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Hits: 236 Question The diagram shows the part of the curve for . The curve cuts the x-axis at A and its maximum point is M. i. Write down the coordinates of A. ii. Show that the x-coordinate of M is e, and write down the y-coordinate of M […]
Hits: 177 Question i. By expanding , and using double-angle formulae, show that ii. Hence, or otherwise, show that Solution i. We have; We apply following addition formula. Therefore; We apply following two formulae. We have the trigonometric identity; Therefore, we can replace; Hence; ii. We are required […]
Hits: 750 Question The sequence of values given by the iterative formula With initial value , converges to . i. Use this iterative formula to find correct to 2 decimal places, showing the result of each iteration. ii. State an equation satisfied by , and hence find the exact value […]
Hits: 182 Question i.By differentiating , show that if then . ii. The parametric equations of a curve are x = 1 + tanθ , y = secθ , for . Show that . iii.Find the coordinates of the point on the curve at which the gradient of the curve is . Solution […]
Hits: 133 Question a. Use logarithms to solve the equation , giving your answer correct to 2 decimal places. b. It is given that , where y > 0. Express z in terms of y in a form not involving logarithms. Solution a. We are given; Taking natural logarithm of both sides; Power […]
Hits: 114 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 […]
Hits: 135 Question The polynomial is denoted by . It is given that is a factor of and that when is divided by the remainder is 12. i. Find the values of a and b. ii. When and have these values, factorise . Solution i. We are given […]