogram ABCD. ii. Find the area of the complete figure ABQCDP. iii. Find the perimeter of the complete figure ABQCDP. Solution i. Expression for the area […]
Question The diagram shows the curve and the line intersecting at points A, O and B. i. Show that the x-coordinates of A and B satisfy the equation . ii. Solve the equation and hence find the coordinates of A and B, giving your answers in an exact form. Solution i. We are given that points A & B are […]
Question The coefficient of in the expansion of , is 30. Find the value of . Solution Expression for the Binomial expansion of is: In the given case: Hence; Since the coefficient of in the expansion of , is 30:
Question The first and second terms of a progression are 4 and 8 respectively. Find the sum of the first 10 terms given that the progression is i. an arithmetic progression ii. a geometric progression. Solution i. From the given information, we can compile following data about Arithmetic Progression (A.P); Expression for the sum of number of terms in […]