Question The function f is defined by , for . i. Solve the equation , giving your answer correct to 1 decimal place. ii. Find an expression for and find the domain of . iii. Sketch, on the same diagram, the graphs of y=f(x) and . Solution i. We are given the function as; We are required to […]
Question The equation of a curve is . i. Find the coordinates of the stationary point of the curve. ii. Find an expression for and hence, or otherwise, determine the nature of the stationary point. iii. Find the values of x at which […]
Question Relative to an origin , the position vectors of points A and B are given by and where p and q are constants. i. In the case where , use a scalar product to find angle AOB. ii. In the case where is parallel to , find the values of p and q. Solution i. It […]
Question a. The first two terms of an arithmetic progression are 16 and 24. Find the least number of terms of the progression which must be taken for their sum to exceed 20 000. b. A geometric progression has a first term of 6 and a sum to infinity of 18. A new geometric progression is formed […]
Question The diagram shows the straight line intersecting the curve at the points A(1,4) and B(4,1). Find, showing all necessary working, the volume obtained when the shaded region is rotated through 360o about the x-axis. Solution Expression for the volume of the solid formed when the shaded region under the curve is rotated completely about the x-axis is; It is evident from […]
Question A curve has equation . i. Find the equation of the tangent to the curve at the point where the curve crosses the x-axis. ii. A point moves along the curve in such a way that the x-coordinate is increasing at a constant rate of 0.04 units per second. Find the rate of change of the […]
Question The diagram shows a circle with radius r cm and centre O. Points A and B lie on the circle and ABCD is a rectangle. Angle AOB = 2 radians and cm. i. Express the perimeter of the shaded region in terms of r and . ii. In the case where and , find the area of the shaded region. […]
Question i. Prove the identity . ii. Hence solve the equation ,for . Solution i. Utilizing ; We have the trigonometric identity; We can write from this identity; Therefore; We have algebraic identity; Therefore; ii. We are required to solve the equation ,for . From (i) we have found that given equation can be written […]
Question The point A has coordinates (-2,6). The equation of the perpendicular bisector of the line AB is 2y=3x+5. i. Find the equation of AB. ii. Find the coordinates of B. Solution i. We are required to find the equation of line AB. To find the equation of the line either we need coordinates […]
Question i. Find the coefficient of x in the expansion of . ii. Hence find the coefficient of x in the expansion of . Solution i. We are required to find the coefficient of in the expansion of given expression. We are given expression as; Expression for the general term in the Binomial expansion of is: First rewrite […]