Question (i) Show that and hence find the exact value of; (ii) The region enclosed by the curve y = tan x + cos x and the lines x = 0, and y = 0 is shown in the diagram. Find the exact volume of the solid produced when this region is rotated […]
Question The diagram shows the curve , for . The x-coordinate of the maximum point M is denoted by . i. Find and show that satisfies the equation tan 2x = 2x + 4. ii. Show by calculation that lies between 0.6 and 0.7. iii. Use the iterative formula to find the […]
Question The parametric equations of a curve are i. Find an expression for in terms of t. i. Find the equation of the normal to the curve at the point for which t = 0. Give your answer in the form ax + by + c = 0, where a, b and […]
Question i. Express in the form , where and , Give the value of correct to 2 decimal places. ii.Hence solve the equation for . iii. State the largest value of k for which the equation has any solutions. Solution i. We are given the expression; We are required to […]
Question i. Find the quotient when the polynomial is divided by , and show that the remainder is 4. ii. Hence, or otherwise, factorise the polynomial Solution i. Hence quotient is and remainder is . ii. We are required to factorise; When a polynomial, , is divided by […]
Question i. Given that 52x + 5x = 12, find the value of 5x. ii. Hence, using logarithms, solve the equation 52x + 5x = 12, giving the value of x correct to 3 significant figures. Solution i. We are given; Let , then; Therefore; It is a quadratic […]
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 […]